Earth. Mars system A simplified model assumes that the
Chapter 10, Problem 109(choose chapter or problem)
Earth. Mars system A simplified model assumes that the orbits of Earth and Mars are circular with radii of 2 and 3, respectively, and that Earth completes one orbit in one year while Mars takes two years. When t = 0, Earth is at 12, 02 and Mars is at 13, 02; both orbit the Sun (at 10, 02) in the counterclockwise direction. The position of Mars relative to Earth is given by the parametric equations x = 13 - 4 cos pt2 cos pt + 2, y = 13 - 4 cos pt2 sin pt. a. Graph the parametric equations, for 0 t 2. b. Letting r = 13 - 4 cos pt2, explain why the path of Mars relative to Earth is a limaon (Exercise 89). 11
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