escape velocity hard

Question

Escape velocity from a moon of half Earth's radius and quarter its mass is (Earth v_e = v):

RankGuru · Accepted Answer

We know $v_e = \sqrt{\frac{2GM}{R}}$, so $v_e \propto \sqrt{\frac{M}{R}}$.
Given:
- $M' = M/4$
- $R' = R/2$
Ratio $k = \sqrt{\frac{M/4}{R/2}} = \sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.
So, $v' = \frac{v}{\sqrt{2}}$.

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escape velocity hard

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