8-17. A particle moves in an elliptical orbit in an inverse-square-law central-force field. If the ratio of the maximum angular velocity to the minimum angular velocity of the PROBLEMS 325 particle in its orbit is n, then show that the eccentricity of the orbit is Vn - 1 Vn + 1

8-17. A particle moves in an elliptical orbit in an inverse-square-law central-force field. If the ratio of the maximum angular velocity to the minimum angular velocity of the PROBLEMS 325 particle in its orbit is n, then show that the eccentricity of the orbit is Vn - 1 Vn + 1

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.17P

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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.

Question

8-17. A particle moves in an elliptical orbit in an inverse-square-law central-force field. If
the ratio of the maximum angular velocity to the minimum angular velocity of the
PROBLEMS
325
particle in its orbit is n, then show that the eccentricity of the orbit is
Vn-1
Vn +1

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