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: