Astrophysics Is Easy! by Michael Inglis

Author:Michael Inglis
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.2 The Masses of Orbiting Stars

It may come as no surprise to you that the mass of a star can be determined. However, the question that needs to be asked is, “How?” Well, usually, we need to use binary stars, as well as the laws of Kepler and Newton. Both men, and their contributions, were covered in the chapter on the Solar System, so it may be wise to re-read that chapter again to get an idea of their laws and how we can use them in an analysis of binary stars.

Kepler’s law, which demonstrates how the time required for a planet orbiting the Sun is related to its distance from the Sun, can be modified to describe the motion of any two bodies that orbit around each other. The person who did this was the great Isaac Newton. To find the mass of the stars in a visual binary, we must first determine their orbits by observing them over several years. It may be that this will take a few years, or even tens of years, but eventually we can determine the time needed for one star to completely orbit the other.

This period of time is called P. By using a plot of the orbit, and forearmed with knowledge of the system’s distance from the Sun, we can then measure the distance of the semi-major axis,7 a, of one star to the other. An important point to note here is that this method only gives us the combined mass of the stars, not their individual masses. To achieve that, we need to go one step further.

From the above description, we can easily determine the combined masses of two stars orbiting each other. To determine individual stellar masses, however, we determine how much one star moves relative to the other. For instance, if one star is much more massive than the other, then it will hardly move at all relative to the less-massive star; the less-massive star will seem to do all of the orbiting in the system in a manner reminiscent of planets orbiting the Sun. To be accurate, we should really say that the stars (and, incidentally, the planets and Sun) orbit about their common center of mass, or center of gravity. In fact, they “wobble.”8

The masses of stars usually orbit the center of mass that is more or less equidistant from both of them. This center of mass is found along a line joining the two stars at a position that depends on the stars’ masses. Think of it as the balance point on a child’s seesaw. If one star is four times as massive as the other, the balance point will be four times closer to the more massive star.

If the two stars have mass M A and M B , their distances from the center of mass (the balance point) are a A and a B ,9 with the larger mass having the smaller distance from the center of mass. So, for example, if the

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