How to Figure out the Mass of a Star

hypergiant star
The hypergiant star VY Canis Majoris, from Rutherford Observatory. It is one of the largest and most massive stars measured by astronomers. Arthunter, via Wikipedia Commons. CC BY-SA 3.0

Nearly everything in the universe has mass, from atoms and sub-atomic particles (such as those studied by the Large Hadron Collider) to giant clusters of galaxies. The only things scientists know about so far that don't have mass are photons and gluons. 

Mass is important to know, but objects in the sky are too distant. We can't touch them and we certainly can't weigh them through conventional means. So, how do astronomers determine the mass of things in the cosmos? It's complicated. 

Stars and Mass

Assume that a typical star is pretty massive, generally much more so than a typical planet. Why care about its mass? That information is important to know because it reveals clues about a star's evolutionary past, present, and future.

Astronomers can use several indirect methods to determine stellar mass. One method, called  gravitational lensing, measures the path of light that is bent by the gravitational pull of a nearby object. Although the amount of bending is small, careful measurements can reveal the mass of the gravitational pull of the object doing the tugging.

Typical Star Mass Measurements

It took astronomers until the 21st century to apply gravitational lensing to measuring stellar masses. Before that, they had to rely on measurements of stars orbiting a common center of mass, so-called binary stars. The mass of binary stars (two stars orbiting a common center of gravity) is pretty easy for astronomers to measure. In fact, multiple star systems provide a textbook example of how to figure out their masses. It's a bit technical but worth studying to understand what astronomers have to do.

First, they measure the orbits of all the stars in the system. They also clock the stars' orbital speeds and then determine how long it takes a given star to go through one orbit. That's called its "orbital period." 

Once all that information is known, astronomers next do some calculations to determine the masses of the stars. They can use the equation Vorbit = SQRT(GM/R) where SQRT is "square root" a, G is gravity, M is mass, and R is the radius of the object. It's a matter of algebra to tease out the mass by rearranging the equation to solve for M

So, without ever touching a star, astronomers use mathematics and known physical laws to figure out its mass. However, they can't do this for every star. Other measurements help them figure out the masses for stars ​not in binary or multiple-star systems. For example, they can use luminosities and temperatures. Stars of different luminosities and temperatures have vastly different masses. That information, when plotted on a graph, shows that stars can be arranged by temperature and luminosity.

Really massive stars are among the hottest ones in the universe. Lesser-mass stars, such as the Sun, are cooler than their gigantic siblings. The graph of star temperatures, colors, and brightnesses is called the Hertzsprung-Russell Diagram, and by definition, it also shows a star's mass, depending on where it lies on the chart. If it lies along a long, sinuous curve called the Main Sequence, then astronomers know that its mass will not be gigantic nor will it be small. The largest mass and smallest-mass stars fall outside the Main Sequence.

Stellar Evolution

Astronomers have a good handle on how stars are born, live, and die. This sequence of life and death is called "stellar evolution." The biggest predictor of how a star will evolve is the mass it's born with, its "initial mass." Low-mass stars are generally cooler and dimmer than their higher-mass counterparts. So, simply by looking at a star's color, temperature, and where it "lives" in the Hertzsprung-Russell diagram, astronomers can get a good idea of a star's mass. Comparisons of similar stars of known mass (such as the binaries mentioned above) give astronomers a good idea of how massive a given star is, even if it isn't a binary.

Of course, stars don't keep the same mass all their lives. They lose it as they age. They gradually consume their nuclear fuel, and eventually, experience huge episodes of mass loss at the ends of their lives. If they're stars like the Sun, they blow it off gently and form planetary nebulae (usually). If they're much more massive than the Sun, they die in supernova events, where the cores collapse and then expand outward in a catastrophic explosion. That blasts much of their material to space.

By observing the types of stars that die like the Sun or die in supernovae, astronomers can deduce what other stars will do. They know their masses, they know how other stars with similar masses evolve and die, and so they can make some pretty good predictions, based on observations of color, temperature, and other aspects that help them understand their masses.

There's much more to observing the stars than gathering data. The information astronomers get is folded into very accurate models that help them predict just exactly what stars in the Milky Way and throughout the universe will do as they are born, age, and die, all based on their masses.