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Archive-name: space/constants |
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Last-modified: $Date: 93/04/01 14:39:04 $ |
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This list was originally compiled by Dale Greer. Additions would be |
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appreciated. |
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Numbers in parentheses are approximations that will serve for most |
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blue-skying purposes. |
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Unix systems provide the 'units' program, useful in converting |
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between different systems (metric/English, etc.) |
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7726 m/s (8000) -- Earth orbital velocity at 300 km altitude |
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3075 m/s (3000) -- Earth orbital velocity at 35786 km (geosync) |
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6371 km (6400) -- Mean radius of Earth |
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6378 km (6400) -- Equatorial radius of Earth |
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1738 km (1700) -- Mean radius of Moon |
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5.974e24 kg (6e24) -- Mass of Earth |
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7.348e22 kg (7e22) -- Mass of Moon |
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1.989e30 kg (2e30) -- Mass of Sun |
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3.986e14 m^3/s^2 (4e14) -- Gravitational constant times mass of Earth |
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4.903e12 m^3/s^2 (5e12) -- Gravitational constant times mass of Moon |
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1.327e20 m^3/s^2 (13e19) -- Gravitational constant times mass of Sun |
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384401 km ( 4e5) -- Mean Earth-Moon distance |
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1.496e11 m (15e10) -- Mean Earth-Sun distance (Astronomical Unit) |
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1 megaton (MT) TNT = about 4.2e15 J or the energy equivalent of |
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about .05 kg (50 gm) of matter. Ref: J.R Williams, "The Energy Level |
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of Things", Air Force Special Weapons Center (ARDC), Kirtland Air |
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Force Base, New Mexico, 1963. Also see "The Effects of Nuclear |
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Weapons", compiled by S. Glasstone and P.J. Dolan, published by the |
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US Department of Defense (obtain from the GPO). |
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Where d is distance, v is velocity, a is acceleration, t is time. |
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Additional more specialized equations are available from: |
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ames.arc.nasa.gov:pub/SPACE/FAQ/MoreEquations |
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For constant acceleration |
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d = d0 + vt + .5at^2 |
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v = v0 + at |
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v^2 = 2ad |
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Acceleration on a cylinder (space colony, etc.) of radius r and |
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rotation period t: |
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a = 4 pi**2 r / t^2 |
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For circular Keplerian orbits where: |
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Vc = velocity of a circular orbit |
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Vesc = escape velocity |
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M = Total mass of orbiting and orbited bodies |
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G = Gravitational constant (defined below) |
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u = G * M (can be measured much more accurately than G or M) |
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K = -G * M / 2 / a |
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r = radius of orbit (measured from center of mass of system) |
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V = orbital velocity |
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P = orbital period |
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a = semimajor axis of orbit |
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Vesc = sqrt(2 * M * G / r) = sqrt(2) * Vc |
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V^2 = u/a |
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P = 2 pi/(Sqrt(u/a^3)) |
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K = 1/2 V**2 - G * M / r (conservation of energy) |
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The period of an eccentric orbit is the same as the period |
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of a circular orbit with the same semi-major axis. |
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Change in velocity required for a plane change of angle phi in a |
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circular orbit: |
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delta V = 2 sqrt(GM/r) sin (phi/2) |
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Energy to put mass m into a circular orbit (ignores rotational |
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velocity, which reduces the energy a bit). |
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GMm (1/Re - 1/2Rcirc) |
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Re = radius of the earth |
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Rcirc = radius of the circular orbit. |
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Classical rocket equation, where |
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dv = change in velocity |
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Isp = specific impulse of engine |
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Ve = exhaust velocity |
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x = reaction mass |
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m1 = rocket mass excluding reaction mass |
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Ve = Isp * g |
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dv = Ve * ln((m1 + x) / m1) |
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= Ve * ln((final mass) / (initial mass)) |
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Relativistic rocket equation (constant acceleration) |
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t (unaccelerated) = c/a * sinh(a*t/c) |
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d = c**2/a * (cosh(a*t/c) - 1) |
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v = c * tanh(a*t/c) |
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Relativistic rocket with exhaust velocity Ve and mass ratio MR: |
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at/c = Ve/c * ln(MR), or |
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t (unaccelerated) = c/a * sinh(Ve/c * ln(MR)) |
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d = c**2/a * (cosh(Ve/C * ln(MR)) - 1) |
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v = c * tanh(Ve/C * ln(MR)) |
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Converting from parallax to distance: |
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d (in parsecs) = 1 / p (in arc seconds) |
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d (in astronomical units) = 206265 / p |
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Miscellaneous |
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f=ma -- Force is mass times acceleration |
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w=fd -- Work (energy) is force times distance |
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Atmospheric density varies as exp(-mgz/kT) where z is altitude, m is |
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molecular weight in kg of air, g is local acceleration of gravity, T |
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is temperature, k is Bolztmann's constant. On Earth up to 100 km, |
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d = d0*exp(-z*1.42e-4) |
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where d is density, d0 is density at 0km, is approximately true, so |
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Atmospheric scale height Dry lapse rate |
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(in km at emission level) (K/km) |
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Earth 7.5 9.8 |
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Mars 11 4.4 |
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Venus 4.9 10.5 |
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Titan 18 1.3 |
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Jupiter 19 2.0 |
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Saturn 37 0.7 |
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Uranus 24 0.7 |
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Neptune 21 0.8 |
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Triton 8 1 |
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Titius-Bode Law for approximating planetary distances: |
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R(n) = 0.4 + 0.3 * 2^N Astronomical Units (N = -infinity for |
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Mercury, 0 for Venus, 1 for Earth, etc.) |
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This fits fairly well except for Neptune. |
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6.62618e-34 J-s (7e-34) -- Planck's Constant "h" |
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1.054589e-34 J-s (1e-34) -- Planck's Constant / (2 * PI), "h bar" |
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1.3807e-23 J/K (1.4e-23) - Boltzmann's Constant "k" |
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5.6697e-8 W/m^2/K (6e-8) -- Stephan-Boltzmann Constant "sigma" |
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6.673e-11 N m^2/kg^2 (7e-11) -- Newton's Gravitational Constant "G" |
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0.0029 m K (3e-3) -- Wien's Constant "sigma(W)" |
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3.827e26 W (4e26) -- Luminosity of Sun |
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1370 W / m^2 (1400) -- Solar Constant (intensity at 1 AU) |
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6.96e8 m (7e8) -- radius of Sun |
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1738 km (2e3) -- radius of Moon |
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299792458 m/s (3e8) -- speed of light in vacuum "c" |
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9.46053e15 m (1e16) -- light year |
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206264.806 AU (2e5) -- \ |
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3.2616 light years (3) -- --> parsec |
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3.0856e16 m (3e16) -- / |
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Black Hole radius (also called Schwarzschild Radius): |
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2GM/c^2, where G is Newton's Grav Constant, M is mass of BH, |
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c is speed of light |
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Things to add (somebody look them up!) |
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Basic rocketry numbers & equations |
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Aerodynamical stuff |
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Energy to put a pound into orbit or accelerate to interstellar |
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velocities. |
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Non-circular cases? |
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NEXT: FAQ #7/15 - Astronomical Mnemonics |
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