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Chapter 13: Q. 7 (page 353)

Why is the gravitational potential energy of two masses negative? Note that saying “because that’s what the equation gives” is not an explanation.

Short Answer

Expert verified

If two masses are placed at infinite distance their Gravitational potential energy is Zero.

This means the negative potential energy has less potential energy than their potential energy at infinite separation.

Step by step solution

01

Given Information

Potential energy of two masses negative

02

Explanation

If two masses are placed at infinite distance their Gravitational potential energy is Zero.

This means the negative potential energy has less potential energy than their potential energy at infinite separation.

The gravitational potential energy is given by

U=Gm1m2r

When r approaches to infinity the value of potential energy approach to 0.

This means two masses infinitely far apart will have no tendency, or potential to move together.

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Most popular questions from this chapter

Let’s look in more detail at how a satellite is moved from one circular orbit to another. FIGURE CP13.71shows two circular orbits, of radii localid="1651418485730" r1and localid="1651418489556" r2, and an elliptical orbit that connects them. Points 1and 2are 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" 1and localid="1651418499267" 2are localid="1651418492993" v1′=2GMr2/r1r1+r2and localid="1651418509687" v2′=2GMr1/r2r1+r2The prime indicates that these are the velocities on the elliptical orbit. Both reduce to Equation 13.22if localid="1651418513535" r1=r2=r.

b. Consider a localid="1651418519576" 1000kgcommunications satellite that needs to be boosted from an orbit localid="1651418573632" 300kmabove the earth to a geosynchronous orbit localid="1651418578672" 35,900kmabove the earth. Find the velocity localid="1651418584351" v1on the inner circular orbit and the velocity localid="1651418590277" v=1at 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" v=2at 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" 13.6.

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