Day 26 Banneker Institute

I was not able to calculate the eccentricity today, but I was able to calculate the limb darkening components $u_1$ and $u_2$. I did this by using the formulas shown below. These formula can be found in my adviser's paper, http://arxiv.org/abs/1308.0009v2.
$$u_1 = 2\sqrt{q_1}q_2$$ $$u_2 = \sqrt{q_1}(1 - 2q_2)$$

Limb darkening is the optical effect that is cause due to the amount of light receive from an object dependent on the distance that you are from the centre of the object, as shown above.

"Work hard for what you want because it won't come to you without a fight. You have to be strong and courageous and know that you can do anything you put your mind to. If somebody puts you down or criticizes you, just keep on believing in yourself and turn it into something positive."

-Leah LaBelle

Day 24 Banneker Institute

Today I finish calculating the inclination of the planets, the temperature of the planets, the transit duration of the planets, and their respective $\frac{a}{R_*}$ values. The next step in the process is to compare this values to the values in the following published paper http://iopscience.iop.org/0004-637X/804/1/10/. After this is done I will calculate the eccentricity of the planets, finally!

"The only place success comes before work is in the dictionary."

-Vince Lombardi

Day 23 Banneker Institute

More complex mathematics was done today. I calculated the transit duration by using the following formula.$$t_{14} = \frac{P}{\pi}arsin(\frac{R_*}{a}\sqrt\frac{(1 + \frac{R_p}{R_*})^{2} - (\frac{a}{R_*}cosi)^{2}}{1 - cos^{2}i})$$
I also calculated the temperature of the planets by using the following formula.
$$T_p = T_*\sqrt\frac{R_*}{2a}$$

"It is difficult to understand the universe if you only study one planet."

-Miyamoto Musashi

Day 22 Banneker Institute

Today I manage to calculate $\frac{a}{R_*}$ which is the ratio of the semi major axis and the radius of the star. Because a >> $R_*$ this is a good approximation to obtain the distance beween the star and the planet. $$\frac{a}{R_*} = \frac{\rho_* G P_p^2}{3\pi}$$

I also calculated the inclination of each planet, by using the impact parameter b and $\frac{R_*}{a}$

$$i = \cos^{-1}(b\frac{R_*}{a})$$

"There is nothing outside of yourself that can ever enable you to get better, stronger, richer, quicker, or smarter. Everything is within. Everything exists. Seek nothing outside of yourself."

-Miyamoto Musashi

Day 21 Banneker Institute

I finish calculating the parameters with their uncertainty for all three planets. After using Multinest in Dr. Kipping's computer which runs a Markov Chain Monte Carlo(MCMC) program. Below are a few of the parameters that I obtained through this process. The numbers on the left are the parameter values, the ones in the middle are the lower bound uncertainty and the the last numbers are the upper bound uncertainty.

Radius ratio: planet over star

[0.035206658283169809, -0.0010722697357797295, 0.0018395676087651774]

Period of planet b

[10.05403551325956, -0.00024616330074600512, 0.00025023083783537459]

Mid-transit time of planet b

[2456813.4188600937, -0.0010220510885119438, 0.0010063056834042072]

"The world is a dangerous place to live; not because of the people who are evil, but because of the people who don't do anything about it."

-Albert Einstein

Day 20 Banneker Institute

I think this is a good time to review all of the progress that has been made in the last 4 weeks working on the planetary system K2-3. From the raw data to the separation of the planetary light curves, and the histograms of the most probable values for the parameters that describe this recently discover system. Below are a few examples of this plots.

"You can search throughout the entire universe for someone who is more deserving of your love and affection than you are yourself, and that person is not to be found anywhere. You yourself, as much as anybody in the entire universe deserve your love and affection."

-Buddha

Day 19 Banneker Institute

Today not a lot of work was done on the project. The focus was mostly on the physics behind the rest of the parameters that I will have to calculate. Most of it is cover in the following paper http://arxiv.org/pdf/astro-ph/0206228.pdf. Dr. Kipping and I were specially looking at equation 3, and how we could used it to calculate the orbit distance divided by the stellar radius.

"Research is what I'm doing when I don't know what I'm doing."

-Wernher von Braun