Question 187: Gravitation

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 × 10
22
kg, Radius of planet = 2 × 10
6
m, Gravitational constant
G = 6.67 × 10
–11
Nm
2
/kg
2
]

Accepted Answer

$${{m{V^2}} \over r} = {{GMm} \over {{r^2}}}$$
$$V = \sqrt {{{GM} \over r}} $$
$$n = {{VT} \over {2\pi r}} = \sqrt {{{GM} \over r}} {T \over {2\pi r}}$$
$$ = \left( {\sqrt {{{GM} \over {{r^3}}}} } ight) 	imes {T \over {2\pi }} = \sqrt {{{6.67 	imes {{10}^{ - 11}} 	imes 8 	imes {{10}^{22}}} \over {{{\left( {202 	imes {{10}^4}} ight)}^3}}}}  	imes {T \over {2\pi }}$$
$$ = {{24 	imes 3600} \over {2 	imes 3.14}}\sqrt {{{6.67 	imes 8 	imes {{10}^{11}}} \over {{{\left( {202} ight)}^3} 	imes {{10}^{12}}}}} $$
$$ = {{24 	imes 3600} \over {2 	imes 3.14 	imes 1242.8}} = {{24 	imes 3600} \over {74.51}} = 11$$

Answer

13

Answer

9

Answer

17

Answer

11

Gravitation

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