Planet transit to derive system parameters

[RHK]

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

R_{sun} = 6.69*10^8 m
L_{bol}=4\pi R_s^2 \sigma T^4

The Attempt at a Solution

For the first point i can calculate the Sun bolometric luminosity with the same Stefan-Boltzmann law:
L_{sun}=4\pi R_{sun}^2 \sigma T_{sun}^4

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 \Delta L= 4\pi(R_s^2 - R_{sun}^2) \sigma T_s^4
where \Delta L= (100 - 1.65)\% L_s

Is it ok?

 

[RHK]

Anyone can suggest if it's the correct way?

 

[RHK]

I'm sorry: the correct eqaution is not (as reported):

Thus, the luminosity difference in the star is \Delta L= 4\pi(R_s^2 - R_{sun}^2) \sigma T_s^4
where \Delta L= (100 - 1.65)\% L_s

but: \Delta L= 4\pi(R_s^2 - R_{planet}^2) \sigma T_s^4

What about this?