Have you ever worked with astronomical data and their graphical representations in real life? Do you think all the heavenly bodies are as beautiful and colorful as they are seen in some pictures on the internet? Do you think you can see the wonderful shape and the color of the Eagle nebulae if you keep your eyes on the telescope?

Most of the pictures of Messier objects in the sky are built by computer simulations and modeling and by artists. All we get are some useful data and plot them on the graph and make their shapes through computer simulations. To know more about how astrophysicists create the shapes of heavenly bodies from data, click on the link - How to take a picture of a black hole

Solving the problem, we will learn how some points and graphs can tell us what happens in space. The idea of this problem has been taken from USAAO, and it has been slightly modified from the actual description. Let's start, and good luck!

Astronomers use an $8$ $meter$ telescope to observe a star with an apparent flux of $3.068×10^{-9}\frac{W}{m^2}$. A spectral analysis reveals a black-body spectrum with two apparent peaks, one at $690.5\space nm$ and the other at $461.8\space nm$. Sustained spectroscopic observations of the hydrogen alpha line (rest wavelength $656.3\space nm$) results in the following plot, in which two periodic variations have been identified and marked.

Note: the $x-­axis$ is in days, and the $y-­axis$ is in nano meters.

Precision photometry of the system shows what appears to be an eclipsing binary light curve. The primary transit lasts $4$ hours $46$ minutes total. Maximum transit depth lasts for $4$ hours $7$ minutes.

The ratio of the radius of the two stars in the system is $13.67$.

Find out the ratio of their luminosities in the nearest integer to your answer.

Hint: Do you know Wien's displacement law?

Second part of this problem - 3rd person (2)