# Planet transit to derive system parameters

1. Oct 4, 2011

### RHK

1. The problem statement, all variables and given/known data

Measuring the flux of a star as a function of the time, the flux exhibit a decrease of 1.65% for 2h 56m, 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;

(iii) The star mass.

2. Relevant equations

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

3. 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*Lsun.
This allow to obtain the stellar radius Rs 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?

Last edited: Oct 4, 2011
2. Oct 7, 2011

### RHK

Anyone can suggest if it's the correct way?

3. Oct 7, 2011

### RHK

I'm sorry: the correct eqaution is not (as reported):
but: $\Delta L= 4\pi(R_s^2 - R_{planet}^2) \sigma T_s^4$