Collection of formulas and equations

[EarthMoon]

I have reconfigured the equation to calculate orbital periods (which are provided below in case someone else needs them too) and thought about a collection of formulas and equations about astronomy by providing common text representations (or Python assuming a user did from math import *, so instead of writing math.sqrt(x) write sqrt(x)) of the formulas/equations and (optionally) normal renderings (like below). It would also be good to provide reconfigured formulas for all variables.

An example (which directly counts to the collection):

Calculate the orbital period (in years), mass of central object (suns) or semi-major axis (AU) from the other two values:

Code: Select all

p = sqrt(a**3 / m)
a = cbrt(sqrt(p) * m)
m = a**3 / p**2


p is the orbital period in (Earth) years
a is the semi-major axis in AU
m is the central body's mass in sun masses

How the formulas look like in normal notation:

form_orbit.png (8.92 KiB) Viewed 6566 times

[EarthMoon]

Here are more formulas, this time about calculating periapsis & apoapsis distance, semi-major axis and eccentricity of an orbit.

a = SMA
e = Eccentricity
q = Periapsis
Q = Apoapsis

Code: Select all

e = (Q - q) / (Q + q)
a = (Q + q) / 2
q = a * (1 - e)
Q = a * (1 + e)


orb_ecc.png (4.41 KiB) Viewed 6510 times