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Chapter 13: Q. 11 (page 353)
Saturn鈥檚 moon Titan has a mass of and a radius of What is the free-fall acceleration on Titan?
The free-fall acceleration on Titan is
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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.
Let鈥檚 look in more detail at how a satellite is moved from one circular orbit to another. FIGURE shows two circular orbits, of radii localid="1651418485730" and localid="1651418489556" , and an elliptical orbit that connects them. Points and are at the ends of the semimajor axis of the ellipse.
a. A satellite moving along the elliptical orbit has to satisfy two conservation laws. Use these two laws to prove that the velocities at points localid="1651418503699" and localid="1651418499267" are localid="1651418492993" and localid="1651418509687" The prime indicates that these are the velocities on the elliptical orbit. Both reduce to Equation if localid="1651418513535" .
b. Consider a localid="1651418519576" communications satellite that needs to be boosted from an orbit localid="1651418573632" above the earth to a geosynchronous orbit localid="1651418578672" above the earth. Find the velocity localid="1651418584351" on the inner circular orbit and the velocity localid="1651418590277" at the low point on the elliptical orbit that spans the two circular orbits.
c. How much work must the rocket motor do to transfer the satellite from the circular orbit to the elliptical orbit?
d. Now find the velocity localid="1651418596735" at the high point of the elliptical orbit and the velocity v2 of the outer circular orbit.
e. How much work must the rocket motor do to transfer the satellite from the elliptical orbit to the outer circular orbit?
f. Compute the total work done and compare your answer to the result of Example localid="1651418602767" .
The centers of a 10 kg lead ball and a 100 g lead ball are separated by 10 cm.
a. What gravitational force does each exert on the other?
b. What is the ratio of this gravitational force to the gravitational force of the earth on the 100 g ball?
FIGURE P13.57 shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter. Find an exact expression for the orbital period T. Hint: Each planet feels two forces.
You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be and its rotation period to be role="math" localid="1648535932335" You have previously determined that the planet orbits from its star with a period of . Once on the surface you find that the free-fall acceleration is What is the mass of (a) the planet and (b) the star?
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