Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies $m_1\,$ and $m_2\,$ standard assumptions are usually the following:

A1: $m_1\,$ and $m_2\,$ are the only objects in the universe and thus influence of other objects is disregarded,
A2: The mass of the orbiting body ( $m_2\,$ ) is far smaller than central body ( $m_1\,$ ), i.e.:

${m_2\over{m_1}} \ll 1$

Results:

A3: As the disparities in masses between $m_1\,$ and $m_2\,$ are so great, standard gravitational parameter ( $\mu\,$ ) includes only the mass of the central body, in each case i.e.:

$\mu=G{m_1}\simeq{G}(m_1+m_2)$

A4: Orbit of orbiting body is not perturbed in any way and the effects of general relativity are so small that they can be ignored, so the only orbits allowed are the circular, elliptic, parabolic and hyperbolic orbits of classical Newtonian theory.
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,

[edit] 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 true. E.g. If a spacecraft were launched from the ground, achieving 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 rocket applying thrust
- An object experiencing atmospheric drag
A2: Orbital motion within a binary star system

If A2 is not fulfilled, many results still apply with a small modification; see the two-body problem in astrodynamics.