What are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4 * 105 J per orbital revolution. Adopting the reasonable approximation that the satellite’s orbit becomes a “circle of slowly diminishing radius,” determine the satellite’s (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f ) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth’s center conserved for (g) the satellite and (h) the satellite–Earth system (assuming that system is isolated)?

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A: Given, REarth=3980 milesdSatellite=900 milesT=6 hrs

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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.