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User:Pt/Formulae

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If a planet's perihelion is and aphelion , then the orbit's eccentricity is:

The longer semi-axis:

And the shorter semi-axis:

The total length of the orbit:

(because the equation of the ellipse is and ; is the complete elliptic integral of the second kind, EllipticE in Mathematica)

Mean orbital speed ( is the planet's orbital period):

If a planet has a satellite at distance with orbital period , then the planet's mass is:

Or, written another way:

The escape velocity from a planet with radius and mass :

Its average density:

Gravitational acceleration on the surface: