Question

An astronaut on moon measure acceleration due to gravity to be $1.7m{s}^{-2}$. He knows that the radius of moon is about $0.27$ times that of earth. what is his estimate of the ratio of the mass of earth to the of moon ? The acceleration due to gravity on earth is $9.8m{s}^{-2}$.

Answer 1

$G{m}_e=g_e{R}_e^2$............(1)
$G{m}_m=g_m{R}_m^2$.........(2)
$\frac{m_e}{m_m}=\left(\frac{g_e}{g_m}\right)\times {\left(\frac{R_e}{R_m}\right)}^2$
$\frac{9.8}{1.7}\times {\left(\frac{R_e}{-27\times R_e}\right)}^2$
$\frac{m_e}{m_m}=\frac{9.0}{1.7}\times \frac{1}{-27\times 0.27}$
$\frac{m_e}{m_m}=79$