User:Pt/Formulae
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< User:Pt
[edit] Celestial mechanics
If a planet's perihelion is q and aphelion Q, 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 
; E is the complete elliptic integral of the second kind, EllipticE in Mathematica)
Mean orbital speed (P is the planet's orbital period):
If a planet has a satellite at distance rs with orbital period Ps, then the planet's mass is:
Or, written another way:
The escape velocity from a planet with radius R and mass M:
Its average density:
Gravitational acceleration on the surface:
