Question

A spaceship orbits around a planet at a height of $20km$ 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 $24hours$ around the planet ?
[Given : Mass of planet = $8\times 10^{22}kg$;
Radius of planet = $2\times 10^{6}m$,
Gravitational constant $G=6.67\times 10^{-11}N{m}^2/k{g}^2$]

• A. 9
• B. 11
• C. 13
• D. 17

Answer 1

Answer: (B)

$F_g=\frac{m{v}^2}{r}$
$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$
$V=\sqrt{\frac{GM}{r}}=\sqrt{\frac{\left(6.67\times 10^{-11}\right)\left(8\times 10^{22}\right)}{2.02\times 10^6}}$
$V=1.625\times 10^3$
$T=\frac{2\pi r}{V}$
$n\times T=24\times 60\times 60$
$n\left[\frac{2\pi \left(2.02\times 10^6\right)}{1.625\times 10^3}\right]=24\times 3600$
$n=\frac{24\times 3600\times 1.625\times 10^3}{2\pi \left(2.02\times 10^6\right)}$
$n=11$