Week 11: Calculations

Hello and welcome back to my blog!

This week was super busy but I managed to finish all of the calculations for Qatar-2 b and TrES-3 b. Astronomers very rarely calculate this data by hand. Instead, they use code such as EXOFAST (NASA uses this one) to take the lightcurve results from EXOTIC and return accurate data regarding specific features of the planet and the star it orbits. Astronomers then use that data to determine the composition and atmospheric conditions of the planet. For the purposes of this project, I decided to do all the math by hand to better understand how each equation works. After I completed the calculations, I ran the lightcurve data through EXOFAST to check my work. Some calculations were definitely more challenging than others, especially finding stellar radius. Here is a snippet from my notebook:

The hardest part was accurately estimating the total duration (Ttotal) and the total eclipse duration (Tfull) of the transit. As seen in the diagram below Ttotal is tIV – tI and Tfull is tIII – tII

To do so I studied the Qatar-2 b lightcurve and estimated the time right before the eclipse started and right after it started. I also measured right before and after it ended.

The next step is to subtract the inner two values and the outer two to get the total duration and the total eclipse duration. Then in accordance to the equation I squared both values and subtracted them then took the square root. This step was difficult because of the inherent error involved. When I first tried I was getting 200% error for the result and realized I was estimating the total eclipse time to be much shorter than it actually was. In reality, Tfull and Ttotal were super similar values. I readjusted my estimations and eventually calculated a stellar radius that was 27% different from the stellar radius calculated by EXOFAST.

Thank you so much for reading my blog this week! Next week, I’ll be finalizing my presentation and final lab report so stay tuned!