Method of measuring distances to stars and galaxies

Looking at a star in the sky, which appears only as a small bright dot and estimates its distance, seems very vague.

The question is how do astronomers determine their distances?

Measuring the distance from us to the stars and galaxies in the universe has always been a big problem, a difficult problem even with today's modern equipment.

Modern astronomers have very powerful tools to observe stars and galaxies, but to determine relatively accurately the distance of a star, we do not have any optimal method yet. any.

Often it is necessary to combine several methods or use the measurement results of many times. Here are some commonly used methods.

Simulates ways to measure the distances between the Earth, the Sun, and the Milky Way.

Parallax

This method is commonly applied to nearby stars in our galaxy, located a few hundred or more than 1,000 light-years from the Solar System at most.

To understand what parallax is, try the following common practice: Raise one finger in front of your face, then close one eye, look at it with only one eye, you will see it is located in the same position. certain against the background of the background.

Next, close your eyes and open the other eye without changing the position of the fingertip, now you will see that the position of the finger relative to the background of the background has changed due to the changed viewing angle.

This phenomenon of changing the relative positions of different objects due to this change in viewing angle is called parallax. The above method is very popularly applied in astronomy, people determine the distance of celestial bodies through the change of angle of view with them.

With the Moon and some nearby celestial bodies in the Solar System, the calculation of parallax is done quite simply and quickly. We know that the Earth rotates on its axis every 24 hours. This period is much smaller than the orbital period of the Moon around the Earth and the planets around the Sun.

It can therefore be assumed that in about 12 hours (half a day) the positions of these objects in their orbits do not change. It turned out to be quite easy to simply determine the change in angle of view of the celestial body on the same day by comparing their positions in the starry sky at two times of the day.

The parallax calculation determines the distance of the Moon by observing it at two different times of the day, in which one of the two times is the Moon in a direct position, that is, the direction of view is perpendicular to the tangent to the Earth. the ground at the observer's position.

Because the observer's position changes (because the Earth rotates on its own), at two different times, the observer sees the Moon at different positions against the starry sky.

From there, it was determined that the parallax angle is the angle between the view of the Moon at the initial position relative to the starry sky and the direction of view at a later time. We also know the exact distance between the two observations (the displacement due to the rotation of the Earth).

Thus, we have a right triangle that knows one right angle side and the opposite angle, from which we can calculate the remaining right angle side by a simple trigonometric formula. The other side of this right angle is the relative distance from the Earth to the Moon.

This method also applies to planets in the Solar System, commonly known as the date parallax method (due to its dependence on the Earth's day cycle).

Now imagine pulling the Moon further away from the Earth, then the parallax angle would get smaller, and possibly so small that it could not be measured with the most precise instruments. For this reason the above method cannot be applied to distant stars (The Moon is only 384,000km from us, equivalent to more than 1 light second.

The closest star to the Sun is 4 light years away.) To deal with this situation, astronomers use the wider field of view parallax, often called the year parallax. In fact, today, the distances from the Earth to the Moon and the planets are well known, so the above-mentioned parallax method is no longer necessary.

But the year parallax, also known as the stellar parallax as outlined below, is still quite commonly used for stars a few hundred or even more than 1,000 light-years away from us.

We all know that, in addition to the rotation around its own axis, the Earth has another movement, which is in orbit around the Sun every 365 days.

The average distance from the Earth to the Sun is 1 astronomical unit (au) which is equivalent to 149.6 million km, which means the distance between the two points of Earth's orthogonal hourly point across the Sun, or the distance between two points. Earth's position 6 months apart is about 300 million km.

This distance is many times larger than the distance between two points on the Earth's surface used in the day-by-day parallax method. So astronomers use the change of perspective at these two locations to determine the distances of stars in the galaxy.

At two locations on Earth 6 months apart, an observer on Earth would see a nearby star in the galaxy at a slightly different position against the background of stars and galaxies very far behind.

The angular parallax angle determination is similar to the day parallax method. The difference is that astronomers need to wait up to 6 months between two times to get the measurement results, and often the measurement must be done continuously because even with the distance in Earth's orbit, the angle of view of the stars is still low. very small even with close stars.

In astronomy, parsec is used. One parsec is 3.26 light years. This is the distance corresponding to the parallax in years as an angular second.

That is, if a star is located 3.26 light-years from us, then at two locations 6 months apart of the Earth in orbit around the Sun (provided that the line joining the two locations is perpendicular to the line connecting the two locations). from the star to the Sun) the observer finds his or her angle of view of that star relative to very distant stellar backgrounds varies by only one angular second - 1 3,600th of a degree.

