Comparison to Wasp-10b

This post is going to compare the parameters we get from analyzing these graphs

both graphs provided on Worksheet 11.1

with actual values from exoplanet.org.  

First, let's start with the impact parameter, b.  

$b=1-\delta^{1/2}\frac{T}{\tau}$

In the light curve above, 

$\delta$=0.028  

T = 102 minutes

$\tau\approx$18 minutes

Using these values and the equation above, I found b=0.99, which is a lot higher than the value given by exoplanet.org, b=0.3.  I believe the reason for this difference is a difference in data.  For example, in the light curve above, the length of the transit looks to be a little longer than an hour and a half, but on exoplanets.org, the transit is at least half an hour longer than that.  

Next, let's look at the ratio of the radii of the planet and star.  

$\delta=\frac{R_P^2}{R_*^2}$

$\frac{R_P}{R_*}=\delta^{1/2}$

For this system, we find that the ratio is equal to 0.17, so the planet is 0.17 times as big as the star.  

On worksheet 11.1, it says that the star is 0.8$R_\odot$.  With this information and the ratio we just found, we can tell that the planet is about 1.36 Jupiter radii big.  This is closer to the website's value of about 1.08 Jupiter radii.  The reason for this difference could be that the website lists the sun as being 0.7 solar radii big.  

Now we'll look at the ratio $a/R_*$.

On the worksheet, not taking into account the impact parameter, I used the equation 

$\frac{a}{R_*}=\frac{P}{\pi T}$

This equation gives us a ratio value of about 13.3, which is pretty close to the website's value 11.9.  The difference can be attributed to the fact that the website found a semimajor axis value dependent on the impact parameter.  

Finally we'll look at the densities of the star and planet.

We all know that density equals mass over volume.  But the fun thing about the mass of a star is that it can be related to semimajor axis and period of the system using Kepler's Third Law.

$M_*=\frac{4\pi^2a_P^3}{GP^2}$

$\rho=\frac{3\pi a_P^3}{R_*^3GP^2}=\left ( \frac{a_P}{R_*} \right )^3\frac{3}{GP^2}$

When we substitute provided values into this equation, we find that the density of the star is about 1.45 grams per cubed centimeter, which is pretty darn close to the website's value of 1.51 g/cm^3.