Q. 9

Expert-verifiedFound in: Page 353

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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 r_{Jupiter} = 5.2r_{earth}. 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’s 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’s speed. f. It’s impossible for a planet of earth’s mass to orbit at the distance of Jupiter.

Option (C) 11.9 yr is correct

Period of Jupiter, T_{Jupiter}=11.9 yearRadius of the Jupiter, r_{jupiter}=5.2 r_{earth}

Use Keplar's law T =kR^{3/2}

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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