How do we measure the distance of stars?
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Understanding the vast distances between stars has long been a challenge for astronomers. However, thanks to ingenious methods like the parallax technique, we've been able to unlock the mysteries of celestial distances with remarkable precision. In this article, we delve into the parallax method, its principles, historical context, and practical applications.
What is the Parallax Method?
Imagine holding your thumb out at arm's length and closing one eye. Now, alternately open and close your eyes. You'll notice your thumb appears to shift against the background, seemingly moving relative to more distant objects. This apparent shift is the basis of the parallax method.
Another relatable example of parallax can be experienced during a journey by car or train. Notice how distant mountains appear to move slower than nearby objects. This effect is due to the difference in their distances relative to your position, akin to the shifting of stars observed in the parallax method.
Similarly, as the Earth orbits the Sun, nearby stars appear to shift against the backdrop of distant stars due to changes in perspective. This apparent change in position, known as parallax, allows astronomers to calculate the distance to nearby stars.
In the above diagram, the position of the red star changes apparently against the background when viewed at different time intervals. The maximum change in position occurs when the interval is of 6 months, i.e. when the earth has made half a revolution.
Why take these “Background Stars” as Reference Points?
In the vast expanse of space, distant stars serve as fixed reference points against which the apparent motion of closer stars can be measured. Any stars that did not move between observations are, for the purpose of the accuracy of the measurement, infinitely far away. This means that the distance of the movement of the Earth compared to the distance to these infinitely far away stars is, within the accuracy of the measurement, negligible.
Measuring Parallax Angle
The key to utilizing the parallax method lies in accurately measuring the parallax angle, which is the apparent shift of a star against the background. This angle is typically measured in arcseconds, with one arcsecond being 1/3600th of a degree. The smaller the parallax angle, the greater the distance to the star.
How to measure the parallax angle p?
The (apparent) movement of star makes a small line segment (or an ellipse if recorded more than two times) on the photographs recorded by the telescope.
Now, from the telescope properties we can know how much angle of the sky is covered in one view. Using that we find out what angle is the major axis of the ellipse making. That angle is twice the parallax angle p.
Knowing the parallax angle p, we can use simple trigonometry to find out the distance d. Tangent of angle (p) = 1 AU/d
Parsec: A common unit of measurement
We would like to take this opportunity to also share with you a very common unit of astronomical distance measurement — parsec. A parsec is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond. The word parsec is a portmanteau of "parallax of one second" and was coined by the British astronomer Herbert Hall Turner in 1913.
One parsec is approximately equal to 3.26 light-years. Proxima Centauri, the nearest known star to earth other than the sun, is about 1.3 parsecs away by direct parallax measurement.
Historical Context
The concept of stellar parallax was first proposed by the ancient Greek philosopher Aristarchus in the 3rd century BCE. However, it wasn't until the 19th century that astronomers achieved significant accuracy with this method. The first successful stellar parallax measurements were done by Thomas Henderson in Cape Town South Africa in 1832–1833, where he measured the parallax of one of the closest stars, Alpha Centauri.
Limitations
Parallax angles of less than 0.01 arcsec are very difficult to measure from Earth because of the effects of the Earth's atmosphere. This limits Earth based telescopes to measuring the distances to stars about 1/0.01 or 100 parsecs away.
Space-based telescopes can get an accuracy of 0.001, which has increased the number of stars whose distance can be measured with this method. However, most stars even in our own galaxy are much further away than 1000 parsecs, since the Milky Way is about 30,000 parsecs across. So, you can well appreciate the ingenuity of scientists and engineers to come up with new methods for knowing more about such far-away objects.