A spaceship orbits around a planet at a height of 20km from its...

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

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}

]

Options

A $17$
B $9$
C $13$
D $11$

Correct answer

D. $11$

Step-by-step solution

T = 2\pi\sqrt{\dfrac{{( R + h )}^{3}}{GM}} = 2\pi\sqrt{\dfrac{8.242 \times {10}^{18}}{6.67 \times {10}^{- 11} \times 8 \times {10}^{22}}}

T \approx 7809sec

Number of revolutions in 24 hours:

n = \dfrac{86400}{7809} = 11.06

\approx

11 revolutions

Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum ℓ is moving in a circular orbit of radius r_0… JEE Advanced 2026 A body of mass m is taken from the surface of earth to a height equal to twice the radius… JEE Main 2026 When one moves from a point 16 km below the earth's surface to a point 16 km above the… JEE Main 2026 The height in terms of radius of the earth (R) , at which the acceleration due to gravity… JEE Main 2026 If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and… JEE Main 2026 A planet (P_1) is moving around the star of mass 2M in the orbit of radius R . Another… JEE Main 2026 Three masses 200 ~kg, 300 ~kg and 400 kg are placed at the vertices of an equilateral… JEE Main 2026 Given below are two statements: Statement I : A satellite is moving around earth in the… JEE Main 2026 Full Gravitation list All JEE Main PYQs