Asked by Glen
If Earth's mass were smaller, how would Earth's gravity be affected?
Answers
Answered by
bobpursley
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.
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.
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