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Chapter 13: Q. 6 (page 353)
The free-fall acceleration at the surface of planet 1 is 20 m/s2. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2?
The value of g on planet 2 is : 10 m/s2
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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" .
Two meteoroids are heading for earth. Their speeds as they cross the moon鈥檚 orbit are
a. The first meteoroid is heading straight for earth. What is its speed of impact?
b. The second misses the earth by What is its speed at its closest point?
Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, making all escape impossible. What is the radius of the event horizon for a black hole with a mass times the mass of the sun? This distance is called the Schwarzschild radius.
Why is the gravitational potential energy of two masses negative? Note that saying 鈥渂ecause that鈥檚 what the equation gives鈥� is not an explanation.
What is the escape speed from Jupiter?
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