A satellite revolving around a planet in stationary orbit has time… | JEE Main 2024 (5 Apr, Shift 2)

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Satellites - Orbital Velocity & Period

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius of orbit of the satellite is:

(Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 10^{4}\text{ km}$ )

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Answer: (d)

$T^2 = \frac{4\pi^2 r^3}{GM} \Rightarrow r^3 \propto MT^2$
$\frac{r^3}{r_e^3} = \frac{M_p}{M_e}\left(\frac{T_p}{T_e}\right)^2 = \frac{1}{4}\times\left(\frac{6}{24}\right)^2 = \frac{1}{64}$
$r = \frac{r_e}{4} = \frac{4.2\times10^4}{4} = 1.05\times10^4$ km
So the answer is (d).

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Satellites - Orbital Velocity & Period question from JEE Main 2024 (5 Apr, Shift 2)

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