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How do I get started in astronomy data analysis?
I am learning some machine learning (I have previous background in statistics) on my own, and I am interested in getting some hands-on practice by doing some ML analysis in R and Python.
Given how mad I am about astronomy, I would love to get my hands dirty on doing some ML using open data. I am aware that organisations like NASA have lots of open datasets. What I am less clear about is the kind of analysis that needs to be done.
So, I'd like to know if there is any website where I can get a repository of space data (images, signals, whatever) and which asks what analysis is required; kind of like Kaggle where one gets the dataset and has the required question which one can attempt.

You might have a look at some courses for statistics or astrostatistics first. That should channel your 'madness' into constructive and instructive channels.

My suggestion is that you should go to arXiv.org, and pick a paper that interests you. Then, you reproduce the analysis, so that you know what data, what methods, and what to aim for.

@KornpobBhirombhakdi Unfortunately, that is often much easier said than done, many papers are not very clear when it comes to describing their analysis in detail. There are a few examples of papers out there that also include the full analysis stack, including Jupyter notebooks etc, but it is way too rare.

@Thriveth, I agree. However, you should have something to hang on and go from there. This strategy is still the best in my opinion, and I always suggest students to start with. While students can ask their professors in schools, a community like this one is important to support others like self learners or homeschool students when they need helps.

A possibility might be a course at a university, youtube, or a self-study-course via a book.
What we've used in our astrostatistics class was "Wall & Jenkins: Practical Statistics for Astronomers" which presents theoretical sections with exercises as follow-ups. No answer sections exist, as you need to do some programing for some of them.
But you can maybe lend this or similar books at a local university library, without the need to spend money.

Thank you! I really appreciate it. I have lifetime membership of my University's library - will search there. If I don't find it there, then I don't mind buying the book if it is not too expensive.

The Python AstroML module might be interesting to you. It is accompanied by a textbook about machine learning applied to astronomical datasets, but if you don't have the cash to spend on the book, there are some exercises and datasets included in the module itself that should give you a lot to dig into.

Any idea what fraction of AstroML is Linux dependent. when I tried last time it seemed  a lot of it needed Linux.

Here is a good source of public data https://pds-imaging.jpl.nasa.gov/ . My fear is that without some basic astronomy courses, there will be many little hassles ( e.g. the coordinates expressed in spherical coordinates etc, and you might expect xyz. FITS format reader) for any new person. Be mentally ready for numerous small obstacles.


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Could a distant black hole (detected due to its mass) be in reality a Dyson sphere?
When the black hole is only detected due to its gravitational effects on other stars and their light, could it be possible that it is in reality a working Dyson sphere?
It would still have at least the mass of the star but also blocks all the emitting light.
I got the idea from watching this Kurzgesagt video about Dyson spheres

The thing here is that a Dyson Sphere doesn't "block all the emitting light" -- that would violate the conservation of energy.  It does absorb the radiation from whatever body it surrounds and then re-radiates it.
As such, it's likely to radiate something like a relatively normal-looking blackbody spectrum, rather than the plasma X-rays from matter falling into a black hole, or the almost-nothing (thus "black") from a black hole with no infall.
As pointed out in @SteveLinton's comment the Dyson sphere would be much larger than the star or a black hole of the same mass in order to not melt, so at that distance the deflection would be far less, since it scales as inverse radius:
$$\approx \frac{m}{r}$$.

It will also be MUCH bigger than a black hole of the same mass, so any light that passes by it will be only very slightly effected by gravity.

Correct. In fact, the way we'd find a Dyson sphere is by finding a star that shines too dimly for its size. A black hole doesn't shine at all.

They could absorb all emitting light, convert as much as they can to electricity, use all the electricity to produce bitcoin (what else?), and dump the waste heat in a direction nobody is looking, while cooling surfaces pointing in the direction of inferior civilisations such as ours down to 2.7K — best stealth space can give? ;-)

Isn't there a theoretical upper limit on the size of a star that a dyson sphere could encompass too? I'd be doubtful that anything could encompass Canis...

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Deducing distance of closest neighbor galaxy from expression of correlation and mean galaxy density
The original post was on physics exchange but I prefer to move it here :
I am trying to estimate the distance of closest galaxy neighbor knowing the expression of number of neighbors $\text{d}N$ into a volume $\text{d}V$, the mean density $n_\text{gal}$ and the correlation function, i.e with this expression:
$$\text{d}N=n_{\text{gal}}\,\text{d}V\,(1+\xi(r))$$
with $\xi(r)=\bigg(\dfrac{r}{r_{0}}\bigg)^{-\gamma}\quad\text{with}\quad\gamma\,\sim\,1.77 \quad\text{and}\,r_{0}\,\sim\,5\,\text{Mpc}$.
I must precise that expression of $\xi(r)$ is valid for $r$ between $0.5\,\text{and}\,10\,\text{Mpc}$
I take into my calculation the following value for $n_{\text{gal}}=0.0420\,\text{h}^{-3}\,\text{Mpc}^{-3}$ : I tried to choose a typical value for this density but it depends on which scale we consider (galaxy cluster, super cluster, very large scales ...), so maybe don't focus on this value.
What it interests me is to have elements to answer to the following question :
How could I infer the distance of the closest galaxy from us?
UPDATE 1: Maybe I should take the lower limit of validity for the definition of $\xi(r)$, i.e $r=0.5\,\text{Mpc}$ and so:
$$\text{d}N/\text{d}V=n_{\text{gal}}\,(1+\xi(r=0.5))$$
So I would have:
$$\text{D}_{\text{closest}}=\bigg(n_{\text{gal}}(1+(0.5/5)^{-1.77})\bigg)^{-1/3}=0.7353\,\text{Mpc}$$
But by taking $r=0.5\,\text{Mpc}$, I am already located myself like the closest neighbor was at $r=0.5\,\text{Mpc}$, am I not ?
Is this reasoning correct?
Any help is welcome

Yes I would say is a circle. ...

@Alchimista . Do you think this is the right method ? As I said, But by taking $r=0.5,\text{Mpc}$, I am already located myself like the closest neighbor was at $r=0.5,\text{Mpc}$, am I not ? this would be an issue, no ?

No I am saying that it seems that you impose the result to be that.... I have the same doubt that you have.

But it somehow correct that if there is a parameter that holds between, say 0.5 and 10, something should be found int between. But indeed one could have chosen every value in that range perhaps. I don't know much about correlation. I would naively work without it once I know the total number of galaxies in a sphere of radius 10 Mpc.

Sorry that I can only comment. In my mind the corf funct account for dishomogeneity at various scales. Once you identify a range you know the average number of objects around. From that you consider them homogeneously distributed in a sphere (or a cube for that it matters) and infer the distance between two neighbours. One is you and the second the closest galaxy.

What the representation of r here and distance ? Are they same ?

@Reign .I think that $r$ reresents the physical distance and $\text{D}{\text{closest}}$ is the mean distatnce of closest between objects like galaxies. I make confusions between both distances since if I chose the lower value $r{0}=0.5,\text{Mpc}$, I am already located mylself at the closest neighbour, am I not ? What do you think about it ? regards

I think r might represent the distance from us to some radius that we are taking as a volume. But from here mean distance definition just makes not much sense..

I understand your concern but I dont know the answer for that sorry.

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Extract anomalies from two-line element set (TLE) on ISS (International Space Station)
I am faced to a problem of interpretation illustrated on figure below :

From wikipedia : Two-line element definition, I can extract the
following meaning anomaly  : 308.7017 ° (in degrees)
But in the 2 questions, I am asked to find :
1) at which anomaly is the ISS at the two lines epcoh
2) at wchich anomaly is the ISS on December 1st 2018.
I think the answer to question 1) is maybe what I have extracted above (308.7017 °)
But how to compute the anomaly of ISS on December 1st 2018 ?
I don't undertand very well the difference between these two anomalies requested.
If someone could help me, this would be nice.
Regards
UPDATE 1: Sorry, I must precise that I talk about mean anomaly.

By "anomaly" do you mean "Mean anomaly". (and not the True Anomaly). Do you understand the question to be asking about the mean anomaly at 00:00 on December 1st? (day 335.0)

@JamesK I don't understand well this notion of meaning anomaly : could you tell me please, if you can, the concept of meaning anomaly, in a simple way ? I saw this is an angle by taking a virtual circular orbit but it causes confusions for me, I don't grasp the subtilities of this notion. Even simple clarifications are welcome, I just want to understand better the 2 questions. thanks

First you should get an idea of what "Anomaly" means.  An anomaly is an angle which can describe the position of the satellite in its orbit. The true anomaly is the actual angle made between the position of the satellite and the perigee. The true anomaly changes quickly when the satellite is close to the Earth and slowly when it is far from the Earth.
The mean anomaly is much simpler: it just increases linearly with from 0 to 360. It is zero when the satellite is at perigee. So if a satellite takes 100 minutes to orbit and it is perigee at time t=0, then it will be at 90degrees at t=25, 180degrees at t=50.  The mean anomaly is just proportional to time.  "Mean" here means "average", not "meaning".
The orbital elements will tell you the mean anomaly at a particular time (given as "days in the year" In your data, at day 320.81254693 of 2018 (the "epoch") the mean anomaly was 308.7017.
You also know that the mean motion is 15.53998777. That is the number of orbits the satellite makes each day. One orbit is 360 degrees, so in 'n' days the mean anomaly will increase by 15.53998777 × 360 × n
You can now find the mean anomaly at any future time. For example 2.5 days after the epoch, at day 323.31254693, the anomaly will be 308.7017 + (15.53998777 × 360 × 2.5). You may need to reduce this angle to the range 0 to 360.
To add accuracy you can also use the fact that the orbital period is slowly changing (It is getting shorter as the ISS falls towards Earth due to drag). But this change is not quick and can be neglected over short periods of time.
Now you can work out how many days pass between the epoch and Dec 1st and you can work out the mean anomaly.
The question is worded strangely. It is an odd use of "which" and is unclear about the time. It should ask "What is the mean anomaly of the  ISS at the epoch" and "What is the mean anomaly of the ISS at 00:00 on Dec 18th 2018"

-@JamesK .Thanks a lot for your very clear explanation. If I want to compute the day for the date 00.00 on Dec 18th 2018, could I do : day(18th 2018 00:00) = (365-31) = 334? Is this a correct calculus ?

