You go where no one has gone before and discover an interesting planet of radius r. When you arrive, you clearly want to do some experiments to learn more about this world. You begin with some simple kinematics and measure the time t for an object thrown directly up with velocity vi to return to your hand. With this information, you find that the acceleration due to gravity gi s much lower than on Earth. a) You decide to orbit the planet in your spacecraft at a distance Rabove the surface of the planet. Find the time required to complete one orbit in terms of R, r, vi, t, and any necessary constants. b) FInd the escape velocity ve–the initial velocity necessary for an object to barely escape the gravitational pull of the planet. Express your answer in terms of vi, r, t,and any necessary constants. c) Find the distance from the planet’s center at which an object launched from the surface with velocity vwill have lost 90% of its initial kinetic energy at the surface in terms of v,vi, r, t, and any necessary constants.
You go where no one has gone before and discover an interesting planet of radius r. When you arrive, you clearly want to do some experiments to learn more about this world. You begin with some simple
a) You decide to orbit the planet in your spacecraft at a distance Rabove the surface of the planet. Find the time required to complete one orbit in terms of R, r, vi, t, and any necessary constants.
b) FInd the escape velocity ve–the initial velocity necessary for an object to barely escape the gravitational pull of the planet. Express your answer in terms of vi, r, t,and any necessary constants.
c) Find the distance from the planet’s center at which an object launched from the surface with velocity vwill have lost 90% of its initial kinetic energy at the surface in terms of v,vi, r, t, and any necessary constants.
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