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Can anyone please solve this question of exoplanets.

I guess it's gonna help

a) From the graph one can easily deduce that the period of the planet is $2.2$ days approximately, as that is the difference between two consecutive drops in the stars brightness.

b) The lowest relative brightness in approximately $0.9935$. Hence the planet is covering up $0.0065 = 0.65%$ surface area of the stellar disk. So we can assume that the ratio of the areas of the planetary disk to the stellar disk is 0.0065 and so -

$\frac{\pi {R_{planet}}^2}{{\pi R_{star}}^2} = 0.0065$

$\rightarrow \frac{ R_{planet}}{R_{star}} = (0.0065)^{.5} \approx 0.0806$

c) Let $\delta m, B_1, B_2$ denote the difference in magnitude, initial brightness and brightness during occultation. Then-

$\delta m = -2.5log\frac{B_2}{B_1}$

$\rightarrow \delta m = -2.5log\frac{0.9935}{1} \approx 7.08 * 10^{-3}$

d) $v = \frac{2\pi a}{P}$, where $v, a, p$ respectively denotes the velocity, distance from the star and period of the planet. Hence $a = \frac{Pv}{2\pi} = \frac{300 * 2.2 * 24 * 3600}{2\pi} km \approx 9.076 * 10^6 km$

Now, we know that if the stellar mass is $M$, then $v^2 = \frac{GM}{a}$.

So, $M = \frac{av^2}{G} \approx 1.224 * 10^{31} kg \approx 6.15$solar mass.

Q.E.D.