So after the recent White House response about Death Stars (well only one) we were talking in the office about how powerful it would need to be to destroy Jupiter (obviously just the power of one Death Star to destroy Earth, right?) and also, if a puny laser won’t work against Jupiter, what effect would deflecting our moon into Jupiter have?
Ah, an easy one.
On the one hand we have the Death Star. The Death Star blows up Alderaan without breaking a sweat, vaporising most of the planet’s mass and giving the rest a decent whack of kinetic energy. One of the weird things about impact physics is that it tends not to draw much distinction between something you just manage to disrupt and something you destroy so completely there’s little of the target body left, but Alderaan is an outcome very much towards the latter end of the scale. If we assume that Alderaan is analogous to one Earth (it certainly seems to be in the film) then we can say that the Death Star is more than capable of disrupting planets even larger than the Earth, and that one Earth is merely the lower bound of its destructive power.
On the other hand we have Jupiter. Jupiter is the big boy of the solar system; it might be slaved to the Sun but otherwise it runs the show, gravitationally speaking. The orbits of nearly every other body in the solar system are highly sensitive to their resonances with Jupiter, which has 318 times the mass of the Earth. Since gravity is the primary factor in determining how hard a particular body is to disrupt, this makes Jupiter the very definition of a hard target if you’re trying to blow the thing up.
You may recognise this graph because I’ve used it roughly half a dozen times before; it’s a computer model of how an object’s critical energy density (read: the amount of energy you have to hit it with to blow it up) varies with object size. Note that despite being composed of two vastly different materials – ice and basalt – the models are practically identical past object diameters greater than 1 kilometre, meaning that it doesn’t matter what your target body is made of. It can be a rocky terrestrial planet like the Earth/Alderaan, or it can be a big gas giant like Jupiter; all that matters is how much mass is contained within the target, and hence how strong it is gravitationally.
Now, let’s extrapolate that model out to Earth- and Jupiter-scale bodies.
Sorry for the rather rough Excel graph; if I had any other graphing software that wasn’t Origin I’d use that instead. This model has several caveats: in the absence of any other data I’ve used information for the 5 km/s impacts onto basalt, and while I do not think the overall density of the body will have an effect on how hard it is to disrupt the same can’t be said for impact velocity. Jupiter in particular is at the bottom of an extremely deep gravity well, and so any body colliding with it is going to have quite a hefty impact speed – the Shoemaker-Levy comet fragments hit at velocities of around 60 km/s, for example. Faster, more energetic impacts are actually slightly less effective at disrupting a target than slower ones thanks to the way cracks propagate through a solid medium, so I doubt using data for 5 km/s basalt is going to be particularly accurate, but it should at least allow us to ballpark the critical energy densities of the Earth and Jupiter.
Some numbers. The critical energy density required to disrupt the Earth is 1.18 × 108 J kg-1. The critical energy density required to disrupt Jupiter is some 26 times larger at 3.06 × 109 J kg-1. Our two scenarios are a) firing the Moon at either body and trying to disrupt them that way, and b) hitting them with an unspecified number of Death Stars.
Scenario a) is easy1 to figure out; you just calculate the impact energy of the Moon given its likely impact velocity and then divide it by the mass of the target.
This is what we’d have to do to destroy each body, then: fire the Moon at the Earth at a rather nippy 138 km/s, and fire it at Jupiter at around four percent of the speed of light. These impact speeds are rather unlikely, to say the least; comets can hit the Earth at velocities of up to 70 km/s but those come all the way in from the Oort cloud and have a lot of time to pick up speed. Something as large as the Moon would get nowhere near those velocities; it would do serious damage to the Earth (and somewhat less to Jupiter) but each planet would eventually recover after a few million years or so.
Then you have the Death Star scenario. This is even easier; if we assume that one Death Star can destroy 2 Earths (as established in the opening paragraph) then it would take the power of 4,000 Death Stars to destroy Jupiter. As far has hard numbers go, one Death Star has a destructive power roughly equivalent to 300,000,000,000,000,000 one megaton nuclear weapons focused into a coherent beam.
Isn’t it great what we can achieve with science?
