The equation 4x2 T = gives Kepler's third law in a form suitable for objects orbiting the Sun. To modify it to a form suitable for objects in the Earth's orbit, we replace the mass of the Sun with the mass of the Earth to obtain the following expression for the period T of the satellite, where G is the constant of universal gravitation, M, is the mass of the Earth, and r is the radius of the satellite's orbit that we found above. T2 = GME Solving for the period of the satellite, we have T = GMĘ 4x2 x 106 m) (6.67 x 10-11 N - m2/kg2)(1 k9 - m/s5.98 x 1024 kg) 1 N x 103 s. Converting from seconds to hours, we find that the period of the satellite is 1h T: x 103 h. 3600 A satellite is in a circular orbit around the Earth at an altitude of 3.29 x 10° m. (b) Find the speed of the satellite.

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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.