I think you are a day out, because the counting of days starts from 001.0000 at midnight on January 1st, so December 1st is day 335.  seehttps://www.epochconverter.com/days/2018

-@James K. ok, I am going to compute the mean anomaly for December 1st 00:00 starting from the day 320.81254693 of 2018 (the "epoch"). You will see if my formula is correct.


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How open is China in sharing data from the Chang'e 4 mission?
It's really good to see that man (well, machine) has gone back to the moon again.
Chang'e 4 is studying potential mantle material from the lunar depths and will be conducting radio astronomy in frequencies that simply aren't possible from Earth.
There's a huge amount to be learned that will fill some gaps in our knowledge of the early Moon, Earth, and the Solar system as well as the wider galaxy and beyond.
Will this information be open for the greater scientific community, or will we have to rely on the Chinese scientists to collate and publish the data as and when they can do?

It's been two years since the question has been asked and a quick check of google scholar for Chang'e 4 staring in 2020 shows plenty of scientific data papers, so it's clear that a fact-based answer is imminent. There's no reason to close this question!

Different space agencies and different governments have different policies about archiving their data.  One commonality that I have found, though, is that their systems are often difficult to find, they are often difficult to navigate or search and get the data, and then just as difficult sometimes to process.  Sometimes, they also require an account.
Doing an internet search for simply "Chang'e 4 data archive" linked me to this conference abstract as the first link, which was presented at the mid-2019 Data Users' Workshop in Flagstaff, AZ.  The abstract explains the different data types (such as level 0A, level 1, level 2C, etc.) and the different instruments, and it also explains their data archiving plan.
Perhaps more important for this question, it provides a link to China's "Data Release and Information Service System" within China's Lunar Exploration Program.
It has a lovely English translation button in the upper-left, so clicking on that (because I do not speak nor read any type of Chinese), and the news to the right shows they have Chang'e 4's 12th data release as their most recent posting.  You can follow through the links and find the data archived there, or, this is a direct link to the search engine.
Of course, as with any mission, agency, or government, you have to assume that they are publishing everything, but I see no specific reason to doubt that in this case.  Keep in mind, though, that there is always a waiting period between the time the data are taken and the time they are posted on public archives.  With NASA, that is usually 6 months, though at the start of mission data returns it can be more like 12 months.  So, just because data might not go up through today in these archives, that does not mean that they won't in 6–12 months.

Thanks for your answer!


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What is the dimensions of the smallest object detectable by an optical fiber from a specific distance?
Optical fibers are well-known to observe astronomical objects, say, galaxies, to generate massive spectroscopic surveys. The galaxies are often very far from the optical fibers of a telescope. However, I'm thinking about the possibility of using optical fibers to observe much smaller objects (compared to galaxies) like satellites in much shorter ranges like from earth to GEO orbit.
In particular, given an object at the distance $r$ from an optical fiber mounted at the focal plane of a telescope, how big (in terms of dimensions) that object should be to be detectable by the signal coming from the optical fiber?  (I couldn't find any related specification in the web. Since I need to use the answer as a part of my research, any cited reference is extremely appreciated.)

Don't the techniques you describe only apply to fixed objects like distant galaxies?  It's not clear to me how one would apply it to moving objects.  Could you elaborate on this?

Have a look at the beginning of this answer and see if there are any more specific bits of information you can add to your question. As long as your object is in space, say 100 km or higher, it's at infinity as far as the telescope's focus is concerned. Some math about that in this answer.

@AlexHajnal: Each optical fiber is often attached to a specific two degree-of-freedom robotic positioner which can move the fiber in a particular work space. This mechanism is well-established in switching the configuration of a set of fibers from one observation mission to another.

Interesting; I'd only heard of the method using fibers mounted in holes drilled in a fixed plate (with a different plate for each part of the sky being observed).

@AlexHajnal: The modern survey projects, including MOONS, DESI, and the family of SDSS projects, all are being (or have been) developed based on these roboticized fibers. So, you have only a single focal plane (or plate, in your terminology).

Interesting, I wasn't aware of that.  This (§2.3, p.3) is what I was thinking of, photo here.  It uses hand-threaded fibers.

Assuming you are using single mode fiber, the entrance (mode diameter) is small, usually a few microns (extremes can range from 1 to say 30 microns, but 2-8 microns is common for visible SMF).
The only constraint: you have is to get enough light into that small spot. You can do that with a single lens or convex mirror, a microscope, or a telescope, or even by proximity (hold the fiber so very close to a tiny object that enough light reaches the core, works for certain nanoparticle or biological experiments).
Size of target object: So far I can not think of any constraint on the size of the object. Really the question is how bright the object is and how sensitive the instrument is at the other end. If you have a high-dispersion spectrometer, you probably need a lot more light than if you are doing broadband photometry by counting photons with a photomultiplier.
Object is moving: It doesn't matter if the object is moving or fixed, as long as your optical system can move to track it so that the focused image falls on the core of the fiber. That's simply a mechanical and tracking issue not related to the fiber.
The big advantage of using a fiber is now obvious, you can move your telescope, but keep your measurement instrument somewhere else and fixed, and the flexible fiber will guide the light to it.

Further background
The trick is to put a very large telescope between the object and the fiber, and to use a robot to place hundreds or thousands of fibers at the focal plane, each at the exact location of a galaxy or a star you would like to collect. This way you can line up the other ends of the fibers along a single slit of a spectrometer and study the spectra of thousands or even millions of objects over time without having to point the telescope to each object one-at-a-time.
Fibers have some big advantages:

Multiplicity and configurability (as mentioned above)
Flexibility (literally) it allows the telescope and the instrument to be mounted separately and not have to be mechanically aligned and stabilized.
Mechanical stabilization of source for instruments: even if the telescope drifts and the object moves slightly with respect to the entrance of the fiber, the physical location of the fiber exit can remain fixed. So tracking errors don't affect the distribution of intensity within the entrance slit (virtual or real) of the fiber and therefore don't cause instrumental spectral shifts.

above: From the astrophysicist Ángel R. López-Sánchez's enjoyable A 2dF night at the Anglo-Australian Telescope

above:: From AAO's The stellar cluster behind Sirius

above: GIF from the video (with exciting music) A 2dF night at the Anglo-Australian Telescope

And if you like that robot then consider the "magic fingers" at the focal plane of the Dark Energy Spectroscopic Instrument:

DESI’s focal plane is designed to sit high atop the Mayall Telescope and to carry 5,000 robotic positioners, each holding a fiber-optic cable. Each of these fiber-toting robots is automatically positioned to fix on a preset sequence of individual galaxies and quasars so that the fibers can collect their light. The movements of these positioners must be carefully choreographed to avoid bumping into one another. The roundish focal plane, which measures nearly a meter in diameter, consists of 10 pie-shaped wedges that are fit snugly together. Each wedge holds 500 robotic positioners. The focal plane also contains sensors and light sources called field fiducials that help ensure the positioners are in proper alignment.

And also these robotic fibers in Australia's TAIPAN instrument at Siding Spring Observatory in North-Western NSW:

and if you liked the music in the video, here is ten more hours of the Inception horn

Some follow-up questions if you please: 1-Is Lens equation accurate from the LEO to GEO range? 2-The math analysis you pointed out in another answer seems like applicable to mirror telescopes not those equipped with fibers and spectrographs. Can you explain how that analysis would be also applicable to the latter case? 3-Since the target object may not be so bright, what if someone uses a multi-channel fiber (say, detecting IR or some other waves from EM spectrum)? Is this considered an advantage or disadvantages in terms of "detecting the target object"?

@Roboticist 1) For an aperture of say LEO to infinity you can use the lens equation to estimate the shift in focal length. For a reasonable telescope the shift will be extremely small (like a micron or probably much less), and this would not produce any measurable difference in your fiber coupling. 2) the spot size is the same no matter if you put a fiber at the spot or the pixel of a CCD. For more on that, try to write a more specific question with some details, and think if you want to ask that here or in Physics SE. 3) I'm not sure what a multi-channel fiber is. There are multi-core fiber

That's a pretty complicated field in itself. The problem with multiple normal fibers is that the cladding is so much bigger than the core that you can't get two cores very close to each other, so you loose most of your light between the cores. I think it will be great for you to look for older articles about fiber coupling in astronomy. These days it's extremely complicated, but 20-30 years ago they were just getting started and there may be very detailed explanations and calculations.


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Computing the local orbital frame vector directions in a geocentric reference frame
In the context of the study of a cubesat (little satellite), I am asked to define the local orbital frame and compute the local orbital frame vector directions as a function of time :
Here the context :

Anyone could give me some tracks or links to find the answer of part 2.1 Local orbital frame ? this would be kind.
Regards

I would interpret this as the Local Vertical, Local Horizontal (LVLH) frame (see, e.g., Vallado and McClain, Fundamentals of Astrodynamics and Applications, 4th ed., p. 156). This is also known as the RIC frame (radial, in-track, cross-track) or the RTN frame (radial, transverse, normal).

The radial or local vertical vector $R$ is just the position vector from the center of the Earth to the spacecraft.
The in-track, transverse, or local horizontal vector $I$ is the vector in the orbital plane that is both prograde and perinduclar to the radial vector. It is not, in general, the velocity vector. (The in-track and velocity vectors are coincident if and only if the flight path angle is zero, i.e., you have one of a) a circular orbit, b) the spacecraft is at apoapsis, or c) the spacecraft is at periapsis). You can construct it by applying the Graham-Schmidt Process to the position and velocity vectors; $I = v - \frac{R\cdot v}{R \cdot R}R$.
The cross-track or normal vector $C = R \times I$ completes the right-handed set.


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What happened to the third planet in the Kepler-47 system?
In 2012, the discovery paper for the multiplanet circumbinary system Kepler-47 mentioned a potential third transiting planet in the system:

A 0.2% deep transit-like event is present at time 2,455,977.363 (BJD) that is not caused by
  either of the two planets. A search for additional transits has revealed several more tentative
  transit events (12), but we caution that the star is faint (the Kepler magnitude is 15.178), there
  are large modulations due to star-spots, and the data contain correlated “red” noise, making
  small, non-periodic transit detection challenging. The marginal evidence at the present time is
  insufficient to place confidence on any additional candidate planet(s).

