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?

729T

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27 T

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T/3

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T/27

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Solution

The correct option is B 27 T
Given : $T_{A} = T$ $R_{A} = a$ $R_{B} = 9 a$
Using Kepler's 3rd law : $T \propto R^{1.5}$
$⟹$ $\frac{T_{B}}{T_{A}} = (\frac{R_{B}}{R_{A}})^{1.5}$

OR $\frac{T_{B}}{T} = (9)^{1.5}$ $⟹ T_{B} = 27$ $T$

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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?

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

The correct option is B 27 T
Given : $T_{A} = T$ $R_{A} = a$ $R_{B} = 9 a$
Using Kepler's 3rd law : $T \propto R^{1.5}$
$⟹$ $\frac{T_{B}}{T_{A}} = (\frac{R_{B}}{R_{A}})^{1.5}$

OR $\frac{T_{B}}{T} = (9)^{1.5}$ $⟹ T_{B} = 27$ $T$