NationMaster - Encyclopedia: Standard assumptions in astrodynamics

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

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

Results:

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

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

where $G\,$ 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,

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 rocket applying thrust
- in the case of atmospheric drag
A2: a binary star

Two bodies orbiting each other

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

standard: Definition, Synonyms and Much More from Answers.com (1418 words)
	The centimeter is defined in terms of the international meter, which is the primary standard of length and is defined as the length of path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.
	In similar fashion, the minute is a time interval defined as 60 s, where the second is the international standard of time and is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine energy levels of the ground state of the cesium-133 atom.
	A standard is set for the following three reasons: (1) to measure performance of a responsibility center; (2) to simplify recordkeeping; and (3) to improve performance by taking appropriate remedial action on an unfavorable deviation from the standard.

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Encyclopedia > Standard assumptions in astrodynamics

Examples where those assumptions do not hold

Two bodies orbiting each other

See also