Calculating the Mass of a Star Using Kepler's Third Law

It may seem impossible to figure out anything about the gaseous stars that are trillions of kilometers away from the earth, but scientists have figured out ways to measure various aspects of a star. While it is possible to calculate the mass of a star, the process is far from easy, and at first it could only be done with binary stars, excluding the sun. However, now scientists are capable of finding the mass of single stars using Kepler’s Law, which can only be used if there is a pair of binary stars — a pair of stars that are orbiting around a common center of gravity. Binary stars make up roughly half of the stars in the Milky Way Galaxy, making this law extremely applicable for astronomers.

Kepler, a German astronomer and mathematician, created a law that scientists use today to calculate the mass of a star. The law, which is called Kepler’s Third law, states, “the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits.” This can then be represented by the formula D3=(M1+M2)P2.

In Kepler’s Third law the P refers to the period of time — measured in years — that the stars are in mutual revolution and go around each other. This is connected to the semimajor axis of the orbits of each of the stars, which is represented by D, in astronomical units. A semimajor axis in astronomy means half of the major axis of the ellipse of a celestial body around another celestial body. M1+M2 is the sum of the masses of the two binary stars. This formula is extremely helpful for astronomers who are looking for the mass of each of the stars. If they know the amount of time that the stars are in mutual revolution, and the size of their orbits, they can figure out the sum of the mass of the two stars. 

To find the speed of the stars scientists must use the doppler effect, which is the change in the wave frequency of sound or light as there is motion between the observer and the source of the sound or light waves. Then scientists will determine the amount of time that it takes for the stars to complete an orbit. With this information, astronomers can calculate the circumference of the orbit. Due to this they will also be able to find the separation between the stars. Given all of this, astronomers will use Kepler’s Third law to determine the sum of the masses of the binary stars.

The sum of the masses can be calculated using the method above, but to find the individual masses requires more calculations. The more massive the star, the closer it will be to the center of mass, and as a result it will have a smaller orbit, causing it to orbit at a slower speed. Then, sorting the speed of each of the stars in relation to each other, scientists will finally know the mass of each individual star. While practicing this, astronomers must know the orientation of the binary star system in their line of sight in addition, to calculate the mass of the stars.

It may seem like there is no point in trying to calculate a star’s mass if it is such a complicated process, but this information is of great importance for scientists. For example, the possibility of a planet being able to host life is dependent on the mass of the star that the planet orbits. So, if humans are thinking about living on a planet other than earth, the mass of stars will be a key factor in deciding whether or not humans can live there.

Works Cited:

https://www.science.org/content/article/astronomers-measure-mass-star-thanks-old-tip-einstein?cookieSet=1

https://hubblesite.org/contents/news-releases/2004/news-2004-24.html

https://pressbooks.online.ucf.edu/astronomybc/chapter/18-2-measuring-stellar-masses/

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Astronomers Measure Mass of a Single Star – First Since the Sun. (n.d.). HubbleSite.Org. Retrieved February 27, 2023, from https://hubblesite.org/contents/news-releases/2004/news-2004-24.html

Astronomers measure the mass of a star—thanks to an old tip from Einstein | Science | AAAS. (n.d.). Science | AAAS. Retrieved February 27, 2023, from https://www.science.org/content/article/astronomers-measure-mass-star-thanks-old-tip-einstein?cookieSet=1

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