Home > Standard assumptions in astrodynamics

• A1: and are the only objects in the universe and thus influence of other objects is disregarded,
• A2: The orbiting body () is far smaller than central body (), i.e.:

Results:

• A3: As the result of disparities in masses between and standard gravitational parameter () includes only the mass of the central body, i.e.:

where is a gravitational constant.

• A4: Orbit of orbiting body is not perturbed in any way, so the only orbits allowed are circular, elliptic, parabolic or hyperbolic.
• A5: One focus of orbiting body's orbit coincides with the center of the central body,

The center of the central body can be taken as the origin of an inertial frame of reference for the orbiting body,

1 Examples where those assumptions do not hold

• A1: although escape velocity is described as a velocity that should allow an orbiting body to coast to infinity and arrive there with zero velocity for most cases this will not be. E.g. even if the spacecraft is launched with escape velocity with respect to Earth it will not escape to infinity (e.g. leave the Solar system) because it will eventually succumb to the gravitational influence of the Sun.

• a binary starA binary star system consists of two stars both orbiting around their barycenter. The term "binary star" was apparently first coined by Sir William Herschel in 1802 to designate "a real double star the union of two stars that are formed together in one sy

2 Two bodies orbiting each other

If A2 is not fulfilled, many results still apply with a small modification, see the two-body problem in astrodynamicsIn mechanics, the two-body problem is a special case of the n-body problem that admits a closed form solution. The most commonly encountered version of the problem, involving an inverse square law force, is encountered in celestial mechanics and the Bohr.

3 See also

• n-body problemThe n body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. Newton's laws of motion and Newton's law of gravity. Mathematical formulation