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Kepler's Law

A double star...

Question

A double star system consists of two stars A and B which have time periods $T_{A}$ and $T_{B}$ . Radius $R_{A}$ and $R_{B}$ and mass $M_{A}$ and $M_{B}$ . Choose the correct option.

A

If

T_{A} > T_{B}

, then

R_{A} > R_{B}

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B

If

T_{A} > T_{B}

, then

M_{A} > M_{B}

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C

{(\frac{T_{A}}{T_{B}})}^{2} = {(\frac{R_{A}}{R_{B}})}^{3}

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D

T_{A} = T_{B}

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Solution

The correct option is A $T_{A} = T_{B}$

$ω = \frac{2 π}{T_{A}} = \frac{2 π}{T_{B}}$ $∴$ $T_{A} = T_{B}$

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