Q&A: How We Measure the Distance to a Star

Question: After reading your explanation about how we measure the distance to the Moon [May 5, 2014] it made me wonder how we measure the distance to a star? Obviously, we can’t bounce a laser beam off a star. — KS, Benson, AZ

Answer: You are correct that a laser wouldn’t reflect, but we have bounced a radar beam off a star. The Stanford Electronics Laboratories did that with the Sun back in 1959. It allowed the first direct measurement of the Sun-to-Earth distance — what astronomers call the astronomical unit (AU).

This method isn’t practical for any other stars, even Alpha Centauri, the closest star at 4.1 light years. The signal power and antenna sensitivity required are way beyond current technology. Plus we’d need to wait 8.2 years for the bounced signal to return. Instead, we use a geometric method (at least for the closer stars) that’s been employed for hundreds of years. Astronomers call it the parallax method, and surveyors and navigators call it triangulation. The top graphic explains the geometry involved.

Note how the line of sight to Alpha Centauri points in different directions depending on where Earth is in its orbit around the Sun. The red star is representative of any star so far away that it does not appear to move over a year of observation. The parallax angle shown is WAY larger than reality. For Alpha Centauri at a distance of 4.1 light years (268,000 AU):

θ = tan-1(2 AU / 268,000 AU) = 0.00043° = 1.5″ (arcseconds)

where 1″ = 1/3600 of 1°. That’s a very tiny shift in position. It’s invisible to the eye but can be measured with a telescope. The animation below shows an exaggerated view what parallax shift looks like from the Earth frame of reference as Earth moves around its orbit. In this case, the white star lies in the plane of Earth’s orbit, but in general, the shifting star traces out an elliptical path where the major axis of the ellipse equals θ:

A shift of 1.5″ isn’t much when you consider the Full Moon has a diameter of 1800″. Fortunately, the best Earth-based telescopes can measure parallax to a precision of 0.01″, and space telescopes to 0.001″. With 0.001″ precision, we can measure the distances of stars out to a few thousand light years — a spherical volume that contains about a billion stars. This is thanks to data from Gaia, ESA’s space telescope.

For more distant stars different methods are employed. The farther out you go, the more indirect the methods, and the more uncertain the calculated distances. Those methods are beyond the scope of this post, but if you’re interested take a look at the cosmic distance ladder.

Next Week in Sky Lights ⇒ Artificial Gravity

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4 comments on “Q&A: How We Measure the Distance to a Star”

  1. Hi Mr. Heim,
    Celestial navigation is based on the FACTS that all stars are equal-distant from Earth and the Earth is flat. It has been 60 years, however, I’m sure of my FACTS.

    1. Greetings Bob. Good to see you’re still a regular reader. Can’t imagine you’re learning a whole lot that’s really new to you. I doubt that stellar parallax ever threw off anyone’s celestial navigation. If it does, just use a more distant star. 🙂

      And watch out for that CAPS LOCK key.

  2. Thank you very much Sir, for sure you make me to wonder a little bit because before reading you’re article I always ask my self lots of questions about how to measure distance of the objects like star and many other up there, but thanks that you make my queues with the right answer, once again l really appreciated you Sir for what you’re always doing. Keep it up, and welcome to Tanzania so that you can share with us much much good that you have at (MMAO).

    1. Thank you Eliatosha. I’m glad this question was asked during our phone call. It’s one of those questions so basic to astronomy that I never really thought about it until you brought it up. I hope my explanation makes it clear how we find the distance to stars. The mathematics is easy, but it is not obvious for beginners.

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