Given $G=6.67\times10^{-11}\ \text{N\,m}^2\text{/kg}^2$, planet mass $M=6.4169\times10^{23}$ kg and radius $R=3390$ km, find the escape velocity (km/s). (round off to one decimal place)
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Solution and Explanation
Step 1: Formula.
\[
v_e=\sqrt{\frac{2GM}{R}}.
\]
Step 2: Substitute (SI).
\[
R=3390\times10^3\ \text{m},\
v_e=\sqrt{\frac{2(6.67\times10^{-11})(6.4169\times10^{23})}{3390\times10^3}}
=5025\ \text{m/s}\approx 5.03\ \text{km/s}.
\]
\[
\boxed{5.0\ \text{km/s}}
\]
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