An object of mass m is released from rest a distance R above the surface of a planet of mass M and radius R. Calculate with which it hits the planet’s surface, v, in m/s, assuming M = 29 × 1026 kg and R = 25 × 102 km.

An object of mass m is released from rest a distance R above the surface of a planet of mass M and radius R. Calculate with which it hits the planet’s surface, v, in m/s, assuming M = 29 × 1026 kg and R = 25 × 102 km.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 4OQ

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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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An object of mass m is released from rest a distance R above the surface of a planet of mass M and radius R.

Calculate with which it hits the planet’s surface, v, in m/s, assuming M = 29 × 10²⁶ kg and R = 25 × 10² km.

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