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Chapter 13: Q4P (page 379)
The Sun and Earth each exert a gravitational force on theMoon. What is the ratioof these two forces? (The average Sun鈥揗oon distance is equal to the Sun鈥揈arth distance.)
The value of the ratio
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Figure 13-46a shows a particleAthat can be movedalong ay-axis from an infinite distance to the origin. That origin liesat the midpoint between particlesBandC, which have identical masses, and theyaxis is a perpendicular bisector between them.DistanceDis. Figure 13-46b shows the potential energyUof the three-particle system as a function of the position of particleAalong theyaxis. The curve actually extends rightward and approaches an asymptote ofas. What are themasses of (a) particlesBandCand (b) particleA?
The Sun鈥檚 center is at one focus of Earth鈥檚 orbit. How far from this focus is the other focus,
(a) in meters and
(b) in terms of the solar radius,? The eccentricity is, and the semimajor axis is.
What multiple of the energy needed to escape from Earth givesthe energy needed to escape from (a) the Moon and (b) Jupiter?
Mountain pulls.A large mountain can slightly affectthe direction of 鈥渄own鈥� as determined by a plumb line. Assumethat we can model a mountain as a sphere of radiusand density (mass per unit volume).Assume alsothat we hang a 0.50mplumb line at a distance offrom the sphere鈥檚 centre and such that the sphere pulls horizontally on thelower end. How far would the lower end move toward the sphere?
The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit, the center of mass of the star-planet system, the star moves toward and away from us with what is called the line of sight velocity, a motion that can be detected. Figure 13-49 shows a graph of the line of sight velocity versus time for the star . The star鈥檚 mass is believed to be of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approximate (a) the planet鈥檚 mass in terms of Jupiter鈥檚 mass and
(b) the planet鈥檚 orbital radius in terms of Earth鈥檚 orbital radius .
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