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Chapter 13: 101P (page 385)
A spaceship is on a straight-line path between Earth and the Moon. At whatdistance from Earth is the net gravitational force on the spaceship zero?
Net gravitational force on the spaceship is zero at a distance of from the earth.
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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.
Question: A certain triple-star system consists of two stars, each of mass m , revolving in the same circular orbit of radius raround a central star of mass M (Fig. 13-54).The two orbiting stars are always at opposite ends of a diameter of the orbit. Derive an expression for the period of revolution of the stars.
We watch two identical astronomical bodies Aand B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation isRi. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this two body system. Use the principle of conservation of mechanical energy (Kf+ Uf=Ki +Ui ) to find the following when the center-to-center separation is 0.5Ri:
(a) the total kinetic energy of the system,
(b) the kinetic energy of each body,
(c) the speed of each body relative to us, and
(d) the speed of body Brelative to body A. Next assume that we are in a reference frame attached to body A(we ride on the body). Now we see body Bfall from rest toward us. From this reference frame, again useto find the following when the center-to-center separation is:
(e) the kinetic energy of body Band
(f) the speed of body Brelative to body A.
(g) Why are the answers to (d) and (f) different? Which answer is correct?
Mile-high building.In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth鈥檚 rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh, to the top of the building.
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.)
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