A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is ℎp=223.0 km,hp=223.0 km, and it is moving with a speed of ?p=8.150 km/s.vp=8.150 km/s. The gravitational constant ?G equals 6.67×10−11 m3·kg−1·s−26.67×10−11 m3·kg−1·s−2 and the mass of Earth equals 5.972×1024 kg.5.972×1024 kg. When the satellite reaches its apogee, at its farthest point from the Earth, what is its height ℎaha above the ground? For this problem, choose gravitational potential energy of the satellite to be 00 at an infinite distance from Earth.

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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.