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Acceleration due to gravity

A satellite revolves with time period T in a circular orbit of

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A satellite revolves with time period $T$ in a circular orbit of radius $R_{2}$ around a planet of radius $R_{1}$ . Then

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IIT JEE Super Course in Physics Mechanics II (Pearson)

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A satellite revolves with time period

T

in a circular orbit of radius

R_{2}

around a planet of radius

R_{1}

. Then

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

E = - K . E = \frac{P \cdot E}{2} = - \frac{GMm}{2 R _{2}} K . E = \frac{GMm}{2 R _{2}}

Kinetic energy to from surface

= \frac{GM m}{R _{1}}

Ratio

= \frac{R _{1}}{2 R _{2}} \leq \frac{1}{2} (∵ R_{2} \geq R_{1})

∴

Velocity ratio

\leq \frac{1}{2}

T = \frac{2 π}{GM} \cdot R_{2}^{3/2} \Rightarrow GM = gR_{1}^{2} = \frac{4 π ^{2}}{T ^{2}} \cdot R_{2}^{3}

g = \frac{4 π ^{2}}{T ^{2}} \cdot \frac{R _{2} ^{3}}{R _{1} ^{2}}

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Question Text	A satellite revolves with time period $T$ in a circular orbit of radius $R_{2}$ around a planet of radius $R_{1}$ . Then
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	127

A satellite revolves with time period $T$ in a circular orbit of radius $R_{2}$ around a planet of radius $R_{1}$ . Then

Text solutionVerified

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