${v_e}$ and ${v_p}$ denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then
${v_e}$ and ${v_p}$ denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then
${v_e} = {v_p}$
${v_e} = {v_p}/2$
${v_e} = 2{v_p}$
${v_e} = {v_p}/4$
${v_e}$ and ${v_p}$ denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then
${v_e} = \sqrt {\frac{{2GM}}{R}} = R\sqrt {\frac{8}{3}\pi G\rho } $
If mean density is constant then ${v_e} \propto R$
$\frac{{{v_e}}}{{{v_p}}} = \frac{{{R_e}}}{{{R_p}}} = \frac{1}{2}$ $⇒$ ${v_e} = \frac{{{v_p}}}{{\rm{2}}}$
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