Answer to Question #89915 in Mechanics | Relativity for alica

Question

The acceleration due to gravity on Earth is about 10 m/s^2. Find the acceleration due to gravity on the moon. (MMoon=7.35*10^22kg, RMoon = 1.74*10^6m).

Answer 1

The acceleration due to gravity

$$g=G\frac{M}{R^2}$$

So

$$g_{\rm{Moon}}=g_{\rm{Earth}}\frac{M_{\rm{Moon}}}{M_{\rm{Earth}}}\times\frac{R_{\rm{Earth}}^2}{R_{\rm{Moon}}^2}$$

$$g_{\rm{Moon}}=10\times\frac{7.35\times 10^{22}}{5.97\times 10^{24}}\times\frac{(6.37\times10^6)^2}{(1.74\times10^6)^2}$$

$$=1.65\:\rm{m/s^2}$$