Example 12-3 The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for the rotation. Calculate this rotation period for Earth.
Example 12-3 The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for the rotation. Calculate this rotation period for Earth.
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12.3
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12.6 Examples
12.6 Examples
Example 12-1
A satellite with a mass of 1000 kg is placed in Earth orbit at an orbit of 500 km above the surface.
Assuming a circular orbit,
a) How long does the satellite take to complete one orbit?
b) What is the satellite's orbital speed?
c) What is the minimum energy necessary to place this satellite in orbit (assume there is no air
resistance)?
d) For how many miles would this energy power an automobile? (Assume 1 gal. of gasoline
produces 1.1*108 J of energy, and this energy is sufficient to operate a car for 25 miles)
Example 12-2
Two spherical objects of masses m, and m, are released from rest at a separation distance of L. Find
their speeds and positions when their separation distance is r. Assume that the first particle initially
is at the origin.
Example 12-3
The fastest possible rate of rotation of a planet is that for which the gravitational force on material at
the equator just barely provides the centripetal force needed for the rotation. Calculate this rotation
period for Earth.
Example 12-4
The Schwarzschild radius is a distance from a black hole where the escape velocity equals the speed
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