Question

If Earth's mass were smaller, how would Earth's gravity be affected?

Answer 1

with the same radius? gravity would be reduced.

An interesting question, is what if Earth had a smaller radius, but with the same density.

F=GMe/re^2

but Me=density*4/3 PI re^3

so as r changes, M(r)=Me(r/re)^3

F=GMe/r^2 * (r/re)^3 = GMe/re^2 (r/re)

which means the gravity is the fraction (r/re) of the new Earth's size.