Question:
The height of a geostationary satellite is
The height of a geostationary satellite is
Updated On: Aug 15, 2022
- 1000 km
- 32000 km
- 36000 km
- 850 km
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The Correct Option is C
Solution and Explanation
A satellite which revalues around the earth in its equatorial plane with the same angular speed and in the same direction as the earth rotates about its own axis is called a geostationary or synchronous satellite.
The height of a satellite above the earth's surface is given by
$h=\left(\frac{T^2R^2g}{4\pi^2}\right)^{1/3} -R$
But T = 24 h = 86400 s
R = radius of earth = 6400 km
$g=9.8 ms^{-2}=0.0098 kms^{-2}$
= $h=\left(\frac{(86400)^2\times(6400)^2\times0.0098}{4\times9.87}\right)^{1/3}$
d = 42330 - 6400 = 35930 km
= 36000 km
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].