Algodoo

This is a very necessary yet obscure equation with a few applications in Orbital mechanics.
I had to derive an approximation myself since Google wouldn't understand
"how to calculate apoapsis given periapsis, the speed a satellite at said periapsis would be going to be in a circular orbit,
and the actual speed of the satellite at said periapsis"
(my function calculates this with the bonus that periapsis and apoapsis are interchangeable)

I knew such an equation was possible, so I (unintelligible nerd gibberish) and
arrived at the rough approximation of what the true function might be.

This can be useful for calculating the new apoapsis of a circular orbit given speed,
And it's inverse (right) is actually even more useful, because it can give you the speed needed to
get to a new apoapsis, which is useful for Hohmann transfers.

Nspeed is the starting speed, the speed of the satellite while it is in circular orbit.
Aspeed is the speed the satellite speeds up or slows down to.
peri is the point where the elliptical orbit and circular orbit meet, and the radius of the circular orbit.
apo is the point opposite the peri

To see where I derived them see: https://www.desmos.com/calculator/mlgj3bkfsg

Not sure if this made any sense... or if these functions work on the first edit... but thanks for reading bai