A satellite of mass m is stationed on the surface of Earth (mass M, radius R). Neglecting Earth's rotation, show that the energy E(h) needed to launch the satellite into a circular orbit at altitude h above Earth's surface is given by GMm (R+2h) 2R(R+h) E(h)

A satellite of mass m is stationed on the surface of Earth (mass M, radius R). Neglecting Earth's rotation, show that the energy E(h) needed to launch the satellite into a circular orbit at altitude h above Earth's surface is given by GMm (R+2h) 2R(R+h) E(h)

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter13: Universal Gravitation

Section: Chapter Questions

Problem 13.39P

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Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

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Problem 4
A satellite of mass m is stationed on the surface of Earth (mass M, radius R). Neglecting Earth's
rotation, show that the energy E(h) needed to launch the satellite into a circular orbit at altitude
h above Earth's surface is given by
GMm (R+ 2h)
E(h)
2R(R+ h)
Hint: Neglecting Earth's rotation implies that you can neglect the kinetic energy of the satellite due
to the Earth's rotation while the satellite is stationed on Earth.

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