6.51. Set Up: The volume of a sphere is Use the assumption that the density of Toro is the same as that of earth to calculate the mass of Toro. Then Apply to the object to find its speed when it is in a circular orbit around Toro. Solve: (a) gives (b) The gravity force on the object is In a circular orbit just above the surface of Toro, its acceleration is Then gives and A speed of corresponds to running 100 m in 16.1 s, which is barely possible for the average person. 6.52. Set Up: and The sun has mass The radius of Mercury’s orbit is so the radius of Vulcan’s orbit is Solve: gives and 6.53. Set Up: Use the measurements of the motion of the rock to calculate the value of g on Mongo. Take upward. When the stone returns to the ground its velocity is downward. The radius of Mongo is The ship moves in an orbit of radius For the ship, and Solve: (a) and gives and (b) gives and T 5 5.54 3 10 4 s 5 15.4 h T 5 2 p r v 5 2 p r Å r Gm M 5 2 p r 3 / 2 " Gm M 5 2 p 1 6.18 3 10 7 m 2 3 / 2 "1
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