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Center of Mass as an Average Point

Using the fac...

Question

Using the fact that the mean radius of an elliptical orbit is the length of the semi-major axis, find the period of $m_{2}^{'} s$ orbit.

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Solution

Mean radius in this case will be

$r = \frac{r_{m a j o r} + r_{m i n o r}}{2} = \frac{1 \times 10^{8} + 1.8 \times 10^{8}}{2} = 1.4 \times 10^{8} k m$

From Kepler's second law,

$T α r^{3 / 2}$

$\frac{T_{1}}{T_{2}} = \frac{r_{1}^{3 / 2}}{r_{2}^{3 / 2}} = {(\frac{1}{1.4})}^{3 / 2}$

$T_{2} = {1.4}^{3 / 2} (2) = 3.31 y r$

Answer is $3.31 y r$

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