# Acceleration due to gravity

If the acceleration due to gravity changed to 9.9 m/s2, what possibly could have happened to the mass of Earth (Me) and/or the radius of Earth (re)?

My answer is that the mass and radius would increase?

## Answers and Replies

Filip Larsen
Gold Member
Think about how the law of gravitation relates surface acceleration with surface radius and planet mass. If you were to increase the surface radius of the earth without changing its mass would surface gravity then increase or decrease?

It would decrease?

Filip Larsen
Gold Member
Indeed. If you still are in doubt if your first answer was (fully) correct, then try look at the equation and think about what you have to do to the mass (but with constant radius) to increase the surface gravity, and likewise what you have to do to the radius (but with constant mass) for the same to happen again. You may also think about if it is possible to achieve the higher level of surface gravity if both mass and radius had increased or if both had decreased at the same time. After all that the answer to the original question would then simply be a list of all the combinations of increase, constant and decrease of mass and radius that allow a higher surface acceleration to be achieved.