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A planet of mass ‘m’ moves around the sun of mass “M” i an elliptical orbit. The maximum and minimum distance of planet from the sun are r and r’ respectively. The time period of planet is proportional to (a) r+r’ (b) (r+r’)^1/2 (c)(r-r’)^3/2 (d) (r+r’)^3/2 Please help

A planet of mass ‘m’ moves around the sun of mass “M” i an elliptical orbit. The maximum and minimum distance of planet from the sun are r and r’ respectively. The time period of planet is proportional to 
(a) r+r’
(b) (r+r’)^1/2
(c)(r-r’)^3/2
(d) (r+r’)^3/2
 
Please help

Grade:12

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
According to Kepler's law
T² is proportional to cube of semi major axis of elliptical orbit.
 
Now semi major axis = (r + r')/2
 
T² is proportional to [(r +r')/2]³
 
T is proportional to  [(r + r')/2 ]3/2
 
Hence option D is correct.
 
Regards
Arun (askIITians forum expert)

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