A Few More Formulae

Here are just a few little things I want to remember for later. This is as much for my own purposes as anyone else’s. Just thought I’d put it out there.

Solar Day

1/p’ = 1/p – 1/P

Where P is the period of revolution(that is, the year), p is the sidereal period of rotation for the planet(the sidereal day), and p’is the solar day(the time between sunsets).

Orbital Velocity

V=(2GM(1/r – 1/(2a)))1/2

Where r is the radius at the given point in the orbit, a is the semajor axis of the orbit, M is the mass of the primary, and G is the universal gravitational constant 6.672×10-11 N*m2*kg-2
At periapsis
V=(2 Pi a)/P ((1+e)/(1-e))1/2 

At apoapsis

V=(2 Pi a)/P ((1-e)/(1+e))1/2

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