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Question Number 11987 by tawa last updated on 08/Apr/17

$$\mathrm{The}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{moon}\mathrm{is}\frac{1}{4},\mathrm{and}\mathrm{its}\mathrm{mass}\mathrm{is}\frac{1}{81}\mathrm{that}\mathrm{of}\mathrm{the}\mathrm{earth}.\mathrm{If}\mathrm{the}$$$$\mathrm{acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity}\mathrm{on}\mathrm{the}\mathrm{surface}\mathrm{of}\mathrm{the}\mathrm{earth}\mathrm{is}9.8\mathrm{m}/{\mathrm{s}}^2.\mathrm{What}$$$$\mathrm{is}\mathrm{its}\mathrm{value}\mathrm{on}\mathrm{the}{\mathrm{moon}}^{\prime }\mathrm{s}\mathrm{surface}.$$

Answered by ajfour last updated on 09/Apr/17

$$g_e=\frac{{GM}_e}{R_e^2};g_m=\frac{{GM}_m}{R_m^2}$$$$g_m=g_e\left(\frac{M_m}{M_e}\right){\left(\frac{R_e}{R_m}\right)}^2$$$$g_m=(9.8m/s^2)\left(\frac{1}{81}\right)\left(16\right)$$$$=1.9358m/s^2.$$

Commented by tawa last updated on 09/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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