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Chapter 13: Q. 49 (page 355)
A starship is circling a distant planet of radius R. The astronauts find that the free-fall acceleration at their altitude is half the value at the planet’s surface. How far above the surface are they orbiting? Your answer will be a multiple of .
The starship is orbiting above above the surface.
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Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton’s third law, the forces that
push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The
gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to
form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of ≈ 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars.
a. Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the speed of a point on the equator of the star?
b. What is g at the surface of this neutron star?
c. A stationary 1.0 kg mass has a weight on earth of 9.8 N. What would be its weight on the star?
d. How many revolutions per minute are made by a satellite orbiting 1.0 km above the surface?
e. What is the radius of a geosynchronous orbit?
FIGURE P13.35 shows three masses. What are the magnitude and the direction of the net gravitational force on (a) the 20.0 kg mass and (b) the 5.0 kg mass? Give the direction as an angle cw or ccw from the y-axis.
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’ll approximate it as a 50-km-diameter circular orbit with a period of 11 days.
a. What was the satellite’s 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—taking about 7 hours—to the surface. What was its landing speed? The comet’s shape is
irregular, but on average it has a diameter of 3.6 km.
NASA would like to place a satellite in orbit around the moon such that the satellite always remains in the same position over the lunar surface. What is the satellite’s altitude?
In Problems 64 through 66 you are given the equation(s) used to solve a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Draw a pictorial representation.
c. Finish the solution of the problem.
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