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57.8: Corrections to the Two-Body Calculation

Last updated

Aug 8, 2024
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- 57.7: The Inverse Problem
- 57.9: Bound and Unbound Orbits

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We've described here the basics of a two-body orbit calculation, but there are a number of corrections that would need to be made to make a more accurate calculation; for example:

The reference frames are actually not fixed, but move in time because of motions of the Earth. A more careful calculation would take these effects (precession and nutation of the Earth) into account.
The orbital elements change with time - notably the longitude of the ascending node $\Omega$ and the argument of pericenter $\omega$ .
Other bodies are always present - not just the planet and the Sun. More complex calculations take the effect of other bodies into account.
Parallax corrections: the position of the body in the sky varies slightly depending on the position of the observer on the surface of the Earth.
Atmospheric refraction can cause small changes in the apparent position of the body in the sky.

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