In 2013, Jerome Orosz gave a talk at the Second Kepler Science conference titled "The Confirmation of a Third Planet in the Kepler-47 Circumbinary System", claiming the detection of two further transits attributed to the third planet and giving the orbital period as 187.3 days and noting that the dynamical fit indicates that transits would stop for four years starting in July 2013.
In 2015, the discovery paper for Kepler-453 b was published, describing this planet as the tenth circumbinary planet discovered by the Kepler mission, which lists Kepler-47 d as the ninth of the previously discovered planets, giving a reference of "Orosz 2015, in preparation".
As far as I have been able to tell, there has been no further update since then - the Orosz 2015 paper never appeared. Is anyone aware of any further updates about this system and whether or not the third planet is still considered to be present?

I would expect it to have been a fluke after all, maybe only discovered in the refereeing process, which is why the paper never came out. This happens all the time, that planets are identified as starspots or as unresolved binaries in Kepler data. Is there any particular reason why you're interested in this system?

@AtmosphericPrisonEscape - I'm interested in it mainly because it's currently the only known transiting multiplanet circumbinary system, and noticed that this third planet had seemingly been abandoned by the literature.

Well it looks like it has finally showed up! The Institute for Astronomy in Hawaii has put up the following press release: Scientists Fill Out A Circumbinary Planetary System. Kepler-47d turns out to be the largest of the planets, with a radius 7 times that of the Earth.
The relevant paper is Orosz et al. (2019) "Discovery of a Third Transiting Planet in the Kepler-47 Circumbinary System".


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Why is Uranus able to support a regular satellite system?
Uranus has an obliquity of 98° which means that the mutual inclination between a satellite orbiting in its equatorial plane and the orbit of Uranus around the Sun would exceed the critical angle for Kozai oscillations. This would drive the satellites to high eccentricities which would likely be extremely damaging to the stability of the system, yet Uranus does host a system of regular satellites on near-circular orbits in its equatorial plane.
This suggests something is suppressing the Kozai oscillations for the regular satellites, so what is doing this? I suspect it is linked either to the non-spherical shape of the planet or gravitational interactions between the moons, but I'm not sure which would be a more relevant factor.

@userLTK - the major moons are located beyond the Roche limit though, otherwise they would be destroyed by tides.

Sorry, I meant inside the stable region of the Hill sphere.    (silly mistake).

The solar perturbations on most of the satellites of Uranus are on a very small scale indeed, which may explain the absence of the instabilities noted in the question.
A perturbational effect depends on the scale of the solar perturbing accelerations relative to the ordinary inverse-square attraction of the primary body. The scale factor (often designated $ m^2 $ in texts on the lunar theory such as Airy's 'Mathematical Tracts' and Godfray's 'Lunar Theory') increases with the separation of the satellite from the primary, it is also as the cube of the distance-ratio satellite-primary : primary-Sun (see detailed calculation below).
Taking as an example the most distant of the major moons of Uranus, Oberon at 583500 km:
The scale factor for the solar perturbing accelerations on Oberon in its orbit relative to Uranus is only about 1/5,000,000 of the gravitational acceleration towards Uranus felt by Oberon (calculation below).
Comparing the corresponding scale factor for Earth's moon and its solar perturbations, the factor is very much larger, close to  1/178, as is well-known.  The Moon has a fairly strongly sun-perturbed orbit relative to the Earth, but the solar perturbations on Oberon are more than four orders of magnitude smaller, really very tiny.
It is possible that the two tiny outermost satellites XVI and XVII of Uranus may be experiencing perturbations large enough to drive growth of their eccentricities, their eccentricities at 0.18 and 0.52  are very large compared with the major satellites, all with eccentricity < 0.004 (source, Astronomical Almanac 2016).
Detail of the approximate calculation:
The 'sampled' solar perturbing acceleration on a satellite is taken for present purposes to be represented by the perturbing acceleration on the satellite when it is close to quadrature with the Sun (as seen from the planet). In this configuration, the solar perturbation on the satellite is directed towards the planet, adding here to the ordinary inverse-square attraction of the satellite towards the planet.
With mass-constants of the Sun, S, and of the planet, P ;  planetary semi-axis a ; and planet-satellite separation d , plus an assumption that the mass of the satellite is very small relative to the other two:
1 ** the planet's accelerative attraction on the satellite is $P/d^2$ ;
2 ** the Sun's accelerative attraction on the planet is $S/a^2$ ;
3 ** and so also (to a quite close approximation) is the amplitude of the Sun's accelerative attraction on the satellite  $S/a^2$ .
4 ** When the satellite is in quadrature, the resolved part of the Sun's vector attraction on it that does not cancel with the Sun's attraction on the planet, i.e. the net perturbation on the satellite at that point, is given very nearly by the proportions of the triangle satellite-planet-sun:  the lengths of two of the sides are approximately a and the third d. In this configuration, the resolved part of acceleration #3 in the direction of the planet, to a close approximation, is thus  --
$ (S/a^2) .  (d/a) $.
The ratio of perturbing acceleration 4 to ordinary planetary attraction 1 is thus
$ (S/P) . (d/a)^3 $.
For the Sun and Uranus, S/P ~= 22902 ,
for the Sun and Earth+Moon, S/P ~= 328901 .
Uranus is approximately 19 au from the Sun to the Earth's 1, the au is  149597871 km, the mean planetocentric distance of Oberon is 583500 km and of the Moon 385000 km.
Using these figures, the ratio
'solar perturbation on satellite : planetary attraction on satellite'
comes to ~ 1/178 for the Earth and Moon, and  ~ 1/5,000,000 for Uranus and Oberon.
The tiny outer satellites of Uranus are farther away from it than Oberon is, in a ratio of about 20.8 for the outer (XVII). Thus the perturbations on it, as a proportion of the ordinary attraction of Uranus at its distance, is $(20.8)^3$ times larger than for Oberon, making the relevant perturbation scale factor as large as about 1/550 , still smaller than for the one for our Moon, but perhaps enough for the disturbing effects to be reflected in its higher eccentricity of about 0.52.
{Update:} It turns out that the orbits of the outer Uranian moons have actually been studied: Brozovic, M.; Jacobson, R. A. (2009), "The Orbits of the Outer Uranian Satellites", The Astronomical Journal, 137 (4): 3834-42. Just one of the (high-eccentricity) outer satellites was found to be disturbed by a Kozai resonance and may be in unstable orbit. It appears that the conditions for the effect are not fulfilled for the others.

It may help if you learn that you can use TeX maths between dollar signs, eg $S/a^2 \times d/a$

I'm not sure that this explains it, because there is evidence for Kozai oscillations in exoplanetary systems in wide binaries where the gravitational force from the secondary star is much weaker than the primary. If I take equation 42 from Antognini (2015) then the timescale for Kozai oscillations of Oberon is about 32,000 years, which is much shorter than the age of the solar system.

Thanks for your comment. Are you able to give a citation to the paper showing the Kz oscillations in a system with 'much weaker' grav. effect from the secondary star? (I also can't see where the Antognini paper considers the effect of perturbation amplitude.)

@terry-s - Kozai oscillations have been implicated for generating the high eccentricities, e.g. HD 80606, HD 20782 and 16 Cyg. The timescale seems to factor in the relative magnitudes of the gravitational pulls as the timescale for inner satellites is longer. Kozai does appear to be operating on the cloud of outer irregular satellites but something must be suppressing it for the regular satellites. I would buy the weak solar influence argument if the timescale for Kozai oscillations were longer than the age of the solar system, but this does not appear to be the case for the major satellites.

@mistertibs -- but have you a citation that shows the evidence and the conditions for the bodies that you name,  and how the amplitude question is taken into account?

@terry-s - do you have a reference for the Kozai mechanism having a cutoff at low ratios of the gravitational force, and if so what is the value for this cutoff? As far as I am aware, there isn't one: what happens is that the Kozai cycles take longer (this can be seen with the formula in the Antognini reference - the timescales for satellites closer to the planet are longer than the ones for outer orbits). Nevertheless, the Kozai cycles for Oberon are still much shorter than the age of the solar system, so what is the mechanism that's disrupting them?


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Tidally locked, and yet spinning?
Reading about Uranus almost 90° tilt, I was wondering if some rocky planet with mass concentration at one pole could possibly spin around its own axis, while still being locked to its star? Which means the more massive pole always points toward the star?

Almost? The axial tilt of Uranus is more than 90°, it's 97.77° relative to its orbital plane.

Maybe it's spinning retrograde with 82.23° axial tilt?

The most improbable is to have mass concentrated at the pole, Unless you have a more generic system in mind rather than planetary

Would be the case if the axe of rotation were right 90°, tough tidally locked might not be the right term (just always facing to. .. instead of locked)?

I think what you are envisioning is having one pole always pointed towards the primary star. So the planet would rotate about that pole, but then the direction of the pole would change over the course of a year to keep the pole pointing towards a star.
This phenomenon of the direction of the pole changing is called "precession". The Earth does it over a period of 26,000 years, but the pole only traces out a fairly small circle in the sky, rather than twisting about a perpendicular line like you envision.
I think your scenario is improbable at best. Planets are like gyroscopes and resist having their axes of rotation be twisted about a perpendicular axis like that. Even a planet with mass concentrations at both poles (maybe a long cigar shape) to maximize tidal force would probably end up losing the perpendicular rotation to tidal friction, and just end up rotating slowly about an axis nearly parallel to the axis of the orbit.


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Can Jupiter's nightside be classified as spectral type Y?
As far as I am aware, the latest spectral types that have been assigned are around Y2, for objects like WISE 0855-0714 that have temperatures around 250 K or so. I've also seen several directly-imaged exoplanets have had their spectra classified as L- or T-type (e.g. Bonnefoy et al. 2016 who find that the giant planets HR 8799 d and e are good matches for L6–L8 dwarfs).
Jupiter is colder and less massive than the observed Y dwarfs and differs from isolated brown dwarfs because it is being illuminated by the Sun, but there is thermal emission which could be observed from the nightside of the planet. Has Jupiter's nightside spectrum (i.e. the spectrum of Jupiter excluding contributions from reflected sunlight) been observed in sufficient detail to compare it to the spectra of Y dwarfs, and if so does it fit the trends observed in spectral type Y or is it so different that it cannot be spectrally classified as a Y dwarf?
For clarity: I am asking purely in terms of spectral classification, i.e. the classification of the spectrum. I am not asking about whether Jupiter is a brown dwarf making the Sun+Jupiter a binary system. That has been asked elsewhere.

