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Chapter 13: Q. 9 (page 353)

The mass of Jupiter is 300 times the mass of the earth. Jupiter orbits the sun with TJupiter = 11.9 yr in an orbit with rJupiter = 5.2rearth. Suppose the earth could be moved to the distance
of Jupiter and placed in a circular orbit around the sun. Which of the following describes the earth鈥檚 new period?
Explain.
a. 1 yr
b. Between 1 yr and 11.9 yr
c. 11.9 yr
d. More than 11.9 yr
e. It would depend on the earth鈥檚 speed.
f. It鈥檚 impossible for a planet of earth鈥檚 mass to orbit at the
distance of Jupiter.

Short Answer

Expert verified

Option (C) 11.9 yr is correct

Step by step solution

01

Given Information

Period of Jupiter, TJupiter=11.9 year
Radius of the Jupiter, rjupiter=5.2 rearth

02

Explanation

Use Keplar's law T =kR3/2

Where, r= radius of orbit, k = constant, T= period

From the Keplar law, we can conclude that the Time period only depends on the radius of orbit.

If earth moved to the distance of Jupiter and placed in a circular orbit then the period will be the same that of Jupiter, which is 11.9 years.

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Most popular questions from this chapter

Let鈥檚 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鈥�=2GMr2/r1r1+r2and localid="1651418509687" v2鈥�=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.

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