Aim: How do we explain energy considerations in planetary and satellite motions?

Mechanical Energy in circular orbits E= -GMm/2r The total mechanical energy must be negative in circular orbits. The kinetic energy of an object in a circular orbit is equal to one-half the magnitude of the potential energy of the system. E=-GMm/2a (Elliptical orbits) where a is the length of the semi-major axis

Thought Question 1 A comet moves in an elliptical orbit around the Sun. Which point in its orbit represents the highest value of The speed of the comet At the perihelion which is the closest point to the Sun The potential energy of the comet-Sun system At the aphelion which is the farthest point from the Sub The kinetic energy of the comet At the perihelion which is the closest point to the Sun The total energy of the comet-Sun system The mechanical energy is the same everywhere

For All Orbits The total energy, the total angular momentum, and the linear momentum of a planet-star system are constants of the motion.

Problem 1 A satellite of 2000 kg is in an elliptical orbit about the Earth. When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2 x 107m and its orbital velocity is 7.1 x 103 m/s. (ME=6 x 1024 kg and RE =6.4 x 106 m) Determine the total mechanical energy of the satellite at point A. Determine the angular momentum of the satellite at point A. When the satellite reaches point B, which is the further point from the Earth, its orbital radius is 3.6 x 107 m, c) Determine the speed of the satellite at point B

Problem 1

Problem 2 A satellite of mass m moves in an elliptical orbit around Earth with r and R the closest and farthest distances from the center of Earth. An identical satellite moves in a circular orbit of radius r. The elliptical satellite has energy E=-GmM/6r. Respond to the following in terms of M, the mass of the Earth,m,r,and G. Determine the energy of the circular satellite. Determine the speed of the elliptical satellite at the closest approach distance. Derive an equation that would allow you to solve for R in terms of the given quantities (don’t attempt to solve).