The distance of stars from our Earth is calculated using some assumptions and a bit of geometric knowledge. The most known method is "parallax". When we align our finger with a distant object and look at it first with our left eye and then with our right eye, we see that our finger changes position relative to the distant object, and this change in position increases as the finger gets closer to the eyes. When the distant object is taken as a reference, there is a trigonometric relationship between this change in position and the distance of our finger from our eyes.

Parallax can be defined as the fact that a star, when observed from either side of the Earth and the Sun, appears in different positions relative to the background stars at a certain angle value. A similar method is used when measuring the distance of stars. First, the star whose distance from us is to be measured is observed from two different points. Then, using the distance between the two points and the angles at which the star is seen from these points, the distance of the star from Earth is calculated. When driving a car on the road, you get the feeling that you are passing objects that are closer to you faster. For example, when looking at a tree right next to the road and a mountain quite far away, the tree seems to be speeding past you, while the mountain appears almost motionless.                                        

Because even the closest stars, excluding the Sun, are very far away, the distance between two points used in parallax calculations must be as large as possible. Therefore, the parallax method usually utilizes the Earth's movement around the Sun. The Earth orbits the Sun in approximately 365 days. Due to this movement of the Earth around the Sun, the Earth shifts slightly relative to the stars.

When there are six months between two observations, the distance between the observation points is approximately 2 AU, which is the maximum distance we can obtain between our observations. The distance between these two positions of the Earth is 2 AU. Thus, we can obtain two images of a star with a 6-month interval.

If a significant difference can be obtained between the angles measured as a result of the observations, the distance to the star can be calculated using the acute angle of the triangle whose vertices are the Earth, the Sun, and the star whose distance is to be determined, and therefore using simple trigonometric operations. Returning to the bridge example, we see that trigonometry can also be used for stars. The parallax method is based on the principle that objects appear to "displace" when viewed from different points. To explain it in its simplest form, bring your thumb to eye level and focus on a distant object. Look at the object first with one eye, then with the other. Your thumb will appear to be displacing.

Since the parallax angle is small, its unit is usually given as arc seconds, and this angle gradually decreases as the distance of the stars increases. When parallax values ​​approach 0.02 arc seconds, measurement errors begin to appear and the method loses its reliability. However, even if measurements are taken from points 2 AU apart, with today's technology we cannot determine the distance between us and stars that are further than 3000 parsecs (~10,000 light-years) using the parallax method. The European Space Agency (ESA) is working to determine the distance of stars much further than 3000 parsecs using the parallax method. Research using the Gaia satellite is expected to observe 1 billion stars.

Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency, determined and cataloged the distances of more than 118,000 stars at a distance of 1600 light-years using the parallax method. The Gaia satellite, also launched by the European Space Agency in 2013, continues to observe stars tens of thousands of light-years away, achieving precisions of one hundred-thousandth of an arc second.

Directly measuring the distances of stars is impossible. Even the closest star to us is 4 light-years away, and traversing this distance is impossible. How is the distance of stars measured using the parallax method? I would appreciate it if you could explain it in a simple way that everyone can understand. Now that we've found the distance to the Sun (which we'll explain in another article), we can apply the same technique to other stars.

1 Astronomical Unit (AU) corresponds to the average distance of the Earth from the Sun, which is 149.6 million kilometers.

The most commonly used unit of length in astronomy is the "light-year," which indicates the distance light travels in one year. One light-year is approximately 9 trillion kilometers. Another unit of length preferred by astronomers is the "parsec." This unit, which corresponds to approximately 3.26 light-years, can be expressed as follows:

Since the parallax (π) angle is obtained from observations in arc seconds, we obtain the relationship d(pc) = 1 / π (arc.s).

The parallax of Proxima Centauri, the closest star to us, is 768 mas (milliarcseconds). This is the amount of shift measured as a result of observations. However, we need the arcsecond value, which is 0.768 arcseconds due to the ratio of 1 in 1000. Applying our simple geometric calculation, we get d=1/0.768, which gives us d=1.3. However, Proxima Centauri is approximately 4.22 light-years away from us. The reason the result is different is because, as mentioned above, the result is in parsecs. 1.3 parsecs = 1.3 x 3.26 = 4.24 light-years.

While the actual distance is determined using the parallax method, the trigonometric relationship can also be used for stars.

Distance measurements are easy in everyday life; we can easily measure the length of a table using a simple ruler. However, as distances decrease or increase, the accuracy of our rulers becomes insufficient. We cannot measure the distance of the Sun from the Earth with any ruler. Distance measurements in the universe can be grouped under 5 headings: for the Solar System, nearby stars, the Milky Way and nearby galaxies, other galaxies, and very distant objects. Distance measurements in the Solar System can be made using radar techniques and the reflection property of light: First, a light wave is sent to the object whose distance is to be measured. The light hits the object; some of it is reflected back to Earth, and thus the reflected light travels the distance to be measured twice. For distance measurements of nearby stars, the parallax method fulfills this requirement.