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Chapter 13: Q. 34 (page 354)
Pluto moves in a fairly elliptical orbit around the sun. Pluto鈥檚 speed at its closest approach of km is 6.12 km/s. What is Pluto鈥檚 speed at the most distant point in its orbit, where it iskm from the sun?
The Pluto's speed at the most distant point in its orbit is.
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A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is less than that at sea level. What is the observatory鈥檚 altitude?
A rogue band of colonists on the moon declares war and prepares to use a catapult to launch large boulders at the earth. Assume that the boulders are launched from the point on the moon nearest the earth. For this problem you can ignore the rotation of
the two bodies and the orbiting of the moon.
a. What is the minimum speed with which a boulder must be launched to reach the earth?
Hint: The minimum speed is not the escape speed. You need to analyze a three-body system.
b. Ignoring air resistance, what is the impact speed on earth of a boulder launched at this minimum speed?
In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we鈥檒l approximate it as a 50-km-diameter circular orbit with a period of 11 days.
a. What was the satellite鈥檚 orbital speed around the comet? (Both the comet and the satellite are orbiting the sun at a much higher speed.)
b. What is the mass of the comet?
c. The lander was pushed from the satellite, toward the comet, at a speed of 70 cm/s, and it then fell鈥攖aking about 7 hours鈥攖o the surface. What was its landing speed? The comet鈥檚 shape is
irregular, but on average it has a diameter of 3.6 km.
FIGURE CP13.72 shows a particle of mass m at distance x from the center of a very thin cylinder of mass M and length L. The particle is outside the cylinder, so x > L/2.
a. Calculate the gravitational potential energy of these two masses.
b. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on m when it is at position x.
a. What is the free-fall acceleration at the surface of the sun?
b. What is the free-fall acceleration toward the sun at the distance of the earth?
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