space faq constants and equations archive name space constants last modified date constants and equations for calculations this list was originally compiled by dale greer additions would be appreciated numbers in parentheses are approximations that will serve for most blue skying purposes unix systems provide the units program useful in converting between different systems metric english etc numbers m s earth orbital velocity at km altitude m s earth orbital velocity at km geosync km mean radius of earth km equatorial radius of earth km mean radius of moon e kg e mass of earth e kg e mass of moon e kg e mass of sun e m s e gravitational constant times mass of earth e m s e gravitational constant times mass of moon e m s e gravitational constant times mass of sun km e mean earth moon distance e m e mean earth sun distance astronomical unit megaton mt tnt about e j or the energy equivalent of about kg gm of matter ref j r williams the energy level of things air force special weapons center ardc kirtland air force base new mexico also see the effects of nuclear weapons compiled by s glasstone and p j dolan published by the us department of defense obtain from the gpo equations where d is distance v is velocity a is acceleration t is time additional more specialized equations are available from ames arc nasa gov pub space faq moreequations for constant acceleration d d vt at v v at v ad acceleration on a cylinder space colony etc of radius r and rotation period t a pi r t for circular keplerian orbits where vc velocity of a circular orbit vesc escape velocity m total mass of orbiting and orbited bodies g gravitational constant defined below u g m can be measured much more accurately than g or m k g m a r radius of orbit measured from center of mass of system v orbital velocity p orbital period a semimajor axis of orbit vc sqrt m g r vesc sqrt m g r sqrt vc v u a p pi sqrt u a k v g m r conservation of energy the period of an eccentric orbit is the same as the period of a circular orbit with the same semi major axis change in velocity required for a plane change of angle phi in a circular orbit delta v sqrt gm r sin phi energy to put mass m into a circular orbit ignores rotational velocity which reduces the energy a bit gmm re rcirc re radius of the earth rcirc radius of the circular orbit classical rocket equation where dv change in velocity isp specific impulse of engine ve exhaust velocity x reaction mass m rocket mass excluding reaction mass g m s ve isp g dv ve ln m x m ve ln final mass initial mass relativistic rocket equation constant acceleration t unaccelerated c a sinh a t c d c a cosh a t c v c tanh a t c relativistic rocket with exhaust velocity ve and mass ratio mr at c ve c ln mr or t unaccelerated c a sinh ve c ln mr d c a cosh ve c ln mr v c tanh ve c ln mr converting from parallax to distance d in parsecs p in arc seconds d in astronomical units p miscellaneous f ma force is mass times acceleration w fd work energy is force times distance atmospheric density varies as exp mgz kt where z is altitude m is molecular weight in kg of air g is local acceleration of gravity t is temperature k is bolztmann s constant on earth up to km d d exp z e where d is density d is density at km is approximately true so d km ft d d km ft d d km ft d d km ft d atmospheric scale height dry lapse rate in km at emission level k km earth mars venus titan jupiter saturn uranus neptune triton titius bode law for approximating planetary distances r n n astronomical units n infinity for mercury for venus for earth etc this fits fairly well except for neptune constants e j s e planck s constant h e j s e planck s constant pi h bar e j k e boltzmann s constant k e w m k e stephan boltzmann constant sigma e n m kg e newton s gravitational constant g m k e wien s constant sigma w e w e luminosity of sun w m solar constant intensity at au e m e radius of sun km e radius of moon m s e speed of light in vacuum c e m e light year au e light years parsec e m e black hole radius also called schwarzschild radius gm c where g is newton s grav constant m is mass of bh c is speed of light things to add somebody look them up basic rocketry numbers equations aerodynamical stuff energy to put a pound into orbit or accelerate to interstellar velocities non circular cases next faq astronomical mnemonics
