A comet orbits the sun (mass m_S) in an elliptical orbit of semi-major axis a and eccentricity e What is the kinetic energy of the comet at perihelion and aphelion in terms of its speeds at these points and its mass mm? (Express your answers in terms of the variables v_a, v_p, and m) What is the potential energy of the comet at perihelion and aphelion in terms of the sun–comet distances at these points, its mass m, and the mass of the sun m_S? (Express your answers in terms of the variables r_a, r_p, m, m_S and gravitational constant G) Derive expressions for the magnitudes of angular momenta with respect to the sun at perihelion and aphelion in terms of comets speeds and the sun–comet distances at these points. (Express your answers in terms of the variables v_a, v_p, r_a, r_p, and m separated by a comma)

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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.