# The Semi-Major Axis of Binary Stars

• B
• Tom MS
In summary, Wikipedia seems to think that a binary system is defined by a single semi-major axis, but I've seen other sources such as hyperphysics that define it using two semi-major axes. Is the semi-major axis of the system simply the average of the two?I do not know what the standard approach is to this problem.
Tom MS
Wikipedia seems to think that a binary system is defined by a single semi-major axis, but I've seen other sources such as hyperphysics that define it using two semi-major axes. Is the semi-major axis of the system simply the average of the two?

I do not know what the standard approach is to this problem. I, too, have seen both. Never for the same system, AFAIK. My take is:

Mass difference of the two stars makes a big difference in the axes of the orbit of each companion. Take this binary as an example:
O type star, mass ~90M☉ and a type G star with mass 1M☉. It is likely to have an orbit , described simply -- the smaller star orbits the bigger one. One semi-major axis.

When companions are closely matched mass-wise a simple one-axis description does not work well. Two semi-major axes, one for each orbital component more closely matches the data. Since the variety of binaries' mass differences is large there must be a more or less standard approach to the problem. Or it may relate to available data for the system. Don't know.

Also note that Wikipedia is never the best final arbiter on scientific questions.

Since two points determine a line, how can you have multiple semi-major axes?

Since two points determine a line, how can you have multiple semi-major axes?

There is the semi-major axis of the distance between the centers of the two objects, and then there are the semi-major axis for the barycentric orbits of each body.

Since the center of mass of the whole system won't move, the orbits of the two stars independently (with two semi-major axes) are simply scaled-down versions of the "orbit" of the displacement between the stars (one semi-major axis that is the sum, not the average, of the other two). The scale factor is set by the mass ratio, where it is 1/2 if the two stars have the same mass, and 1 for the lower-mass star in the limit that the ratio goes to 0. So the scale factor for the individual orbit of star 1 is $m_2/(m_1+m_2)$, and its orbit is just a miniature copy of the orbit of the total displacement, shrunk by that factor (and of course, the two stars' independent orbits are in phase with each other but mirror reflected).

## What is the semi-major axis of binary stars?

The semi-major axis of binary stars is the average distance between the two stars in a binary star system. It is the longest axis of the elliptical orbit that the stars follow around their common center of mass.

## How is the semi-major axis of binary stars measured?

The semi-major axis of binary stars is typically measured in astronomical units (AU), which is the average distance between the Earth and the Sun. It can also be measured in kilometers or miles.

## Why is the semi-major axis important in studying binary stars?

The semi-major axis is important because it provides information about the stability of the binary star system. The larger the semi-major axis, the more stable the system is, and the longer the orbital period of the stars.

## Can the semi-major axis change over time?

Yes, the semi-major axis of binary stars can change over time due to various factors such as gravitational interactions with other nearby stars, tidal forces, and mass loss from one of the stars. These changes can cause the orbital period of the stars to change as well.

## How is the semi-major axis of binary stars related to the masses of the stars?

The semi-major axis is directly related to the masses of the stars in a binary system. The larger the masses of the stars, the larger the semi-major axis will be. This relationship can also be used to estimate the masses of the stars in a binary system.

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