# Calculating the velocity planets need to have to be in circular orbit around a star

I'm toying with the idea of making a little 2D space orbiter game so I've implemented Newton's universal gravity law into this little app. It works really well, even.

The problem I'm having is when I want to create an asteroid-belt. I spawn little asteroids randomly around an area around the sun and give them a starting velocity vector v that is based on their position relative to the sun. Then I rotate v 90 degrees by multiplying with a transformation matrix.

After that I'm just guessing basically. Though I have tried many different ideas based on some calculations. At the moment I multiply v by r^-2 (where r is the distance to the center of the sun) but that sure isn't it. Help?

Related Linear and Abstract Algebra News on Phys.org
phyzguy

An object is in circular orbit when its centripetal acceleration is equal to the gravitational acceleration:
$$\frac{v^2}{r} = \frac{G M}{r^2}$$
solving for v:
$$v = \sqrt{\frac{G M}{r}}$$

Hah! It works!
Now the problem turned out to be that my vectors were rotated incorrectly, but your answer helped me realize what wasn't wrong so thank you very much!

Here's a li'l pic of it at the moment:
http://img814.imageshack.us/img814/3983/gasim.png" [Broken]

Last edited by a moderator: