Small Body Orbiting A Central Body
Under standard assumptions in astrodynamics we have:
where m is the mass of the orbiting body, M is the mass of the central body, and G is the gravitational constant.
For all circular orbits around a given central body:
where r is the orbit radius, v is the orbital speed, ω is the angular speed, and T is the orbital period.
The last equality has a very simple generalization to elliptic orbits:
where a is the semi-major axis. See Kepler's third law.
For all parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits μ = 2a|ε|, where ε is the specific orbital energy.
Read more about this topic: Standard Gravitational Parameter
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As Eastern Summers are,
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Add light to some small Star.”
—Sir William Davenant (1606–1668)
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