Question

Calculate the height of the communication satellite. [Given G = 6.67 x 10⁻¹¹ Nm² /kg² , M = 6 x 10²⁴ kg, R = 6400 km]
(Ans : 35.9 x 10⁶m)

Answer 1

Answer:

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Answer 2

Height of the communication satellite is $\bold {35.9\times 10^6}$ m

Explanation:

Given,

Gravitation constant, G = $6.67\times 10^{-11}$

Radius of earth , $R_E$ = 6400 km

$R_E$ = $6.4\times 10^{6}$ m

Mass of earth M =$6\times 10^{24}$ kg

Geosynchronous means that the satellite has same period as the earth, back to the same place in 24 hours.

T = 24 hrs = 86400 s

We know that,

$h = \left( \frac{G\times M_E}{4\times\pi^2}\times T^2 \right)^{\frac{1}{3}} - R_E$

$h = \left( \frac{ 6.67\times 10^{-11}\times 6\times 10^{24}}{4\times 3.14^2}\times 86400^2 \right)^{\frac{1}{3}} - 6.4\times 10^{6}$

$h = 35.9\times 10^6$ m

Height of the communication satellite is $\bold {35.9\times 10^6}$ m