# Motion in a circle

1. Apr 25, 2012

I was thinking about how planets revolve around sun. Although they subscribe a elliptical motion, my question is very similar.
A heavy body exerts a force on a point mass, say with an acceleration of "a". If we take the direction of this acceleration to be X, what is the linear uniform velocity with which it must travel in Y direction, so that the body travels in a perfect circle?..
Can we analyze this without taking any force into consideration, I mean the force exerted could be gravitational or magnetic, it doesn't matter. What matters is the acceleration "a", and the linear uniform velocity "u".

2. Apr 25, 2012

### pellman

If the motion of the point mass is such that its direction is perpendicular to the direction of the acceleration and its speed is $$v=\sqrt{ar}$$ where r is the distance between the heavy body and the point mass, then the point mass will describe a circle of radius r around the heavy body.

http://en.wikipedia.org/wiki/Circular_motion

If the force between the two bodies does not have a 1/r^2 dependency, then tiny deviations from circular motion may cause the orbit to be unstable.

3. Apr 25, 2012