The distance between the sun and the earth is r and the earth takes time t to make one complete revolution around the sun. Assuming the orbit of the earth around the sun to be circular, the mass of the sun will be proportional to

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$\frac{r^{3}}{T^{2}}$

$\frac{r^{2}}{T^{3}}$

$\frac{r}{T}$

$\frac{r^{2}}{T^{2}}$

answer is C.

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Detailed Solution

we know that $\frac{GmM}{r^{2}} = \frac{{mv}^{2}}{r} ∴ M = (v^{2} r / G)$
Further, $V = (2 πr / T)$
$∴ M = \frac{4 π^{2} r^{3}}{T^{2} G} or M \propto \frac{r^{3}}{T^{2}}$

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