This is a very small number and usually cannot be measured with rudimentary angle instruments.

The closest star to the Sun is 4 light years away, which is more than 1 parsec. That is, its parallax angle is less than 1 angular second. With more distant stars (several tens or hundreds of light-years) this angle narrows even further, so precise measurement requires great care in each measurement.

This parallax method has been known for a long time and was also used by ancient Greek astronomers. An unfortunate and equally funny coincidence is that with the rudimentary tools of that day, they could not measure too small angles and assumed that there was no change in viewing angle.

That immediately became a testament to the geocentric model of the time: the Earth was at the center and the distant stars were fixed on the same fixed sphere (so it was impossible for a star to change position in the same way). for other stars).

The year-by-year parallax method is widely used with stars located within a few hundred light-years, sometimes with some stars more than 1,000 light-years away. It doesn't work with stars many thousands of light-years away, though, or with other galaxies that are millions of light-years away.

Then the parallax angle is so small that it cannot be accurately determined by any device. Even if it could be determined, it would not be able to eliminate error because the stars themselves have motions that make the measurements themselves completely inaccurate.

To measure the distances of distant stars, astronomers need to use other methods or a combination of methods.

The Galactic Distance is calculated in different ways.

Spectroscopic parallax

For distant stars or other galaxies, the parallax method based on the change of perspective cannot be used. Astronomers use a different method called false spectroscopy, which relies on the difference obtained from the star's spectrum to determine the distance.

The Hertzsprung - Russel (HR) diagram is used to divide the stars in the universe based on their obtained spectral colors. From the colors of the spectrum obtained and compared on this chart, one knows which group the star belongs to and its absolute luminosity can be verified with relative accuracy.

Absolute luminosity is the luminosity obtained by any star when observed at a conventional distance of 10 parsecs, which is therefore independent of the star's distance from Earth.

To determine the star's false spectrum, this absolute luminosity is compared with the apparent luminosity. This apparent luminosity is the luminosity of the star that we see every night in the sky. This brightness depends on the distance.

The stars in the galaxy have different distances from us, if two stars have the same absolute luminosity, the more distant star will have a smaller apparent luminosity. Comparing these two brightnesses, astronomers can work out the star's distance.

For galaxies other than stars in our own Milky Way galaxy, the HR chart cannot be used because it is not intended for large aggregates such as galaxies, clusters of galaxies. The erroneous spectroscopy method in this case is taken in the other direction, which is based on Cephied variable stars.

Cephied variable stars are stars in the main sequence of the spectral chart, they are old stars that have reached the end of their lives, with very strong variations in brightness. Astronomers observe the variation in their luminosity in the galaxy from the brightest to the smallest.

Its period of variation tells them the star's absolute luminosity. The comparison here is somewhat more complicated than that of measuring the individual distance of a star because astronomers need a relatively accurate estimate of the total number of Cephied stars in the galaxy and their total luminosity. Usually this is applied to galaxies that are relatively close, namely those in the Local Group.

With cluster galaxies that are so distant, it is difficult to accurately estimate the luminosity of Cephied variable stars. Astronomers use another object of observation, type 1a supernovas - the explosions of stars that have reached the end of their lives that destroy the crust.

Supernovas are much more luminous than Cephied variable stars, whose luminosity has proved to be much easier for relatively distant galaxies.

Hubble's Law

The last method I mentioned is the most common method for measuring distances to distant galaxies today.

In 1929, Edwin Hubble discovered that the separation of galaxies is due to a redshift in their spectrum. This discovery led to the conclusion that we live in an expanding universe, accompanied by Hubble's law about the speed of galaxies moving relative to us.

The formula for this law is as follows: v+Hr where v is the galaxy's displacement velocity, H is the Hubble constant, and r is the current distance of the galaxy.

The Hubble constant has been determined so far with relative precision because it gives a calculation of the age of the universe that is very similar to that calculated from observing the background radiation of the universe. The velocity v can be calculated by tracking the red shift of the galaxy. From this one can immediately calculate the distance r of the observed galaxy.

This method of using Hubble's law is widely used in measuring the distances of distant galaxies. However, it does not apply in the above parallax and spectral use cases, because stars in our same galaxy do not have a distant motion according to Hubble's law, and galaxies too far away. close, there is a small redshift, difficult to determine precisely.