A satellite is revolving around a planet in a circular orbit close to its surface. Let $ρ$ be mean density and $R$ be the radius of the planet; then the period of the satellite is
( $G$ = Universal constant of gravitation).

Question

TestHub · Accepted Answer

The time period of a satellite revolving close to the surface of a planet is given by $T = 2 π \frac{R ^{3}}{GM}$ .

The mass of the planet can be expressed in terms of its mean density $ρ$ and radius $R$ as $M = \frac{4}{3} π R^{3} ρ$ .

Substituting the value of $M$ in the expression for $T$ :

$T = 2 π \frac{R ^{3}}{G ( \frac{4}{3} π R ^{3} ρ )}$

$T = 2 π \frac{3}{4 π Gρ}$

$T = \frac{4 π ^{2} \times 3}{4 π Gρ}$

$T = \frac{3 π}{ρG}$

Answer: $\frac{3 π}{ρG}$

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