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A planet of mass m moves in an elliptica...


A planet of mass m moves in an elliptical orbit around sun with sun at its Focus. (e=eccentricity of ellipse). Then `T_(ACB)//T_(BDA)` is `[T_(ACB)` is time taken to travel from A to C B & `T_(BDA)` is time taken to travel from B to D to A]

A

`(pi+2e)//(pi-2e)`

B

`1`

C

`(pi+e)//(pi-e)`

D

`pi//(pi-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`because(dA)/(dt)={"Kepler's 2nd law"]`
`therefore(T_(1))/(T_(2))=(A_(1))/(A_(2))=((piab)/(2)+(1)/(2)xx2bxxae)/((piab)/(2)-(1)/(2)xx2bxxae)`
or `(T_(1))/(T_(2))=((pi+2e))/((pi-2e))`
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