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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)
$$T_p=6$$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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