The escape velocity of an object from the earth depends upon the mass of the earth $(M)$, its mean density $(\rho )$, its radius $(R)$ and the gravitational constant $(G)$. Thus the formula for escape velocity is
The escape velocity of an object from the earth depends upon the mass of the earth $(M)$, its mean density $(\rho )$, its radius $(R)$ and the gravitational constant $(G)$. Thus the formula for escape velocity is
$v = R\sqrt {\frac{{8\pi }}{3}G\rho } $
$v = M\sqrt {\frac{{8\pi }}{3}GR} $
$v = \sqrt {2GMR} $
$v = \sqrt {\frac{{2GM}}{{{R^2}}}} $
The escape velocity of an object from the earth depends upon the mass of the earth $(M)$, its mean density $(\rho )$, its radius $(R)$ and the gravitational constant $(G)$. Thus the formula for escape velocity is
$\frac{-G M m}{R}+\frac{1}{2} m v^{2}=0$
$v=\sqrt{\frac{2 G M}{R}}$
$M=e \times \frac{4}{3} \pi R^{3}$
$v=\sqrt{\frac{2 G}{R} \times e \times \frac{4}{3} \pi R^{3}}$
$v=R \sqrt{\frac{8}{3} G \rho}$
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