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Question

# Two planets, A and B, orbit a star. Planet A moves in an elliptical orbit whose semi major axis has length a. Planet B moves in an elliptical orbit whose semi major axis has a length of 9a. If planet A orbits with a period T, what is the period of planet Bs orbit?

A
729T
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B
27 T
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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 27 TGiven : TA=T RA=a RB=9aUsing Kepler's 3rd law : T∝R1.5⟹ TBTA=(RBRA)1.5OR TBT=(9)1.5 ⟹TB=27 T

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