# How do Astronomers Measure the Distance to the Stars?

#### The distance to nearby astronomical objects, such as the planets in our solar system, can be calculated using radar, but for more distant bodies, this method no longer works.

The nearest star, Proxima Centauri, is 4.24 light years away. A light year is 9.44 trillion km and a journey there would take 43,000 years. So how can we measure the distance to the stars?

Trigonometry gives us the answer. Hold out your hand and close one eye. Now open one eye and close the other. You will notice that the hand has moved against the background. Your two eyes and your hand form a triangle. If we know the distance between the eyes and the angle with which the hand moved, we can calculate the length of the arm. The angle with which the hand moves is called parallax.

Of course, we can measure arm length using a meter, but the parallax method is useful for calculating long distances. Instead of the eyes, as the base of the triangle, astronomers use our planet, in 2 different periods of the year (when it is in opposite parts of the solar system). Using Parallax to measure a star as seen from earth 6 months apart. Credit: ESA Science & Technology. Planetary Sciences, Inc.

Astronomers take one photo at an interval of 6 months to measure, the distant stars, and the deviation of the stars. This method of distance measurement is good for stars located several hundred light-years away. Beyond this distance, this method no longer works because the measured angle is too small to be accurately measured.

In the image, the line of sight to the star in December is different from the one in June when the Earth is on the other side of the Sun. Half of the resulting angle is parallax, and parallax decreases once with distance.

Since even the nearest stars are very far away, the largest measured parallaxes are very small; less than an arcsecond. For example, the nearest star, Proxima Centauri, has a parallax of 0.722 — arcsec, the largest observed parallax.

For larger distances, the photometric parallax method is used — the light of the galaxies is observed and how much it tends to red in the electromagnetic spectrum (galaxies moving away from us tend to be red and those approaching to blue). Thus we can calculate the distance using the Doppler effect.

Cepheids are used to measure the distance to other galaxies. Cepheids are variable stars that have a close correlation between the oscillation period and brightness. The relationship between oscillation and brightness could be established based on Cepheids located close enough to us to use the parallax method. Then, astronomers only had to measure the apparent brightness and the oscillation period to find out the distance. The Cepheid method can be applied both in our galaxy and in nearby ones.

A star with a parallax of one arc-second is at a distance of 3.26 light years. This distance became known as the “parallax of a second”, or parsec for short.