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Question

A science-fiction author asks for your help. He wants to write about a newly discovered spherically symmetric planet that has the same average density as the earth but with a 25% larger radius. What is g on this planet?

Solution

VerifiedAnswered 8 months ago

Answered 8 months ago

Step 1

1 of 3(b) If the explorers need to weigh the same, than the constant $g'$ must be equal to $g$.

Mass of the new planet must now be different and densities and masses of the both planets are:

$\begin{aligned} &\rho_e=\dfrac{M_e}{V_e}\\ &M_e=\rho_e \cdot \dfrac{4 \pi r^3}{3}\\ &\rho_p=\dfrac{M_e}{V_e}\\ &M'_p=\rho_p \cdot \dfrac{4 \pi \cdot1.95 \cdot r^3}{3}\\ \end{aligned}$

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