- He said, as it took him forty minutes to get his measurement units properly sorted out. Don’t do science when you’re tired and running a fever. ↩
"Kama ilivyoelezwa katika taarifa ya White House kuhusu nyota moja ya kifo, ""Tunazungumza katika ofisi kuhusu jinsi nguvu itakavyohitajiwa kuharibu Jupita, kwa kweli nguvu ya nyota moja ya kifo kuharibu Dunia.""" na pia, kama laser ndogo haitafanya kazi dhidi ya Jupita, ni athari gani itakayokuwa na kupotosha mwezi wetu ndani ya Jupita? Ah, moja rahisi. Kwa upande mmoja tuna Nyota ya Kifo. Nyota ya Kifo huvunja Alderaan bila kuvunja jasho, kuharibu sehemu kubwa ya wingi wa sayari na kutoa wengine pigo nzuri ya nishati ya kinetic. Moja ya mambo ya ajabu kuhusu athari fizikia ni kwamba inaelekea si kuchora tofauti sana kati ya kitu wewe tu kusimamia kuvuruga na kitu wewe kuharibu hivyo kabisa kuna kidogo ya mwili lengo kushoto, lakini Alderaan ni matokeo sana kuelekea mwisho wa mwisho wa kiwango. Ikiwa Alderaan ni sawa na Dunia moja (inaonekana kuwa katika filamu), basi tunaweza kusema kwamba Nyota ya Kifo ina uwezo wa kuvuruga sayari kubwa kuliko Dunia, na kwamba Dunia moja ni tu kikomo cha chini cha nguvu yake ya uharibifu. Kwa upande mwingine tuna Jupita. Jupita ni mtoto mkubwa wa mfumo wa jua; inaweza kuwa mtumwa wa Jua lakini vinginevyo inaendesha show, gravitationally akizungumza. Mzunguko wa karibu kila mwili mwingine katika mfumo wa jua ni nyeti sana kwa resonances yao na Jupita, ambayo ina 318 mara ya uzito wa Dunia. Kwa kuwa mvuto ni sababu kuu katika kuamua jinsi vigumu mwili maalum ni kuvuruga, hii inafanya Jupita ufafanuzi sana wa lengo ngumu kama wewe ni kujaribu kulipua kitu juu. Unaweza kutambua grafu hii kwa sababu nimeitumia karibu nusu ya mara kumi na mbili kabla; ni mfano wa kompyuta ya jinsi wiani wa nishati muhimu ya kitu (soma: kiasi cha nishati unahitaji kumpiga ili kuipiga) inatofautiana na ukubwa wa kitu. "Ili kuweza kuonekana kama ""mchanganyiko wa vitu viwili tofauti sana"" - barafu na basalt - mifano ni sawa kabisa, na kwa hivyo, haijalishi mwili wako umefanywa na nini." Inaweza kuwa sayari ya ardhi kama Dunia au Alderaan, au inaweza kuwa kubwa gesi kubwa kama Jupita, wote kwamba mambo ni kiasi gani cha wingi ni ndani ya lengo, na hivyo jinsi nguvu ni gravitationally. Sasa, hebu tuchukue mfano huo kwa miili ya ukubwa wa Dunia na Jupita. Samahani kwa ajili ya grafu badala mbaya Excel; kama nilikuwa na programu nyingine yoyote ya grafu kwamba hakuwa Asili ningeweza kutumia kwamba badala yake. "Mfano huu una caveats kadhaa: katika kukosekana kwa data nyingine yoyote mimi kutumika habari kwa ajili ya 5 km s athari juu ya basalt, na wakati mimi si kufikiri jumla wiani wa mwili itakuwa na athari juu ya jinsi vigumu ni kuvuruga, sawa haiwezi kusemwa kwa ajili ya kasi ya athari. """ Jupita ni sehemu ya chini ya shimo la nguvu ya uvutano, na kwa hivyo mwili wowote unaogongana nayo utakuwa na kasi kubwa ya athari - vipande vya kometi ya Shoemaker-Levy viligonga kwa kasi ya karibu kilomita 60 kwa sekunde. "Mashambulizi ya haraka zaidi na yenye nguvu zaidi ni ya ufanisi kidogo katika kuvuruga lengo kuliko wale wa polepole, shukrani kwa njia ambayo nyufa zinaenea kupitia njia thabiti, kwa hivyo nina shaka kutumia data kwa basalt ya 5km s itakuwa sahihi sana, lakini inapaswa angalau kuturuhusu ""kuzunguka"" wiani muhimu wa nishati ya Dunia na Jupita." Nambari fulani. Kiasi cha nishati muhimu kinachohitajika kuvuruga Dunia ni 1.18 × 108 J kg. Kiasi cha nishati muhimu kinachohitajika kuvuruga Jupita ni karibu mara 26 kubwa kwa 3.06 × 109 J kg-1. "Mfano wa kwanza ni ""kufyatua mwezi kwa kila mwili na kujaribu kuvuruga yao kwa njia hiyo, na b" Hali ya a) ni rahisi kugundua; unahesabu tu nishati ya athari ya Mwezi kutokana na kasi yake ya uwezekano wa athari na kisha kuigawanya kwa wingi wa lengo. "Kama vile tunavyojua, ""Mwezi"" huelekea Dunia kwa kasi ya karibu kilomita 138 kwa sekunde na ""Jupiter"" kwa kasi ya karibu asilimia nne ya mwanga." "Kama ilivyoelezwa hapo juu, ""mbele ya mwendo wa dunia, kometi inaweza kugonga dunia kwa kasi ya hadi 70 km s, lakini hizo huja kutoka kwa wingu la Oort na zina muda mwingi wa kuongeza kasi.""" Kitu kikubwa kama Mwezi hakingeweza kufikia kasi hizo; ingefanya uharibifu mkubwa kwa Dunia (na kidogo kwa Jupita) lakini kila sayari hatimaye ingepata baada ya miaka milioni chache au zaidi. Kisha kuna hali ya Nyota ya Kifo. Hii ni rahisi zaidi; ikiwa tunadhani kwamba nyota moja ya kifo inaweza kuharibu dunia mbili (kama ilivyowekwa katika kifungu cha ufunguzi), basi itachukua nguvu ya nyota 4,000 za kifo kuharibu Jupita. Kwa mujibu wa takwimu, nyota moja ya kifo ina nguvu ya uharibifu sawa na 300,000,000,000,000,000 ya silaha za nyuklia za megaton moja zilizowekwa katika mhimili wa mhimili. Je, si jambo zuri sana kile tunachoweza kufikia kwa kutumia sayansi? - Alisema, kama ilichukua yake dakika arobaini kupata vitengo vya kipimo yake vizuri sorted nje. Usifanye sayansi unapokuwa uchovu na kuwa na homa. 