Mars has a mass of 6.417*1023 kg, a radius of 3390 km, and a rotation period of 24.62 hours. (a) Calculate the acceleration due to gravity on the surface of Mars. (b) What is the period of a simple pendulum of length 1.000 meters on the surface of Mars? (c) What is the radius of a Mars-synchronous orbit? (d) What is the speed of a satellite in a Mars-synchronous orbit? (e) What launch speed from Mars’s surface is required to get a satellite into Mars-synchronous orbit? You may neglect air resistance and any rotation effects at the Martian surface in your analysis. The universal gravitational constant is G = 6.674*10-11 N m2 kg-2

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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.