Celestia Forums

I've been searching for an answer to this particular subject, but I've come up short.

I'm searching for a way to accurately calculate the orbital velocity of an object around its host star. Right now, most of my planets in my systems are either going too slow or too fast, and would obviously either escape the host star's gravity, or get pulled in by it.

Is there a solution to this - some sort of formula I could run the numbers through, or some sort of calculator I could use that would translate the output into numbers usable for an SSC file?

It's quite easy to calculate the period of a planet orbiting a given distance from a star. The formula is simple:

Period = MassOfStar * SemiMajorAxis ^ 1.5

The units are Earth years for the period, solar masses for the star, and AU for the semimajor axis. Once you know the orbital period, it's a simple matter to compute the mean orbital velocity, but you're probably only interested in the period for Celestia.

--Chris

You can derive the formula from 2 common physics formulas:

acceleration due to gravity
a = GM/r^2

and rotational acceleration
a = v^2/r

set them equal to eachother

GM/r^2 = v^2/r

after cancelling out one of the r's, and re-arranging to solve for v:

v = sqrt (GM/r)

v is your orbital velocity for a circular orbit expressed in meters/second, G is the gravitational constant (6.672e-11) M is the mass of the object being orbited in kg (Earth=5.97e24, Sun=1.98911e30) and r the distance of your satellite to the center of the object being orbited. If you want to solve for a particluar altitude instead of distance, make r the radius of the object being orbited and use

v=sqrt (GM/r+a) where a is your altitude in meters.