Asatellite moves in a stable circular orbit with speed vo at a distance r from the center of a planet. for this satellite to move in a stable circular orbit a distance 2r from the center of the planet, the speed of the satellite must be? ? i said that f=ma, but m doesn't matter since it's constant. so, a0=a1. a=v^2/r. so v1^2/2r = v0^2/r. i ended up with v1 = v0sqrt(2). but that's not the answer. all the multiple choice answers have sqrt's, 2's, and v0's scattered around, but none are what i have. what did i do wrong? ?

The new speed must be

Explanation:

In order for the satellite to be on a stable orbit around the planet, the gravitational attraction must be equal to the centripetal force that keeps the satellite in circular motion:

where G is the gravitational constant, M is the mass of the planet, m is the mass of the satellite, V0 the speed of the satellite at distance R from the center of the planet.

We can re-write V0, the initial satellite speed, by re-arranging the equation:

Now, if we want the satellite to orbit at a distance of 2R, the new tangential speed must be: