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Chapter 13: Q. 1 (page 353)
What is the ratio of the sun鈥檚 gravitational force on you to the
earth鈥檚 gravitational force on you?
Ratio sun's gravitational force on me to earth's gravitational force on me is
Fs/Fe=5.98 x 10-4
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A projectile is shot straight up from the earth鈥檚 surface at a speed of . How high does it go?
a. What is the free-fall acceleration at the surface of the sun?
b. What is the free-fall acceleration toward the sun at the distance of the earth?
A 55,000 kg space capsule is in a 28,000-km-diameter circular orbit around the moon. A brief but intense firing of its engine in the forward direction suddenly decreases its speed by 50%. This
causes the space capsule to go into an elliptical orbit. What are the space capsule鈥檚 (a) maximum and (b) minimum distances from the center of the moon in its new orbit?
Hint: You will need to use two conservation laws.
FIGURE CP13.72 shows a particle of mass m at distance x from the center of a very thin cylinder of mass M and length L. The particle is outside the cylinder, so x > L/2.
a. Calculate the gravitational potential energy of these two masses.
b. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on m when it is at position x.
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" .
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