Question 6

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

Solution

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$T_p=6$h, $M_p=M_E/4$. For geostationary orbit: $T²\propto r³/M$.

$r_p³=\frac{M_p}{M_E}\cdot\frac{T_p²}{T_E²}\cdot r_E³=\frac{1}{4}\cdot\frac{36}{576}\cdot r_E³=\frac{1}{4}\cdot\frac{1}{16}\cdot r_E³=\frac{r_E³}{64}$.

$r_p=r_E/4=4.2\times10^4/4=1.05\times10^4$ km.

The answer is Option (2): $1.05\times10^4$ km.

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