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Interaction of Two Bodies under Gravitation

The areas A 1...

Question

The areas $A_{1}, A_{2}$ , and $A_{3}$ are equal. Time taken for a planet to move from point M to N is $T_{1}$ , and from point O to Q is $T_{2}$ . Find the ratio of $T_{1}$ and $T_{2}$ .

1:1

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1:2

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2:1

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Solution

The correct option is B 1:2
Kepler’s second law states that the time taken for a planet to sweep equal areas are equal.

Here, $A_{1} = A_{2} = A_{3}$
Let the time taken to sweep area $A_{1} =$ time taken to sweep area $A_{2} =$ time taken to sweep area $A_{3} = t$
Time taken to sweep area $A_{1} +$
Time taken to sweep area $A_{2} = 2 t$ Hence, $\frac{T_{1}}{T_{2}} = \frac{t}{2 t} = \frac{1}{2}$
Hence, $T_{1} : T_{2}$ = 1 : 2

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