Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationSatellite MotionEasy2 minPYQ_2020

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A satellite is revolving in a circular orbit at a height $h$ from the earth's surface, such that $h ≪ R$ where $R$ is the radius of the earth. Assuming that the effect of the earth's atmosphere can be neglected. What should be the minimum change required in the speed so that the satellite could escape from the gravitational field of earth?

Options:

Answer:

Solution:

Orbital velocity $v_{0} = \sqrt{\frac{G M}{(R + h)}}$

Velocity required to escape the gravitational field, $v_{s} = \sqrt{\frac{2 G M}{(R + h)}}$

Change in velocity $= \sqrt{\frac{2 GM}{(R + h)}} - \sqrt{\frac{GM}{(R + h)}}$

If $h < < R$ ,
$Δ v = \sqrt{\frac{2 G M}{R}} - \sqrt{\frac{G M}{R}}$
$Δ v = \sqrt{2 g R} - \sqrt{g R}$

Subject:PhysicsTopic:GravitationSubtopic:Satellite Motion

⏱ 2mℹ️ Source: PYQ_2020

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