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Chapter 13: Q1P (page 378)
A massMis split into two parts,and role="math" localid="1657189921712" , which are0 then separated by a certain distance. What ratiomaximizes the magnitude of the gravitational force between the parts?
The magnitude of the gravitational force between the parts is maximized at
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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 .
(a) What is the escape speed on a spherical asteroid whose radius is500 kmand whose gravitational acceleration at the surface is ? (b) How far from the surface will a particle go ifit leaves the asteroid鈥檚 surface with a radial speed of ? (c)With what speed will an object hit the asteroid if it is dropped fromabove the surface?
Figure 13-27 gives the gravitational acceleration for four planets as a function of the radial distance rfrom the center of the planet, starting at the surface of the planet (at radius ). Plots 1 and 2 coincide for plots 3 and 4 coincide for.Rank the four planets according to (a) mass and (b) mass per unit volume, greatest first.
The first known collision between space debris and a functioning satellite occurred in 1996: At an altitude of, a year old French spy satellite was hit by a piece of an Ariane rocket. A stabilizing boom on the satellite was demolished, and the satellite was sent spinning out of control. Just before the collision and in kilometresper hour, what was the speed of the rocket piece relative to the satellite if both were in circular orbits and the collision was
(a) head-on and
(b) along perpendicular paths?
The three spheres in Fig. 13-45, with masses, , and , have their centers on a common line,with and . You move sphereBalong the lineuntil its center-to-center separation fromCis . Howmuch work is done on sphereB(a) by you and (b) by the net gravitational force onBdue to spheresAandC?
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