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 $G=6.67\times 10^{-11}$ $N{m}^2/k{g}^2$]

Answer 1

Answer: 11

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
$T=2\pi \sqrt{\frac{{\left(202\right)}^3\times 10^{12}}{6.67\times 10^{-11}\times 8\times 10^{22}}}$ sec
$T=7812.2s$
$T\simeq 2.17hr$
$\Rightarrow 11$ revolutions