Question

A spaceship orbits around a planet at a height of $20$ km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in $24$ hours around the planet ? [Given : Mass of Planet$ = 8 \times 10^{22}$ kg, Radius of planet $ = 2 \times 10^{6}$ m, Gravitational constant $G = 6.67\times 10^{-11}$ $Nm^{2}/kg^{2}$]

Answer 1

Time period of revolution of satellite,
$T = \frac{2\pi r}{v}$
$v =\sqrt{\frac{GM}{r}}$
$\therefore T = 2\pi r \sqrt{\frac{r}{GM}} =2\pi\sqrt{\frac{r^{3}}{GM}}$
Substituting the values, we get
$T = 2\pi\sqrt{\frac{\left(202\right)^{3} \times10^{12}}{6.67 \times10^{-11} \times8 \times10^{22}}}$ sec
$T = 7812.2s$
$T\simeq 2.17hr$
$\Rightarrow 11$ revolutions