A planet is growing by accretion of material from the solar nebula. Suppose that as it grows, its density remains constant. Does the force of gravity at its surface increase, decrease, or stay the same? Why?

Question

A planet is growing by accretion of material from the solar nebula. Suppose that as it grows, its density remains constant. Does the force of gravity at its surface increase, decrease, or stay the same? Why?

Also, What would happen to the surface gravity as the radius of the planet doubled? Why?

Answer 1

Consider the following:

Gravityfield=GMass/radius

but Mass= density*volume
= density*4/3 PI rad^3

so Gravity field = G*density*4/3 PI rad^3/radius or Gravityfield=constant*radius^2

So it looks like the gravity force increases.