Two planets, X and Y, revolving in a orbit around star. Planet X moves in an elliptical orbit whose semi-major axis has length a. Planet Y moves in an elliptical orbit whose semi-major axis has a length of 9a. If planet X orbits with a period T, Find out the period of planet Y's orbit?
- 729T
- 27T
- 3T
- T/3
- T/27
Kepler's third law of planetary motion gives T2∝r3
where T= time period of revolution , r= length of semi major axis of elliptical orbit
by this relation we get , TXTY=r3Xr3Y
T2XT2Y=a3(9a)3
but given TX=T
therefore T2T2Y=a3729a3
or TY=27T
Two planets of equal mass orbit a much more massive star (figure). Planet m1 moves in a circular orbit of radius 1×108 km with period 2 year. Planet m2 moves in an elliptical orbit with closest distance r1=1×108 km and farthest distance r21.8×108km, as shown. Using the fact that mean radius of an elliptical orbit is the length of the semi-major axis, find the period of m′2 s orbit.
Two planets of equal mass orbit a much more massive star (figure). Planet m1 moves in a circular orbit of radius 1×108 km with period 2 year. Planet m2 moves in an elliptical orbit with closest distance r1=1×108 km and farthest distance r21.8×108km, as shown. Using the fact that mean radius of an elliptical orbit is the length of the semi-major axis, find the period of m′2 s orbit.
