A spaceship orbits around a planet at a height of $20 k m$ 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 $= 8 \times 10^{22} k g$ ,
Radius of planet $= 2 \times 10^{6} m,$
Gravitational constant $G = 6.67 \times 10^{- 11} N m^{2} / k g^{2}$ ]

Question

A spaceship orbits around a planet at a height of

20 k m

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} k g

,
Radius of planet

= 2 \times 10^{6} m,

Gravitational constant

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

]

Aicharya · Accepted Answer

T = 2 π ( R + h ) 3 G M = 2 π 8.242 × 10 18 6.67 × 10 - 11 × 8 × 10 22 T ≈ 7809 s e c Number of revolutions in 24 hours: n = 86400 7809 = 11.06 ≈ 11 revolutions

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