# Is this question right?

1. Dec 8, 2005

### fahd

hi
i have this queston to do which says..

*)A particle moves in a elliptic orbit under the influence of a central force F= -k/r^2.Prove that the product of the maximim and minimum speeds is equal to [2 pi a/t]^2 where 'a' is the semi major axis of the ellipse and 't' is the period of its motion..

Dont u think it should be the semi minor axis 'b' instead of the semi major axis 'a'..in the question..because im getting the former as the right answer..
please help!!

2. Dec 8, 2005

### emptymaximum

wow. i have the exact same problem.
you can express the 'right answer' in terms of b
$$( \frac{2 \pi a} { \tau } )^2$$ eqs 1
recall:
$$\tau = \frac{2 A} {l}$$ eqs 2
where A is the area of an ellipse and is given by ╥ab
substituting 2 into 1 gives:
$$( \frac{2 \pi a} { \tau } )^2 = \frac{l^2} {b^2}$$

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