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 × 10⁴ km)
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Question

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 × 10⁴ km)

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G1 Physics · Accepted Answer

For a satellite: T = 2πr³ᐟ²/√(GM) Therefore: T ∝ r³ᐟ²/√M Using: T₁/T₂ = 6/24 M₁/M₂ = 1/4 r₂ = 4.2 × 10⁴ km we obtain: r₁ = 1.05 × 10⁴ km