The maximum distance from the Earth to the Sun (at aphelion) is 1.521 × 1011 m, and the distance of closest approach (at perihelion) is 1.471 × 1011 m. The Earth’s orbital speed at perihelion is 3.027 × 104 m/s. Determine (a) the Earth’s orbital speed at aphelion and the kinetic and potential energies of the Earth–Sun system (b) at perihelion and (c) at aphelion. (d) Is the total energy of the system constant? Explain. Ignore the effect of the Moon and other planets.

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A: Please see the answer in step 2

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A: Solution

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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.