PROBLEM 5 Given: The angular momentum of the Moon about the center of the Earth O is due almost entirely to its orbital motion; the average value for this is Lo ~ 2.89 x 103420 k using the axes shown. The gravitational force of the Sun, however, will cause this value to change as the Moon orbits the Earth. Note: at Location 1, the line from the Moon to the Sun would make an angle 0 = 0.146 with the x-axis. Find: a) At Location 1, what is the rate at which the magnitude of Lo is changing due to the Sun? b) At Location 2, what is the rate at which the magnitude of Lo is changing due to the Sun? c) A colleague tells you that the rate of change for the magnitude of Lo at Location 3 is simply the negative of the rate of change at Location 1. Is this true or false? Justify your answer. d) The same colleague tells you that the rate of change for the magnitude of Lo at Location 4 is equal to the rate of change at Location 2. Is this true or false? Justify your answer. e) Based on your results from parts a) - d), at which location would you expect the Moon have its largest angular velocity? Justify your answer. X - Moon Sun 2 O X Earth X W Universal gravitational constant: G = 6.67 x 10-11 m3 (kg. 52) Mass of the Earth: 5.972 x 1024 kg Mass of the Moon: 7.348 x 1022 kg Mass of the Sun: 1.989 x 1030 kg Radius of the Earth: 6.371 x 105 m Radius of the Moon: 1.737 x 105 m Radius of the Sun: 6.963 x 105 m Distance from Sun to Earth (center-to-center): 1.506 x 1013 m Distance from Earth to Moon (center-to-center): 3.844 x 108