Question

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.

Short answer

Option (C) 11.9 yr is correct

Step-by-step solution

Given Information

Period of Jupiter, T_Jupiter=11.9 year
Radius of the Jupiter, r_jupiter=5.2 r_earth

Explanation

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.