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## Homework Statement

Measuring the flux of a star as a function of the time, the flux exhibit a decrease of 1.65% for 2

^{h}56

^{m}, periodically every 57.22 days. Such decrease is ascribed to a planet transit.

The continuous spectrum of the star is like a black body with T= 9500 K, and its bolometric luminosity is 22 times the bolometric luminosity of the Sun (that has a black body spectrum with T=5600K).

Assuming that the planet transit is projected on the star equator, and that the planet is on a circular orbit, calculate:

(i) The planet diameter;

(ii) The orbit planet radius;

(iii) The star mass.

## Homework Equations

[itex]R_{sun} = 6.69*10^8 m[/itex]

[itex]L_{bol}=4\pi R_s^2 \sigma T^4 [/itex]

## The Attempt at a Solution

For the first point i can calculate the Sun bolometric luminosity with the same Stefan-Boltzmann law:

[itex]L_{sun}=4\pi R_{sun}^2 \sigma T_{sun}^4 [/itex]

and then calculate the bolometric luminosity of the star, that is 22*L

_{sun}.

This allow to obtain the stellar radius R

_{s}by using the S-B law.

Thus, the luminosity difference in the star is [itex]\Delta L= 4\pi(R_s^2 - R_{sun}^2) \sigma T_s^4 [/itex]

where [itex]\Delta L= (100 - 1.65)\% L_s[/itex]

Is it ok?

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