Astronomy 162:
Introduction to Stellar, Galactic, & Extragalactic Astronomy

Lecture 8: Binary Stars: Stellar Masses & Radii

Key Ideas:

Binary Stars

Apparent Binaries:

True Binary Stars:

Types of Binaries

Visual Binary:
Can see both stars and follow their orbits over time.
Spectroscopic Binary:
Cannot separate the two stars, but see their orbit motions as Doppler shifts in their spectral lines.
Eclipsing Binary:
Can separate the stars, but see the total brightness drop when they periodically eclipse each other.

Visual Binaries

Two stars orbiting about their center-of-mass.

Visual Binary Star

Center of Mass

Two stars orbit about their center of mass.

Center of Mass

Here are two movies showing visual binary stars, one with a circular orbit, the other with an elliptical orbit, emphasizing the point about their orbits around their common center of mass in all cases.

Measuring Masses

Newton's Form of Kepler's Third Law:

Newton's Form of Kepler's 3rd Law


  1. Measure the period, P, by following the orbit.
  2. Measure semi-major axis, a, and the Mass Ratio, M1/M2, from the projected orbit on the sky.
  3. Solve the equation above and separate Masses.
We need to follow the orbits long enough to trace them out in detail: Everything depends on knowing the distance: Small errors add up quickly.

Spectroscopic Binaries

Most binaries are too far away to be able to see both stars separately.

But, you can detect their orbital motions by the periodic Doppler shifts of the spectral lines:

Spectroscopic Binary Star

Here is a movie showing a spectroscopic binary star.

Cannot see the two stars separately:

Everything depends critically on knowing the distance.

Eclipsing Binaries

Two stars orbiting nearly edge-on to our line-of-sight. With the best data, one can find the masses of the stars without having to know the distance!!!

Eclipsing Binary Star

Here is a movie showing an eclipsing binary star and its light curve.

Eclipsing Binary stars are very rare.

Measurement of the light curves is complicated by details:

Stellar Masses

From a combination of visual and eclipsing binaries, masses are known for about 150 stars.

Range: ~0.1 to 50 Solar Masses

Stellar Radii

Radii are very difficult to measure because stars are so far away.


Radii have only been measured for about 25 stars.

Advances in optical interferometry should greatly increase that number in the next decade.