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Yes, You Can Figure Out The Mass Of A Binary Star! It's Easy!

Yes, you can do it! Trust me! You can figure out the mass of a binary star - two stars that revolve around a common center of mass. Don't be afraid. Let the magic of mathematics carry you away . . .
To perform this stupendous feat, you only need to know the average distance between the two stars in astronomical units, and how long it takes for the two stars to revolve around each other in Earth-years. Once you know the average distance between the two stars (d) and the the orbital period (t), the following equation is your ticket to solving the great puzzle.

mass = d3/t2 whereby d = distance and t = orbital period

Orion's Belt points to SiriusOur sample star is Sirius, the brightest star in the nighttime sky. You can easily see this star in the predawn and dawn sky at this time of year, drawing a line downward using Orion's Belt. Although Sirius looks like a single star to the unaided eye, the telescope shows that this star is a binary.
Image credit: jem1386
According to Jim Kaler, the two stars making up the binary are an average distance of 19.8 astronomical units apart, and have an orbital period of 50.1 years. Let's plug these numbers in our easy-to-use yet magical formula to see what we get for the mass, with d = distance = 19.8 au and t = orbital period = 50.1 years
mass = d3/t2
mass = 19.8 x 19.8 x 19.8/50.1 x 50.1
mass = 7762.392/2510.01
mass = 3.0925741 solar masses
This answer gives the mass of both stars added together. To find the mass of the individual stars, we need to know the distance of each star from the center of mass. We'll tackle that problem in our November 2011 feature.
In the meantime, see if you can figure the mass for Procyon, another binary star. According to Jim Kaler, the two stars in the Procyon system have an average distance (d) = 15.0 astronomical units and an orbital period (t) = 40.8 years.

mass = d3/t2

Yes, you can do it!!!

copyright 2011 by Bruce McClure

September 2011 Feature * November 2011 Feature