Question

points A newly discovered planet is in a circular orbit around a distant star with an orbital period of 400 Earth days. The planet also rotates on its axis, making one full rotation every 4.00 Earth days. The radius of the planet is rp = 7.00 × 106 m and the radius of the planet's orbit about the star is r 7.00×1011 m. My Notes Ask Your Tea Determine the ratio of the radial acceleration, due to the rotation of the planet, of an object at the equator of the planet (acp) to the radial acceleration of the planet in its orbit about the star (ac) Submit Assignment Save As t Prograss Home My Assignments Extension Request 0 卩@囮컸豳鄂包dave E201

Answer 1

a_cp, Radial acceleration of planet due to rotation of the planet Time period, T_cp = 2 pi r_p/v_p v_p = 2 pi r_p/T_cp = 2 pi times 7 times 10^6/4 m/days therefore a_cp = v^2_p/r_p = (2 pi times 7 times 10^6/4)^2 times 1/(7 times 10^6) a_cp = 4 pi^2 times 7 times 10^6/16 m/a a_cs, the radial acceleration of the planer in its orbit about the star. T_cs = 2 pi r_s/v_p = > v_s = 2 pi r_s/T_cs = 2 pi times 7 times 10^11/400 m/days Now a_cs = v^2_s/r_s = 4 pi^2 times 7 times 10^11/160000 m/day^2 therefore from (1) and (2) a_cp/a_cs = 4 pi^2 times 7 times 10^6/16 times 160000/4 pi^2 times 7 times 10^11 = 1/10 = 0.1 therefore a_cp/a_cs = 0.1