The moon completes one revolution around the earth in $27$ days in an orbit of radius $3.8\times {10}^5\mathrm{km}.$ The earth completes one revolution around the sun in $365$ days in an orbit of radius $1.5\times {10}^8\mathrm{km}.$ Compare the masses of the sun and the earth.

Taking moon's period of revolution around the earth as $30 \mathrm{days}$  (and neglecting the effect of sun and other planets on its motions)' Calculate its distance $\mathrm{r}$ from the earth. $(\mathrm{G}=6.67\times {10}^{-11}{\mathrm{Nm}}^2{\mathrm{kg}}^{-2},$ mass of earth $\mathrm{Me}=6\times {10}^{21}\mathrm{kg}.)$

With what velocity must a body be thrown from earth's surface so that it may reach a height $4{\mathrm{R}}_{\mathrm{e}}$ above the earth's surface?(Radius of the earth ${\mathrm{R}}_{\mathrm{e}}=6400\mathrm{km},\mathrm{and} \mathrm{g}=9.8{\mathrm{ms}}^{-2}$)