Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies m1 and m2 standard assumptions are usually the following:
*A1: m1 and m2 are the only objects in the universe and thus influence of other objects is disregarded,
*A2: the mass of the orbiting body (m2) is far smaller than the central body (m1), (m1 >> m2)
*A3: the effects of general relativity are so small that they can be ignored.
Consequences of these assumptions are:
*C1: because of A1, the orbit of orbiting body is not perturbed in any way.
*C2: because of A1, the only orbits possible are the circular, elliptic, parabolic and hyperbolic orbits of classical Newtonian theory.
*C3: because of A2, the standard gravitational parameter of the system can be approximated to
::<math>\mu=G \left(m_1 + m_2 \right) \simeq G m_1</math>
where G is the gravitational constant.
*C4: because of A2 the center of the central body is the center of mass of the system and can be taken as the origin of an inertial frame of reference for the orbiting body; no distinction is needed between the position of the smaller body in an inertial frame of reference and its position relative to the other body; either way one of the foci of the orbiting body's orbit coincides with the center of the central body.
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 with velocity tending to zero, for most cases this will not be true. E.g. If a spacecraft were launched from the ground, achieving escape velocity with respect to Earth, it will not leave the Solar System because that requires a higher escape velocity.
*A rocket applying thrust
*An object experiencing atmospheric drag
;A2
* Orbital motion within a binary star system
Two bodies orbiting each other
Even just the combination of A1 and A3 keeps the problem relatively simple. If the other assumptions are not fulfilled, many results still apply with a small modification; see gravitational two-body problem.

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