According to this article:
(https://iopscience.iop.org/article/10.3847/1538-4365/ac886a#:~:text=The%20visual%20and%20near%2Dinfrared,and%20ammonia%20(NH3).)
"The visual and near-infrared (below 3.5 μm) spectrum of Jupiter is dominated by reflected solar light with absorption bands primarily from methane (CH4), phosphine (PH3), and ammonia (NH3)."
Now, Wikipedia states that water, methane, carbon monoxide, carbon dioxide, and ammonia, were detected in a class Y brown dwarf (WISE 0359−5401). We see that there are many similarities with the spectra of WISE 0359−5401 and Jupiter, in particular the methane and ammonia. So there are many similarities between the spectra of Jupiter and the spectra of brown dwarfs. One main difference is that Jupiter would be colder, so its peak wavelength would be longer. (0.01776 millimeters), as opposed to 0.005796 millimeters for class Y brown dwarfs assuming a temperature of 500 K (I used Wein's Law). So Jupiter and class Y brown dwarfs do have many similarities, but the temperature difference and the absence of deuterium fusion in Jupiter cause differences.
Edit: "A planet absorbs energy from the Sun in the form of light and converts the energy into heat. The heat is then reradiated back into space (mostly from the nightside of the planet). Based on how much energy Jupiter absorbs from the Sun, then its mean temperature should be 105 K (about -280 F). However, IR and radio measurements of Jupiter show that it has a mean temperature of 125 K, or 20 degrees too warm. In other words, Jupiter radiates about twice as much energy as it receives. Conservation of energy requires that this heat come from someplace and the only reservoir is the core of Jupiter. Thus, this extra heat is leftover energy from the time of Jupiter's formation." This article from http://homework.uoregon.edu/pub/emj/121/lectures/jupint.html
does indicate similarities from Jupiter and Class Y brown dwarfs. They both gain energy from gravitational contraction. However, Jupiter's emission is mostly from remitted radiation from the Sun, unlike Brown dwarfs which undergo deuterium fusion.

The coolest Y dwarfs have temperature similar to Jupiter. Why are you discussing a 500K object? The question also specifically asks about the night side Jupiter spectrum, which of course is not dominated by reflected light from the Sun. Deuterium fusion does take place in brown dwarfs.

I used the average temperature of class Y dwarfs, and analyzing the absorption lines from reflected sunlight after being reflected allows us to detect the composition of Jupiter's atmosphere.

I added more information about Jupiter's emission on its night side

Pretty sure that deuterium fusion is not happening in Y dwarfs though. That phase of the evolution takes place whilst they are class M or L. How would that affect the spectrum anyway - are deuterium features obvious in Jupiter's spectrum?

This Wikipedia page lists Jupiter as a disputed sub-brown dwarf because its mass reportedly is sufficient to qualify for one. Distance to another star like the Sun doesn't matter, nor does the visibility in the infrared spectrum either since every planet is emitting some infrared light. The fact that Jupiter emanates more energy than it gets from the Sun can't be accounted for either, since that's also a matter of distance from the Sun, and Saturn and Neptune do so too. But, as the article states, Jupiter obviously has enough mass to possibly count as a sub-brown dwarf. Sub-brown dwarfs are still planets because they don't undergo nuclear fusion unlike brown dwarfs and hydrogen-fusing stars and never did.
Edit: There is no reason to only classify the night side just because the day side is illuminated by a(nother) star. Spectral classifications are given to the entire object. Since sub-brown dwarfs reportedly have a mass of at least one Jupiter mass, you may want to classify Jupiter a Y9V sub-brown dwarf.

This doesn't really answer the question, which is about the classification of Jupiter's spectrum. It isn't about whether or not Jupiter qualifies as a brown dwarf.

@antispinwards We don't know where a lower limit of Y-type objects might be set and therefore this is hard to answer with a number. Reportedly, sub-brown dwarfs have a mass of at least a Jupiter mass, so Jupiter would qualify as a sub-brown dwarf. In my opinion, the entire Y-type sub-brown dwarf class is unnecessary since they're actually planets (gas giants) if they don't undergo nuclear fusion.

Once again, this is not about whether or not Jupiter is a (sub-)brown dwarf. It's about its spectrum and how it compares to objects that have been classified as spectral type Y.

@antispinwards You already stated "Jupiter is colder and less massive than the observed Y dwarfs". So the spectrum is obviously less intensive than that of the observed ones. When looked from outer space on the objects, all of them have a pitch dark night side or are entirely like this when not illuminated by a star. No visible light is emitted on the exterior.

Yes, they're dark in the visible spectrum. That's why these objects are observed in the infrared.

@antispinwards You may want to change your question title to "How does the spectrum of Jupiter's night side compare with that of observed sub-brown dwarfs?" since this is what you're really asking.

No, I'm specifically asking whether it fits into spectral class Y, which is what is in the question title and the body of the question. If I were asking about whether Jupiter is a brown dwarf or a planet (which is another question entirely), I would have asked that. Spectral classification is the classification of spectra. It is not the classification of the objects that produce those spectra. To take a different example, some late M-type dwarfs are hydrogen-burning stars, some are young brown dwarfs, but the spectra are classified as type M regardless.

@antispinwards I wonder if there is just a difference in semantic interpretation here? Perhaps some feel that "spectral classifications" are tentative classifications of the object based on the object's spectrum, where others feel that it is a classification of the spectrum itself. Some might be bothered by the concept of classifying Jupiter's night side. I certainly understand what you're asking but maybe a shift in wording of the title could help? "Would a measured spectrum of Jupiter's nightside be classified as spectral type Y?"


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Is the Ordovician meteor event detectable in the lunar cratering record?
Approximately 468 million years ago there were a large number of L-chondrite meteorites falling to Earth. This is called the Ordovician meteor event and was probably the result of a large collision in the asteroid belt.
Does the lunar cratering record also show evidence of this event?

Can't find (quick skim) any papers on lunar Ordo. I suspect that's due to lack of collecting samples from the far side of the moon, since it is statistically impossible for this meteor cluster to have missed the moon entirely.

Earth and Moon impact flux increased at the end of the Paleozoic has some data.

The very, very short answer to your question is: "Not that's detectable by any current methods or data that we have."
The longer answer has to do with how we know how old anything is on the Moon or other planetary surfaces.  What we do is we use craters themselves to date a surface: The more craters, the older the surface because it's been around longer to accumulate those craters.  We can tie to those to an absolute age by saying that X rock sample collected by Apollo or Luna or Chang'e is Y years old (dated via radiometric methods) and it is from a surface that has Z craters.  Do this a lot and you can build up a function that relates the number of craters to an age.
The problem comes in using this to date any specific craters to try to find a non-uniform function (e.g., an age spike):  You have already assumed a crater chronology function that does NOT have that spike, so using it to find a spike becomes a circular argument that is very difficult to get out of.  There are some proposals on how to do that, but they're based on models and not actual data (such as, the large objects that form large craters would show those spikes, but the small objects that form small craters are a steady "clock" of impacts).
Right now, the lunar crater chronology has roughly a dozen points on it, so we don't have the resolution to say anything about a spike ≈468 million years ago.  It is certainly possible (likely, even) that the lunar crater record would show that spike if we had the resolution to measure it by dating many more craters through methods other than superposed crater measurements, and, indeed, it is generally assumed that the lunar crater chronology really should have lots of little spikes in it when asteroids break up / asteroid families form, but again we just don't have the data to really measure that ... yet.


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Is an elliptical orbit around a black hole, or an orbit consisting of three bodies (including the black hole) possible?
If this is possible, would it then lead to an object undergoing varying time dilation (predictable variation with elliptical and random variation with three body)?

Elliptical Orbit
Yes, an elliptical orbit around a black hole is possible.  Provided the orbit doesn't cross too near the event horizon, the orbital mechanics are the same as orbiting any massive object.  Gravitational time dilation is a function of distance only, so the time dilation experienced at any point in the orbit should be easily calculated and presumably predicted ahead of time or calculated for past times.
Three Body Orbit
When you mention an orbit consisting of three bodies, do you mean the black hole, another massive object, and a much smaller object?  Or do you mean three massive bodies?

If the orbit consists of the black hole, another massive object, and a smaller body, the system should be predictable as a restricted three body system.  This is made even easier if the smaller body finds its way to a Lagrange point, or resides in a stable repeating orbit.  There are limits to the predictability of the restricted three body cases, which differ based on requisite constraints (e.g. circular vs. elliptical orbit for the smaller body).  If the constraints are not met, or near their limits (not hard limits), the predictability of the orbit will suffer and thus the predictability of the time dilation will suffer as well.  Constraints for the elliptical restricted three body problem include the mass of the small body being "negligible" relative to the two larger bodies, and the ability to approximate the co-orbit of the larger bodies as Keplerian between point masses.  Thus if the mass of the smaller body is some appreciable fraction of either larger body, or if the larger bodies orbit very closely to one another, this may not hold.  The circular restricted three body problem adds the constraint that the co-orbit between the larger bodies must be circular, so if it is near-circular that condition may or may not be said to be met.  Whether constraints are met would be most easily judged by setting a time over which predictability of the system may be maintained.  So if the goal is to be able to predict the system for 1000 years, and the smaller mass is small enough that the system is predictable under the restricted three body problem, the system can be said to meet the constraints for those purposes.
If the orbit consists of the black hole and two other massive bodies, the system will not be perfectly predictable (this may not be totally true, apparently solutions exist in the form of convergent power series though they may not be practical due to their size).  If this is the case, time dilation will not be predictable, but will be calculable for the present and past (provided there is position data from the past).

To calculate both the gravitational shift and the time dilation to first order around an elliptical orbit, you can use the equation in this answer (also used here).


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Is there any habitable exoplanet around Tau Ceti?
I was wondering.. is there any habitable exoplanet around Tau Ceti?

Have you checked Wikipedia, and if so, is there anything there that doesn't address your question?

