Satellite A of mass m orbits a planet of mass M at a distance of R from the center of the planet. The speed of the satellite is v. Answer in terms of m, M, R and v.

Question

(a) What is the speed of a satellite B whose mass is 2 m? The distance from the center of the planet to the satellite B is R and the mass of the planet is M. (The answer is v I just don't know how to get there)

Answer 1

Drawing a picture, I get something like this:

Drawing a free body diagram on the satellite I get this:

where the only force is the force of gravity pulling it toward the planet. We can write an equation for the force of gravity using Newton's law of universal gravitation F = GMm/R²

We can also write an equation that equates the centripetal force with the velocity F = mv²/R

These two things must be the same because there is only one force in the free body diagram, so:

GMm/R² = mv²/R

canceling "m" and one "R" on both sides, we get:

GM/R = v²

Solving for v by taking the square root of both sides we get: