We can simplify this two-body problem by making use of center-of-mass coordinates wherein we define the reduced mass. In the context of this system, we encounter what is called the two-body problem of which there exists a special case known as the Kepler Problem (by the way let me know if that would be something that you guys would want to see…). The total mass of the binary orbit is the sum of the individual masses of each component. The masses of Alpha Centauri A and B are, and, respectively. The orbital radius vector of Alpha Centauri A is and the orbital radius vector of Alpha Centauri B is. These two stars orbit each other about a common center of mass a point called a barycenter. Setup: Consider the nearest binary star system to our solar system: Alpha Centauri A and Alpha Centauri B. ![]() Leave a comment if you would like me to consider that in another post.ĭerivation of the Total Energy of a Binary Orbit: While writing this I stumbled upon the Kepler problem, the two-body problem, and the N-body problem. ![]() In order to conceptualize it I have used the binary Alpha Centauri A and Alpha Centauri B. ![]() I derive the total energy of a binary system making use of center-of-mass coordinates. Here is my solution to one of the problems in the aforementioned text. SOURCE FOR CONTENT: An Introduction to Modern Astrophysics, Carroll & Ostlie, Cambridge University Press.
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