A satellite of mass m is orbiting Earth in a stable circular orbit of radius R. The mass and radius of Earth are ME and RE , respectively. The satellite is replaced with a similar satellite that has twice the mass. The new satellite is placed into the same orbit as the original satellite. Is the new satellite’s orbital speed greater than, less than, or equal to the original satellite’s orbital speed?  Why? The original satellite can be placed in many different circular orbits of radius r. On the axes, sketch a graph of the mechanical energy E of the satellite-Earth system as a function of the orbital radius r. (attached as photo1)

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Q: m il- R

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A: Fc = mv2/r  GMm/(Re+h)2 = mv2/(Re+h)

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.