Why do planets move faster around a sun with a larger mass?

F - for simplification - we assume the orbits are circular (which they approximately are), we have a centrifugal force of m v2 R m v2 R, where m is the mass of the planet, v its speed, and R the distance from the (center of the) sun. This force must be equal to the centripetal force, which comes from the sun's attraction, and it is mG M R2 mG M R2. Here, M is the mass of the sun, and G is a constant. We don't care about the actual numbers, so we write C be the product MG and observe that it is a constant independent of the orbit. These forces have to cancel out, so we have v2 R=C R - 2 v2 R=C R - 2, or v2 = C R - 3 v2 = C R - 3, so we have that the speed is proportional to R - 3 2 R - 3 2. Which means that if you decrease the distance to the sun, the speed goes up.