Might this question be inspired by the mention of "Tau Cetian" in the latest Star Trek: Discovery episode? :)

TLDR version: probably not, and claims for the habitability of planets in this system are on shaky ground.
Long version follows.
Planets
So as of Feng et al. (2017), there are four planet candidates around Tau Ceti:

Planet
Minimum mass ($M_\odot$)
Semimajor axis (AU)

Tau Ceti g
$1.75^{+0.25}_{-0.40}$
$0.133^{+0.001}_{-0.002}$

Tau Ceti h
$1.83^{+0.68}_{-0.26}$
$0.243^{+0.003}_{-0.003}$

Tau Ceti e
$3.93^{+0.83}_{-0.64}$
$0.538^{+0.006}_{-0.006}$

Tau Ceti f
$3.93^{+1.05}_{-1.37}$
$1.334^{+0.017}_{-0.044}$

Note that the designations Tau Ceti b, c and d refer to planet candidates that are no longer thought to exist. The error bars refer to the 1% and 99% percentiles. $M_\oplus$ is the mass of the Earth.
The Feng et al. (2017) paper also notes that the system is dynamically packed, which does not bode well for the prospects for additional planets between the known planet candidates (note that their figure 17 shows the regions where the planets would interfere with each other, not the regions of stability for an additional planet).
The habitable zone
The conclusion of the paper gives the luminosity of Tau Ceti as 0.52 times solar and the effective temperature as 5344 K. Using these values, the habitable zone limits can be calculated from Kopparapu et al. (2013), which assumes that habitable conditions are maintained by the carbonate-silicate cycle with carbon dioxide as the main (non-condensible) greenhouse gas.
Inner boundaries

Boundary
Distance (AU)

Recent Venus
0.551

Runaway greenhouse
0.723

Moist greenhouse
0.729

The moist greenhouse limit is the most conservative inner boundary, it occurs where sufficient water vapour enters the upper atmosphere that water loss begins to occur from the planet. In our solar system, Earth is located close to this limit in the inner part of the most conservative habitable zone.
The runaway greenhouse limit occurs where the positive feedback from water vapour overwhelms the stabilising negative feedback from the silicate-carbonate cycle, driving further evaporation of the oceans and higher temperatures. This is thought to have occurred on Venus, leaving the planet in the state it is in today.
The recent Venus limit is based on the possibility that Venus may have retained oceans for several billion years. This is not known for certain as our knowledge of Venus's evolution is rather incomplete and the conditions on the planet's surface are not favourable for driving rovers around investigating the geology.
From this we see that Tau Ceti e is located close to the recent Venus limit and is closer to the star than the runaway greenhouse limit. This suggests that any oceans that may once have existed would likely have boiled off, leaving the planet in a Venus-like state.
Planets g and h are too close to the star.
Outer boundaries

Boundary
Distance (AU)

Maximum greenhouse
1.279

Early Mars
1.330

The maximum greenhouse limit is the furthest distance from the star that a cloud-free carbon dioxide atmosphere can support conditions compatible with liquid water. Beyond this, the increased scattering leads to increased reflectivity of the planet and the CO2 would begin to condense, removing it from the atmosphere and leading to runaway cooling. This is the most conservative outer habitable zone boundary. Note that by this point, the planet would require several bars of CO2 which would make it toxic for humans.
The early Mars limit is based on the observation that Mars managed to maintain surface water (e.g. various rivers, and a possible northern ocean) in the early solar system when the Sun was significantly fainter than it is today. Tau Ceti f is located right at this limit.
Extensions to the habitable zone
None of the planets fall into the most conservative habitable zone, and Tau Ceti e and f are at the boundaries of the most optimistic estimates for the habitable zone boundaries. There are nevertheless options for extending the habitable zone.
At the inner boundary, a runaway greenhouse effect could be avoided on dry planets, where there simply isn't enough water to evaporate to drive the positive feedback, see Zsom et al. (2013). It isn't clear to me that such a planet can be described as habitable, since such planets may lack the hydrothermal systems that could act as the sites for abiogenesis. Their geological evolution would likely be substantially different to Earth's without water to lubricate plate tectonics.
Another possibility is on slowly-rotating planets, where substantial cloud layers can build up on the day side of the planet and increase the reflectivity, as noted by Yang et al. (2014). On the other hand, Scholz et al. (2018) have noted that there appears to be a universal mass-spin relationship that extends from planets to brown dwarfs. This predicts that super-Earths would likely spin too fast for this mechanism to work unless they have been spun down by stellar tides or a large moon.
On the outer boundary, adding additional greenhouse gases such as methane may work to extend the outer habitable zone, see for example Ramirez & Kaltenegger (2018). This has been suggested as the mechanism for allowing surface water on Mars, which would suggest that the "Early Mars" limit is an observed data point within the methane habitable zone. Another possibility is that a dense hydrogen atmosphere could maintain liquid water, e.g. Pierrehumbert & Gaidos (2011) though the pressure of such an atmosphere may well have implications for the geology of the planet and hence the potential for abiogenesis.
Planets whose climates are stabilised by something other than the carbonate-silicate cycle, or have substantially different atmospheric compositions would have different habitable zone boundaries (if subsurface oceans on icy worlds are habitable, there may be interesting prospects for dwarf planets in the outer debris belt), but this is already getting speculative enough, besides there is another possible objection to the habitability of these planets...
Planetary masses
A limitation of the radial velocity method is that only the minimum masses can be derived. With Tau Ceti, we have a possible means to estimate the true masses: the star is surrounded by a debris disc (this would likely provide a source of impactors onto the planets, how bad the situation is depends on how much material is being perturbed into the inner system). Using Herschel observations, Lawler et al. (2014) give an inclination of 35±10 degrees. Assuming that the planets lie in the same plane as the disc, the true masses would therefore be approximately 1.74 times greater than the minimum masses.
Under this assumption, the true masses of the planets e and f both come out as about 6.85 Earth masses. Taking the 99% lower limit on the minimum mass error bars and a 45° orbital inclination as a low estimate, these would be 4.65 Earth masses for e and 3.62 Earth masses for f.
The nature of the planets
According to Rogers (2014), the transition between rocky and Neptune-like planets is somewhere in the region of 1.4 to 1.6 Earth radii. Using the mass-radius relationship from Zeng et al. (2016) and their core mass fraction of 0.26 for typical terrestrial planets, these radius limits correspond to terrestrial planets of roughly 3.3 to 5.4 Earth masses.
This suggests that Tau Ceti e and f are fairly likely to be sub-Neptunes rather than rocky planets, although the caveats are that in the optimistic case they can have masses below the rocky/Neptune-like transition, and that there do seem to be a few cases of rocky planets above the transition (most of those are likely to be evaporated cores of Neptune-like planets, which wouldn't apply to Tau Ceti e and f as they have much lower levels of stellar irradiation).
Conclusion
Given the current state of knowledge, Tau Ceti does not look like a good prospect for habitable planets. Tau Ceti e and f are rather marginal in terms of their location within the habitable zone, and their masses are sufficiently high that there is a good chance that they are sub-Neptunes rather than rocky planets. The dynamical packing of the system makes it unlikely that there can be a smaller, temperate planet in the habitable zone between the known planets.

While I like this answer more than the previous one, you're missing out on pointing out that the habitable zone as is employed by those and most authors, is the Earthly-climate habitable zone. It is only valid as derived for this one particular atmospheric composition at this particular time. We don't even know how the HZ of early Earth would look like, let alone those of planets with different/unknown atmospheric compositions.

@AtmosphericPrisonEscape - actually that's not the case, the habitable zone for an Earth-composition atmosphere is much narrower than these estimates. The maximum greenhouse requires far higher levels of carbon dioxide in the atmosphere than present-day Earth. It does assume a silicate-carbonate cycle with carbon dioxide as the non-condensible greenhouse gas though, will update the answer to reflect that.

Well, that's still essentially Earth plus a small epsilon, as we simply don't understand the planetary climates of terrestrial planets well enough to predict their behaviour.

@AtmosphericPrisonEscape - several bars of carbon dioxide may be a "small epsilon" to you (Venus is presumably that small epsilon plus the other small epsilon of removing all but a trace amount of water), but it is rather lethal to me. And besides, these worlds are probably sub-Neptunes anyway. Nevertheless I have updated the answer with a discussion of various possible HZ extensions.


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Astronomy/Astrophysics Project With C++/C/Python
I am a Computer Science Engineering student, in the 1st year of college. I'm insanely interested in making a project regarding astronomy/astrophysics but I don't know where to begin from. I know C, C++, Python(not Scipy,Numpy or Astropy, but the basics. But I'm willing to learn those too). Can someone please give me some insights on what do make/do which would satisfy my aptitude in this field? My C++ and C knowledge are almost up to date, and I know basics of python, with all the data structures and basic libraries of Python. I'm interested in simulation stuff, but I don't exactly have relevant resources to learn those.

Knowing how to write code that compiles and runs has nothing to do with knowing how to produce algorithms that simulate the system you  are interested in.

Hi @KumarTatsat, two kinds of projects come to mind that are related to Astronomy, 1) orbital simulators (seeing how planets, moons, spacecraft) move in space under the influence of their mutual gravity, and 2) visualizing how the planets, Sun, Moon, asteroids, etc. appear and move in the sky. Stack Exchange is a great place to ask specific questions, don't worry that this one was considered too broad, find something specific, do a little reading, find specific questions, then ask again! Try to add a bit of your own work to the question as well so people have a better idea how to best answer.

For orbit simulation, here are examples in python that range from simple to complicated. For visualizing things in space and from Earth, you can try installing the python package Skyfield and have some fun.

For general discussion and questions you can also try the Stack Exchange chat rooms. For Astronomy SE it's The Observatory and for Space Exploration SE it's The Pod Bay


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Could there be additional Neptunian satellites between Larissa and Hippocamp?
Plotting the moons of Neptune in terms of semimajor axis and eccentricity using the values given on the Wikipedia page for the moons of Neptune, there appears to be a fairly large gap between the orbits of Larissa and the newly-named satellite Hippocamp.

Are there stable orbits within the gap, and are there likely to be additional moons there?

There is a good possibility, but I would doubt such. I don't know enough about Neptune to confirm this.

The diagram of the Moons don't show any considerable gap between the moons where a stable moon could possibly exist at. Perhaps somebody confirm this?
https://i.stack.imgur.com/6njj7.jpg

@Max0815 you can fit one in if you use smaller pixels ;-) Seriously though, I'm just curious how much of a considerable "gap" is necessary. Are there guidelines? How can one tell?

@uhoh Its very late for me I am in the middle of writing an answer I'll post it tomorrow.

@Max0815 super, take your time!

@mistertribs do you need any clarification? If not, would you mind to mark my answer as correct?

@mistertribs seriously... do you need any further explaination? Why do you ignore me? I would gladly explain my answer more if you need me to.

@mistertribs its funny you just mention that there are other things to do it life. xD. I just said to myself, there are other things to do in life other than SE after I was on Math SE for 4 hours. But, hey, I have these 'periodical" go-SE periods where I can do nothing in life but SE...

@mistertribs what about now?

[My answer may be a bit off as astronomy is just my hobby]

First off, I would assume eccentricity has little function into the investigation because why would it be a moon when it can escape Neptune's gravity?[assuming you mean Neptunian eccentricity] I mean, unless you are thinking about a moon escaping?
Now, let's move onto the distances. You notice when you graph the moons that there is a considerable gap in distance between S/2004 N 1 and Larissa. I believe, after checking this on multiple sites, that there is indeed such a gap.
Neptune Moon Origin
First, let's take a look at one of the most accepted theories on Neptune and its moons. It is well known that Neptune is very close to the Kuiper Belt. In the Kuiper belt, there are objects like Pluto in orbit around the Sun. Well, Neptune having a very strong gravitational pull would actually yank objects out of orbit into its orbit. Most people believe that this is what happened with Triton. Making up more than 80% of the mass of all of Neptune's Moons,  if would have wreaked havoc on the then stable orbits of its original moons.
This consequently could have cause many moons that were large[relatively speaking] to gain/lose eccentricity which would have cause some to spiral inside of the Roche Limit of Neptune ultimately causing the formation of several rings around Neptune. However, in the case of Saturn, we see moons inside of the Roche limit, so we can also deduce that the Roche limit of a planet varies on how massive/large an object is.
We can now conclude that almost all of Neptune's current moons and their orbits are not its original ones. To answer your question, we look at the three body problem. I am not a physicist to I don't know much on the relative equations for the three body system to calculate the exact orbits of possible moons or calculate proof why there isn't a moon. However, I will give you a relative, not full equation blast, explanation.
Three body problem
The three body system states that in long term, the three body problem may lead to either and for the most part, stabilization of the orbits of moons around a planet or, for some period ratios, be the cause of the chaotic motions.
In Neptune's case, Triton introduction has cause for a short period, chaotic motions, which then stabilized into new stable orbits.

In the image here, it shows the relative orbits of stable moons and Neptune's rings. We can conclude that the respective Roche limit of Neptune would cause any possibly try of ring matter collapsing into a moon to be foiled if the mass was too high. This means that only small moons form between rings Adams and Galle, with Galle marking the "will tear anything apart no matter the size" Roche limit.
Moons between the gaps
There can be many moons there in the gaps between the rings, as long as the moon is small enough to fit, and its gravity is not influencing the rings so much that it is noticeable, most likely very small to be picked up by our telescopes. It brings up another problem: How small must a moon be to be no longer a moon?
Moon definition
There isn't a restriction. However, the most widely accepted one is that a moon is an object with a relatively clear orbit[little debris]. We can say that there may be many moons between the rings, but are too small to be detected.
Moons in the large gap you notice
Now moving on, we have a gap between Larissa and Proteus / S/2004 N 1. Clearly, no rings call this area a home. So this gap is somehow mysteriously "uninhabited".
I doubt that there isn't a "moon" there, even if it were really small. Hippocamp is a very small object. In fact, it is the smallest moon discovered around Neptune. The relative Roche limit is not here, so it probably is possible for ring material to recondense into a moon with a stable orbit, and many times, a moon might happen to be covered up when we search. As I said, there is no size limit to a moon, so, because this area is clear of debris, there might be quite a few that we can't find.
A possible scenario [saying that there are a lot of moons] might be that the moons will gravitationally interact with each other, such as kick each other out, part of the three body problem. However, this can be easily detected, as rings would be seemingly affected. This obviously isn't so, due to everything being in a stable orbit, because the "chaotic" period is already passed, and debris settles down and recondense whenever possible.
Note: There can be moons also at the lagrange point if the point is near the "gap" you are taking about.
Another Note: Similar to lagrange points, uhoh mentioned another very good concept of co-orbital configurations, which is the interaction between two celetrial objects. Places with extremely possible stable orbits are called Trojan Points. One example of this is the Trojan asteroid groups which share the orbit with Jupiter. There are two Trojan Points near a given object so those points might harbor many stable moon orbits there too.
Answer
So my guess is that yes, there are stable orbits within this gap, and there is a good chance there are additional moons out there.
We are discovering more and more moons today. Jupiter is one good example.

@uhoh I would think that a considerable gap must be necessary, because moons would kick each other out or collide if the space were too small, forming another chaotic period. Orbits must have settled for moons to reform and since there isn't another gravitational disturbance, there shouldn't be more chaos. Depending on the size of a given moon, the gap must be large enough so that the moon's gravity shouldn't disturb another moon's orbit. Such events would quickly settle if it would happen because objects tend to move to stable places.

Very nice! At some point you might just mention co-orbital configurations, at least as a caveat.

@uhoh thanks! I'll be sure to add the 2 body system as a note ASAP :)


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Can Fermi Bubbles be produced in non-spiral galaxies?
In 2010 observations with the Fermi Gamma-ray Space Telescope discovered giant bubbles which have been named Fermi Bubbles. Similar structures have also been discovered by Pshirkov et al. (2016) surrounding M31 (the Andromeda Galaxy).
Our galaxy and M31 are barred spirals. Could Fermi Bubbles also form around other galaxy types, for example lenticular or elliptical galaxies?

The discovery paper (Su et al. 2010) mentions that bipolar shells on the order of $0.5\text{ kpc}$ were found on both sides of the nucleus of Centaurus A (Quillen et al. 2006). Centaurus A is a galaxy of contested morphology, likely either elliptical or lenticular - certainly not a spiral. This would seem to be a strong indicator that similar bubbles can indeed be found in non-spiral galaxies.
Now, the nuclear shells Quillen et al. detected were seen at mid-infrared wavelengths (5.8, 8.0 and 24 $\mu\text{m}$), rather than via the gamma rays with which Su et al. discovered the Fermi bubbles. However, the authors believe they may have been caused by a burst of star formation a few million years ago, driven by winds. This is one of two main scenarios considered by Su et al. for the formation of the Milky Way's bubbles (the other being AGN activity), meaning that the same processes could indeed have been at work in both galaxies. I don't know if corresponding gamma-ray emission from the nuclear bubbles in Centaurus A has since been detected, but it certainly seems plausible.
I find it a little strange that Pshirkov et al. were so careful to focus on spiral galaxies. It's clear that starburst galaxies and the host galaxies of AGN can obviously have non-spiral morphologies. Perhaps the group was just interested in searching for other nuclear bubbles on galaxies similar to the Milky Way which might have similar conditions and evolutionary histories.


text:
Finding angle between a given sky position and ecliptic pole
Given a right ascension in degrees and declination in degrees (say, 88 degrees RA, -63 degrees DEC) I want to find the angle between that location and the ecliptic pole (90 degrees RA, -66 degrees DEC... are these the right values? What are the decimals following the 66? Most of my values that I'm working with are similar to the one I give, so which ecliptic pole, if any, does this correspond to?) How would I find this angle, I need a convenient formula (such as a dot product to find this angle). Thank you!

The question about finding the angle between two celestial positions is a duplicate of other questions, such as How to calculate the angle formed between 2 planets? https://astronomy.stackexchange.com/questions/26625/how-to-calculate-the-angle-formed-between-2-planets

The angle between an ecliptic pole and another sky position is complementary to the ecliptic latitude of that position.
To find ecliptic (λ, β) coordinates, one method is to convert the equatorial (α, δ) to Cartesian form:
$$ \begin{align}
x_\mathrm{equ} &= \cos \alpha \cos \delta \\
y_\mathrm{equ} &= \sin \alpha \cos \delta \\
z_\mathrm{equ} &= \sin \delta
\end{align}$$
then rotate by ε = 23.44° on the x axis:
$$ \begin{align}
x_\mathrm{ecl} &= x_\mathrm{equ} \\
y_\mathrm{ecl} &= y_\mathrm{equ} \cos \varepsilon + z_\mathrm{equ} \sin \varepsilon \\
z_\mathrm{ecl} &= z_\mathrm{equ} \cos \varepsilon - y_\mathrm{equ} \sin \varepsilon
\end{align} $$
and convert to spherical form:
$$ \begin{align}
\lambda &= \mathtt{atan2}(y_\mathrm{ecl}, x_\mathrm{ecl}) \\
\beta &= \arcsin z_\mathrm{ecl}
\end{align} $$
If you are not interested in the ecliptic longitude λ, you can express the ecliptic latitude as
$$ \beta = \arcsin (\sin \delta \cos \varepsilon - \sin \alpha \cos \delta \sin \varepsilon) $$
Then the angle off the north ecliptic pole (α=18h0m, δ=+66.56°) is 90° - β.
Working your example (α=5h52m, δ=-63°),
I get (λ=75.63°, β=-86.34°),
and the angle off the south ecliptic pole (α=6h0m, δ=-66.56°) is β + 90° = 3.66°.

+1 Though not necessary, it looks like you are already close to including a second answer using dot product as mentioned in the last line of the question.


text:
What is the orientation of the M87 black hole image relative to the jet?
On the image of the M87 black hole released today by the Event Horizon Telescope team, which direction points towards the jet? Is it on the brighter side of the ring?
To resolve ambiguity, I'm talking about the main observed jet, not the fainter counterjet.

The jet is projected onto the image roughly in the E-W direction with the (main) jet coming towards us to the right of the black hole.
The brightening in the ring is perpendicular to this. It is probably caused by the spin of the black hole (aligned with the jet), which drags emitting material around and Doppler boosts the emission seen to the south.
This picture is from the fifth event horizon telescope paper published today. The jet is E-W (actually, I believe it is at PA=288 degrees, so rotated 18 degrees anticlockwise) and the black hole spin axis (indicated with the black arrows) is projected at the same PA and into the screen (the two left hand plots).


text:
Eddington luminosity in various plasmas
So I know that the Eddington luminosity is given by:
$L_{Eddington} = 4\pi GMc/\kappa$.
I want to calculate this luminosity for a plasma of purely ionized helium, as well as for an electron-positron plasma.
How do I find $\kappa$ in each of these cases? I know sometimes this is approximated as $m/\sigma_T$, but I'm not sure when to invoke this approximation, and what the respective mass would be.

electron-positron plasma Do you really mean an electron-proton plasma?

No, I meant electron-proton, so that's been fixed.

I think you mean that kappa = sigma / m.   The sigma is the "cross section," like the area you expose when you slice a watermelon in half.  The m is the mass of the particle that has the cross section in question (it's not literally the cross section of the physical particle, but an effective cross section for interaction with light), or more often, the mass of all the particles that come along with the cross section in question (often there is one particle contributing most of the cross section, but several particles that come with it which provide the mass).  For example, if you mix protons and electrons, the electrons have a larger cross section because their low mass makes them interact more easily with light, but that lower mass also means it is not the electrons, but the protons, that provide the "m" in the above formula.
So these quantities depend on the composition of the gas you have in mind.  It's easy for an electron-proton [edited] plasma, because if you don't worry about resonant interactions in the plasma, you can just consider the cross sections of the individual particles, and you get "Thomson opacity" of 0.4 square centimeters per gram (that's sigma/m for the sigma of an electron and the m of a proton, rounded to one significant figure because nothing is ever really a pure electron-proton plasma).  Purely ionized helium is also easy, because if you again ignore any resonant interactions between the electrons and the nuclei, it's just the same Thomson opacity except reduced by the extra neutrons [edited] in the heavy helium nuclei.  Since there is one neutron per proton, that reduces 0.4 by factor of 2, yielding 0.2.  [edited for forgetting that the 0.4 already includes the protons.]


text:
What is "g-98" in plots of stellar spectra?
I was looking to find some example carbon star spectra and came across this page on the Harvard website which shows several plots of carbon star spectra. The horizontal axis is labelled as wavelength in ångströms, but the vertical axis appears to be labelled with "g-98" which I am not familiar with - any idea what quantity this is?

This is a guess, but it could be the result of a text wrapping bug. The top line of each plot ends with "Mon [time] 03-Au", and if you append "g-98" to this, you have a date: August 3rd, 1998, which is presumably when the plots were generated.

@HDE226868 is right. These plot are made in IRAF, which writes the dates exactly there. If you google iraf spectrum, you'll find similar plots. The standard header is something like "NOAO/IRAF [version] [user-email] [date] [file name] [title]"

@pela - great, thanks. Put that as an answer and I'll accept it.

I think @HDE226868 deserves that credit :)

Links rot over time so I've captured an example plot so that future readers will be able to understand the question if the page is ever moved or deleted.

It looks like the floating "g-98" is just an extension of the header of the plot (made by IRAF), which has wrapped around the image for lack of room on the right-hand side. Looking at the N0 plot, we see that the header should read
NOAO/IRAF V2.10.4EXPORT perry@sparky.sao.arizona.edu Mon 06:04:51 03-Aug-98

which just contains information about the software, user and creation date behind the plot.
(Hat tip to Pela for confirming my guess!)


text:
How to find inverse steradian from $\text{arcmin}^{-2}$ for density of galaxy
I am using a code on EUCLID future mission.
The original author of this code has set a value for the density of galaxy equal to :
ng = 354543085.80106884

I think this is expressed in inverse steradian. I think that EUCLID mission has a $30\text{ arcmin}^{-2}$ value for density of galaxies.
Is the conversion correct betweeen $30\text{ arcmin}^{-2}$ and $354543085.8010688 \text{ sr}^{-1}$ ?
and how to do this conversion ?
Indeed, I would like to calculate ng with a density of $48 \text{ arcmin}^{-2}$.
Regards

There are 60 arc minutes in a degree and $180/ \pi$ degrees in a radian.
So 1 radian is 57.2957795 degrees or 3437.746771 arc minutes.
As long as you are talking about units, you can square any of these angular units to obtain solid angle units.
So 1 steradian is 3282.80635 square degrees, or 11818102.860 square arc minutes.
Let's try your theory:
1/354543085.801 steradians is 9.259259E-06 square degrees, or 0.0333333 square arc minutes.
The answer is that it is 1/30th of a square arc minute, so YES it is 30 inverse square arc minutes!
Then 48 per square arcminute is:
$$48 \times 60^2 \times \frac{180^2}{\pi^2} \approx 567268937.282 \ \ \text{sr}^{-1}.$$


text:
What does "negligible mass" mean in the formulation of geodesics equation?
Wikipedia says:

According to Einstein's theory of general relativity, particles of
  negligible mass travel along geodesics in the space-time.

Does that "negligible mass" only refer to particles or objects like a spacecraft, whose mass are literally negligible to that of a black hole, are also taken into account?
If the mass of a spacecraft is not negligible, how has one to modify the geodesics equation corresponding to that mass?

It really means photons, particles with no rest mass. Everything else might become questionable under some circumstances. E.g. neutrinos are very close to being massless, so they must move very close to geodesics, but in some rare cases pretty major deviations may happen.

@Florin But photons travel on null geodesics. I assume that Roboticist is also interested in timelike geodesics.

Yes its means that you ignore the effect that an object such as a spacecraft has on the central mass that it is orbiting, that the orbiting body has infinitely less mass.
Unfortunately, I think there is no exact solution found of the geodesics equations when that approximation is no longer valid or when you try to devolop geodesics equation for a spacecraft under the influence of two (or more) spherically symmetric mass distributions such as the combination of planets and the Sun in our solar system.
In the solar system JPL who calculates orbits of planets and other celestial objects use what is called the "post Newtonian expansion". You can look at their official documentation, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation, expression 4-26 on page 4-19. Some of the the terms may be zero if you only have two non-neglibly massive objects.
Note that this is not really a "geodesics equation" per se. Nasa/JPL uses what I believe is a first order expansion of the Schwarzshild solution in isotropic coordinate and then uses a scheme I do not quite follow to get to the relativistic acceleration terms of the post-Newtonian that they add to the classical Newtonian gravitational acceleration term to calculate the orbits.
I do not know if there is a simpler way to do it.

Thus, one may conclude that (if approximated solutions are fine) the geodesics equation can be used to study the motion of a hypothetical spacecraft around "only one" super massive object, right?

The Schwarzschild solution is only applicable to the case of an "infinitely lighter" object moving around a spherically symmetric mass distribution. When you have more than one spherically symmetric mass distributions you cannot simply add the contributions like in Newtonian gravitation.

@Roboticist The idea is that the "particles of negligible mass" is light enough that the curvature it causes in spacetime is tiny relative to the curvature caused by the body(s) it's orbiting. So you can pretend that it's moving in a static spacetime, which is a lot easier to calculate than one where the orbiting body is drastically modifying the curvature as it moves.

Something of a tautology. Objects of negligible mass have a mass that can be neglected. By definition.
To put it another way, if you have decided to not bother calculating in the mass of some object, because you have decided for whatever reason that it's small enough that it won't significantly affect the result of some calculation, then you would compute that that object travels along a geodesic.

while this is certainly a good first answer, it does not appear to answer the specifics of the question.


text:
Is there a term for asteroseismology as applied to giant planets?
Giant planets such as Jupiter have oscillations which enable analyses using the techniques of asteroseismology, for example Gaulme et al. (2011) detected global modes on Jupiter via radial velocity measurements. Is there a specific term for this technique as applied to giant planets instead of stars?

Is there a specific term for this technique (asteroseismology) as applied to giant planets instead of stars?

No it seems there is not.
Instead, people just use normal literal constructions.

arXiv: "Seismology of Giant Planets""
arXiv: "Jovian Seismology" and "giant planet seismology" or (your planet here) seismology in general
Space SE: "Planetary normal-mode seismology"

A good example of the Fourier imaging technique is SYMPA:

SYMPA, a dedicated instrument for Jovian seismology I. Principle and performance
SYMPA, a dedicated instrument for Jovian seismology
II. Real performance and first results

JOVIAL is next-gen implementation, also from Earth:

JOVIAL; Jovian Oscillations through radial Velocimetry ImAging observations at several Longitudes.
Jupiter’s interior: from gravimetry to seismology

note: after posting I realized that one of the linked papers is the same as in the OP"s question. I'll leave it here for completeness.

Yes. Although there is not much point looking for them on the surfaces of the giant planets, as those are too dynamic, unfortunately.
However, the rings of Saturn can give us some insight into internal oscillation modes, this area of research is then dubbed Kronoseismology.
According to my (very limited) view of the developments in this subfield of planetary science, results were coming in only slowly and with low accuracy.
But since Cassinis grand finale hit us, we have close up observations of moving density waves in the rings, together with high-precision orbital data, so it seems research is picking up speed in recent years.


text:
Could an Earth-like magnetic field protect life at exoplanet Proxima Centauri b?
I took a look at Wikipedia's page for Proxima Centauri b, the exoplanet that orbits Proxima Centauri, where it is said it is expected to receive 2000 times of stellar wind pressures than on Earth.
It does not say anything about Proxima b having a magnetic field, but I found this paper where a magnetic field for the planet is predicted:

In our simulations, most Proxima b analogues develop intrinsic dynamos
  that last for 4 Gyr (the estimated age of the host star). If alive,
  the dynamo of Proxima b have a dipole moment . These results are not
  restricted to Proxima b but they also apply to earth-like planets
  having similar observed properties.

My question is if an Earth-like magnetic field, if Proxima b has one, could protect life as it does on Earth, or, conversely, habitability could not be possible due to stellar wind.

Jorge I.Zuluaga, Sebastian Bustamante (2018): "Magnetic properties of Proxima Centauri b analogues". Planetary and Space Science.
Volume 152, March 2018, Pages 55-67

The problem here is "define life".  We've only one planet to go by and there's no reason to assume differently based life cannot develop in quite different conditions.  We can't even say that an atmosphere is a requirement for life.

