Two planets have same acceleration due to gravity, but diferent escape speeds..

timer Asked: Dec 9th, 2018

Question description

Two planets, P1 and P2, have the same acceleration due to gravity at their surfaces but, P1 has twice the escape speed of P2. From this, you would conclude:

a. P1 has double the mass of P2

b. P1 has four times the mass of P2

c. P1 has twice the radius of P2

d. P1 has half the radius of P2

e. P1 has four times the radius of P2

So I know the answer is e. by trial and error and plugging in the possible answers to v=sqrt(2GM/r), while not altering g=GM/r^2, but how could I solve this if if was not multiple choice? I could quickly find that 2v = sqrt(4*2GM/r), but how would I end up with 2v = sqrt(16*2GM/4r)?

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