A new asteroid is discovered in a circular orbit or radius 41/3 AU about the Sun,4 Its period of revolution is precisely 2 years. Assume that at t = 0 it is at its distance of closest approach to the Earth. rt
(a) Find its coordinates [x(t), y(t)] in a frame of reference fixed to Earth but whose axes remain fixed in orientation relative to the Sun. Assume that the x-axis points toward tire asteroid at t = 0.
(b) Calculate tire velocity of the asteroid, relative to Earth, at t = 0.
(c) Find the x- and y-components of the acceleration of the asteroid in dais frame of reference. Integrate them twice to show that tire resulting positions as a function of time agree with part (a).
(d) Plot the trajectory of the asteroid as seen from die rotating frame of reference attached to Earth for its 2-year orbital period. (Hint: Use Mathematica’s ParametricPlot graphing tool.)
4The radius of the Earths nearly circular orbit is 1 AU, or 1 astronomical unit. Both die Earth and the asteroid revolve counterclockwise in a common plane about the Sun as seen from the north pole star, Polaris.
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