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An artificial satellite of earth is launched in circular orbit in equatorial plane of the earth and satellites moving from west to east. With respect to a person on the equator, the satellite is completing one round trip in 24 hrs. Mass of earth is $M = 6 \times 10^{24} kg$ . For this situation orbital radius of satellite is

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2 .66 \times 10^{4} km

6400 km

3600 km

29,600 km

answer is A.

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Detailed Solution

Here time period of satellite w.r.to observer on equator 24 hrs and satellite is moving from west to east, so west of satellite with respect to earth axis of rotation

$ω = \frac{2 π}{T_{S}} + \frac{2 π}{T_{E}}$

$ω = \frac{2 π}{24} + \frac{2 π}{24} = \frac{2 π}{12} = \frac{π}{6} = 1.45 \times 10^{- 4} rad/s$

$r^{3/2} = \frac{\sqrt{GM}}{ω}$

Substitution we get $r = 2.66 \times 10^{7} m$

$= 2.66 \times 10^{4} km$

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