What is the acceleration due to gravity on the surface of a planet that has twice the mass of the Earth and half its radius?
The mass increases linearly but radius decreases exponentially, so the result is
Let's first look at the equation for the force of gravity:
which is often simplified for working with objects on the surface of the Earth (since we know the gravitational constant and the mass of the Earth) to
where M is the mass experiencing Earth's gravity.
So what happens when we double the mass of the Earth and reduce its radius to 1/2? Let's multiply
then make the substitutions:
So the numerator increases linearly (
The force of gravity on Earth is roughly