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Please solve this

Can anyone please solve this question of exoplanets.

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I guess it's gonna help

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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.