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Chapter 13: Q. 14 (page 353)
Planet Z is in diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827"
(a) What is the mass of Planet Z?
(b) What is the free-fall accelerationabove Planet Z鈥檚 north pole?
(a) The mass of planet Z is
(b) The free-fall acceleration above Planet Z鈥檚 north pole is
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a. At what height above the earth is the free-fall acceleration of its value at the surface?
b. What is the speed of a satellite orbiting at that height?
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鈥檚 surface. How far above the surface are they orbiting? Your answer will be a multiple of .
A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.
a. What is the ratio F1/F2 of the gravitational force on the first satellite to that on the second satellite?
b. What is the ratio a1/a2 of the acceleration of the first satellite to that of the second satellite?
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" .
Saturn鈥檚 moon Titan has a mass of and a radius of What is the free-fall acceleration on Titan?
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