If the mass of a satellite orbiting the earth were to increase, what would happen to that satellite?
Increasing the mass of a satellite would have very little effect as long as it isn't too massive.
When a satellite orbits the Earth what actually happens is that the satellite and the Earth orbit around their centre of mass. As satellites have a very small mass compared to the Earth, the mass of the satellite can effective;y be ignored when calculating the orbit.
Only is the satellite has a mass which is significant compared to the Earth would the effect be noticed. As the Moon has a significant mass compared to the Earth, the Earth and Moon both orbit about their centre of mass which is called the Earth-Moon barycentre. It lies about 1,600km below the Earth's surface.