Answer to Question #283014 in Mechanics | Relativity for Gamer

Question #283014

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

1
Expert's answer
2021-12-27T07:55:43-0500

v=gR=GMR=GρVR=Gρ43πR3R=R43πρG,v=\sqrt{gR}=\sqrt{\frac{GM}R}=\sqrt{\frac{G\rho V}R}=\sqrt{\frac{G\rho \frac 43 \pi R^3}R}=R\sqrt{\frac 43\pi \rho G,}

vR,v\sim R,

v2=4v1.v_2=4v_1.


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