Question

# 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?

A
729T
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B
27T
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C
3T
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D
T/3
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E
T/27
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Solution

## The correct option is B 27TKepler'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)3but given TX=T therefore T2T2Y=a3729a3 or TY=27T

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