Would this work better on the Worldbuilding Stack Exchange?

According to Garcia-Sage et al. (2017) "On the Magnetic Protection of the Atmosphere of Proxima Centauri b", who assume that Proxima b has a magnetic field strength identical to the Earth, the situation does not look promising:

With an O+ and H+ escape at 1600 km altitude of 4.2×109 cm−2 s−1 as found for thermospheric densities of 3×T,
  the total mass-loss rate is 4.3×105 g s−1 over the dayside
  hemisphere. Using a total atmospheric mass of 5×1018 kg
  (Trenberth & Smith 2005) results in a loss of the entire mass of
  the atmosphere over 365 million years.

(T is the thermosphere temperature of the Earth)
They go on to note that Proxima would have had higher EUV and X-ray emission in the past, which would have made things worse. Ongoing outgassing of volatiles might be possible to create habitable conditions but the resultant situation would be very different from the Earth.


text:
How Did Early Astronomers Measure Distances?
Prior to the era of radar and other forms of radio/RF/EM ranging, what approaches, methods, and techniques did early astronomers (e.g., Kepler, Cassini, Copernicus) use to measure the distance(s) from Earth to various objects (such as: Mars, Venus, Alpha Centauri, etc.)?
Is there an especially informative article (say, Scientific American, Sky) or book that explains their efforts and results (e.g., how accurate were their computations?)?

References and citations are warmly welcomed!

They were not very successful, but not for a want of trying.
The ancient greeks tried to measure the angle between the sun and the moon when the moon is half full. They got a value of 87 degrees, (when really it is 89.85). From this they could estimate the relative distances of the Moon and the sun.
Further observations of the moon from different locations on Earth could, in principle find the relative distance to the moon in terms of the radius of the Earth. And the radius of the Earth could be determined by noting the different lengths of shadows at the same time in different locations.
Several Greeks attempted to put these together to find the distance of the sun, and while their methods were geometrically correct, their observations were not accurate enough to achieve an accurate value for the distance of the sun. Typically they estimates were about 5% of the true distance. Attempts based on similar methods were made in other centres of astronomy, in China, India and the Middle East. They all tended to dramatically underestimate the distance.
Even after the invention of the telescope allowed the observations to be done more accurately the distance was usually under-estimated. only when careful measurements of the transit of Venus were made, was Jerome Lalande able to calculate the distance of Venus, and use Kepler's laws to derive the distance of the sun and other planets.
Kepler had created a model of the solar system that predicted the relative distances of each planet very successfully, but not the absolute distance
Nearly all other distances are based on the Earth-sun distance. The distances of the planets can be found using Kepler's laws. The actual distance of stars was unknown we were able to measure the slight change in position of a star as the Earth orbits the sun. If you know the distance to the sun you can calculate the distance to a star. Prior to the observation of this "stellar parallax" estimates of the distanct to stars was essentially guesses, and usually significant underestimates.
So prior to radar ranging, the methods were geometric, and based on a ladder of measurements. The size of the Earth was used to determine the distance to the moon and sun. Then the distance to the sun was used to find the distance to the stars.
For more distant stars there can be considerable uncertainty about the distance. If a star is too far to have parallax, then it's true distance will not be known to accuracy.


text:
What constraints are there on solid material in the ice giants?
Recently there has been experimental verification of superionic water ice (suggested to be called ice XVIII, not sure if this nomenclature is official yet), which turns out to be a solid (or at least, solid-ish). This has been proposed to comprise a substantial fraction of the volume of ice giant planets like Uranus and Neptune, which is something of a departure from the idea that the bulk of these planets is fluid, though potentially the presence of substances other than water may modify things.
My question is whether there are any observational constraints on the presence of solid material in Uranus and Neptune, e.g. from the gravitational moments, tidal parameters, or global oscillations ("seismology") - I'm aware that the K2 mission failed to detect any global oscillations on Neptune so I'd guess this latter method may not help much.
(There is a previous question about solids in gas giants, but that one seems to be more focused on rock rather than ice and has ended up addressing Jupiter rather than the ice giant planets.)

slightly related in Chemistry SE: What would superionic water ice look like?

NASA conducted a study on the Ice Giants in 2016 after recognition as a high-priority flagship mission target in the 2013-2022 Planetary Decadal Survey (overview of the Decadal Survey from The Planetary Society), a community document which helps set priorities and goals. The full report and summary are available from LPI's Ice Giants Mission Planning page and is intended to review the science and mission options leading into planning for the next decadal survey report. In the Science section starting on page 29, the introduction has a table of the major components of the different planet types (terrestrial, gas giant and ice giant) where ice giants are listed as ~10% gas, ~65% ice, ~25% rock with a total mass of ~15 times that of the Earth. This is in comparison to terrestrial planets which are almost 100% rock and gas giants which are ~85% gas. This is illustrated in the figure below taken from the report (their Figure 3-1):
In the lead-in to the subsections on the various science questions and subsections, the report goes on to say:

We  therefore  consider  the  objectives  of determining  the  interior  structure  of an ice  giant  (Section  3.1.1)  and  the  bulk  composition (including noble gases and key isotopic ratios, Section 3.1.2) as the highest-priority science to be done.

Section 3.1.1 on interior structure states that there is a presumption that these "ice giants" are dominated by water but there is very little direct evidence. It then explains that ice giants are normally modelled with three layers: an outer Hydrogen/Helium envelope, below that a thick fluid ionic water layer (or water mixed with other ices like ammonia and methane), and at the center, a small rocky core. However the limited amount of gravity field data from the Voyager 2 flybys showed that both planets are not as centrally condensed (less mass in the center) as expected in the simple 3 layer structure and also:

"there is no strong motivation, beyond computational convenience, for a 3-layer structure (Helled et al. 2010)." Link to Helled et al. 2010 journal article (free access)

Both Uranus and Neptune have bulk densities a little under compressed water, implying that there has to be Hydrogen/Helium (H/He) envelope and which is indeed seen in spectra of the visible surface. Below this envelope though little is known apparently. The low density and the limited gravity data would imply a mostly water interior with other gasses such as ammonia or more H/He to keep the density lower than water and a very small amount of rock in the core Nettelmann et al. 2013 (arXiv paper link). This model however predicts an ice:rock ratio of more than 10:1 which is not seen in any of the other icy moons and the model does not explain well the heat flux coming from the interior. This presentation by Nettelmann at a 2014 ice giants meetings talks more about these models, the constraints from the gravity data from Voyager 2 and the heat flux problems and shows possible internal structure diagrams.
The interior structure section of the Ice Giants report ends by calling for measurements of the higher order gravitational moments J2, J4 & J6 to higher precision, particularly for Neptune. However this is limited to the bulk structure and doesn't constrain the layering which would need a Doppler imager on a spacecraft to measure planetary oscillations analogous to solar helioseismology and/or an entry probe. The Doppler imager is discussed more in Sections 3.3.1 and 3.3.2 of the report which note that these new instruments have the potential to provide great information on the interior structure, but that Doppler imagers are technologically immature and that even with the largest telescopes on Earth or near-Earth spacecraft it has not been possible to see if the oscillations exist and the oscillation amplitude may be too small to detect. The report also notes such an instrument is also large, power hungry and produces a large data volume, all risks on a constrained mission to the outer planets but the benefits outweigh the risks. (Using up most of your mass and power budget on an instrument that may fail, or not produce a measurable result, makes people very nervous...)
In summary, there are some limited constraints on the bulk components of the ice giants but this is still a poorly constrained and understood problem which is a subject of ongoing research but is need of additional constraints and data from a dedicated mission. Such a mission would need to be flagship class which makes it expensive and would need broad support from the majority of the planetary community and would likely need to be the top-ranked mission from the next decadal survey covering the 2023-2032 timeframe to stand a chance of being funded and flying.

Planetary seismology on Jupiter at least works and is done from the ground. But I think you are suggesting that it's the case of Neptune that would require the largest telescopes on Earth or a flagship class space mission?

Report says: More  problematic is that while oscillations have likely been detected on Jupiter (Gaulme et al. 2011) and  Saturn  (Hedman  and  Nicholson  2013),  we  do  not  know  if  the  oscillation  amplitudes  on Uranus  or  Neptune  will  be  detectable,  and  their  excitation  mechanism  is  not  well-enough understood  to  even  make  an  accurate  prediction  from  what  we  see  on  the  gas  giants.  (pages 71-72)


text:
Question on dec 2013 answer to"How to measure the altitude and azimuth of a star?"
I am looking at your response to the above question.  You stated:

For Northern Hemisphere, a star that is crossing the North local meridian (that is, between the Zenith and the North Horizon) the latitude is 90−alt=dec−lat
For Northern Hemisphere, a star that is crossing the South local meridian (that is, between the Zenith and the South Horizon) the latitude is 90−alt=lat−dec.

I am simply not seeing this when I looked at image for the culimination of X in : http://star-www.st-and.ac.uk/~fv/webnotes/chapter4.htm" ???

Pleasee put a link to the question and answer that you refer to!

Or even better, write what you wrote here under the question that you refer to.

Mike G's answer pertained to a star that is at zenith (i.e., directly overhead), not just at culmination.


text:
How actively is Deep Learning being used in exoplanet identification?
Papers, like this one from Google, show that Deep Learning and Machine Learning are effective in detecting exoplanets from luminosity data provided by telescopes like TESS or Kepler.
These models seem extremely quick and lightweight. Has it become somewhat of a standard practice to use these on freshly obtained TESS data? If not, why, and what is done with the data instead? Are there drawbacks to using these seemingly accurate models?

Also called Astronet-K2, the deep learning A.I is efficient at spotting data that could find exo-planets, but that's were the issue is. That's all it is capable of doing, so it misses or ignores other potentially interesting data that human astronomers would classify as curious or odd, and could lead to other potentially new discoveries. It's missing the human factor, more or less. In both the source linked in the question and mine, it has only found 2 new exo-planets, so it doesn't look like is has free reign In the field. Even if the A.I is currently used automatically, it's work would be monitored and checked by humans.  My source material was from 2019, so if I missed a more recent accounting of the system that has different or upgraded methods, please let me know.
https://www.google.com/amp/s/www.technologyreview.com/2019/04/01/136239/deep-learning-has-found-two-exoplanets-that-human-astronomers-missed/amp/