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b. The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value on A?

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g=\(GM\over R^2\)

\(M=\tfrac{gR^2}{G}\) 

Acording to the given data , \(\tfrac{gB}{gA}=\tfrac{1}{2}\)

and \(\tfrac{{R_B}}{R_A}=2\) 

yes

\(\tfrac{M_B}{M_A}=\tfrac{g_B}{g_A}( \tfrac {R_B}{R_A})^2\)

\(\tfrac{M_B}{M_A}=\tfrac{1}{2}2^2\)

\(M_B=2M_A\)

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