Planetary Motion Problem: On August 27, 2003, Mars was at its closest position to Earth

Chapter 4, Problem 13

(choose chapter or problem)

Planetary Motion Problem: On August 27, 2003, Mars was at its closest position to Earth. It then receded at an increasing rate (Figure 4-9k). In this problem you will analyze the rate at which the distance between the two planets changes. Assume that the orbits of the two planets are both circular and are both in the same plane. The radius of Earths orbit is 93 million mi and the radius of Mars orbit is 141 million mi. Assume also that the speed each planet moves along its orbit is constant. (This would be true if the orbits were exactly circular.) Mars orbits Figure 4-9k the Sun once each 687 Earth-days. The Earth, ofcourse, orbits once each 365 Earth-days. Answerthe following questions.a. What are the angular velocities of Earth andMars about the Sun in radians per day? Whatis their relative angular velocity? That is,what is d /dt?b. What is the period of the planets relativemotion? On what day and date were the twoplanets next at their closest position?c. Write an equation expressing the distance, D,between the planets as a function of .d. At what rate is D changing today? Convertyour answer to miles per hour.e. Will D be changing its fastest when theplanets are 90 degrees apart? If so, prove it.If not, find the angle at which D ischanging fastest. Convert the answer todegrees.f. Plot the graph of D versus time for at leasttwo periods of the planets relative motion.Is the graph a sinusoid?