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This assignment was given by Krittika Club of IITB as a task in their application form for Summer Projects. The following is the actual question given in their form. You can find more about the club here: https://www.facebook.com/KrittikaIITB/ So, the task is as follows:
This assignment requires the knowledge of plotting with Matplotlib, curve fitting using SciPy and also NumPy. You have been provided with the Doppler shift data (download here: https://drive.google.com/file/d/1sThNaS5kgOKpCjhgXIvo3LcOflslTKaH/view?usp=sharing) in the Balmer line of two stars in a binary star system orbiting about a common centre of mass.
Following points are given for the problem:
Cosmological redshift can be ignored The orbital plane of the system is assumed to be parallel to the line of sight The orbit is circular, and the whole system (or the centre of mass) is moving radially towards/away from us Your task is to:
Provide an expression for the mass of each star in terms of orbital velocities of both stars, the time period of revolution and universal constants. Obtain the radial velocity of the centre of mass of the system. Having accounted for the radial velocity, plot only the orbital velocity. Fit the resultant data with a sine curve. Obtain orbital velocities of each star and hence find their masses using the result obtained in part 1. You are required to submit:
Derivation of result obtained in part 1. The scatter plot of orbital velocity with a sine curve fitted to the data. The entire code for the assignment. Output should have the format:
Period of revolution is:
Mass of lighter star is:
Mass of heavier star is:
Some things to note: You may have to manually set the range on the Y axis to make the plot more readable. Also if you choose to find the frequency using Lomb-Scargle method, make sure you discard garbage values and accept the one that appears to satisfy the data best.
