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’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, TJupiter=11.9 yearRadius of the Jupiter, rjupiter=5.2 rearth
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.
Three satellites orbit a planet of radius R, as shown in figure given below.
Satellites S1 and S3 have mass . Satellite S2 has mass Satellite S1 orbits in and the force on S1 is
a. What are the periods of S2 and S3?
b. What are the forces on S2 and S3?
c. What is the kinetic-energy ratio K1/K3 for S1 and S3?
A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.
a. What is the ratio F1/F2 of the gravitational force on the first satellite to that on the second satellite? b. What is the ratio a1/a2 of the acceleration of the first satellite to that of the second satellite?
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