Astronomical Parallax: How Do We Measure Distances in the Universe?

“The space is large. Really big. I can’t believe how disproportionately, inconceivably, incredibly large it is. You might think it’s a long way from your home to the pharmacy, but it’s nothing compared to space. “

This sentence in Douglas Adams’ introduction to The Hitchhiker’s Guide to the Galaxy shows in a very amusing way just how big our Universe is. And when it comes to astronomical distances, you can’t use a yardstick to measure them. One of the most common ways to take these measurements is a very natural method known as parallax.

Parallax is basically the measure of the difference in the apparent position of the same object seen from two different points. From this measure, we can calculate the distance to it using very simple mathematics.

Our brain naturally calculates the distance of nearby objects from parallax. If you hold your finger in front of your eyes, you will see that its apparent position changes with respect to the background depending on which eye you are looking at. Our brain is able to calculate the distance when we look at the finger with both eyes open. This gives us a sense of depth.

And in astronomy we do the same thing, but to calculate the distance to distant objects we need a greater distance between our eyes.

If two astronomers, for example, observe the Moon at the same time from two places distant from the Earth, they will notice a small difference in its position relative to the background of the stars. This difference can be measured in degrees, as the observed directions form a triangle, with the Moon at one end and observers at the other. Since the distance between the observers is known, we can calculate, by means of trigonometry, the distance from the Moon.

It is a very simple and very effective method, but it presents a problem: the farther the object is, the smaller the angle formed by the two crosshairs, up to the point where that angle tends to zero. Hence, to calculate larger measurements, we will need a greater distance between observers.

Fortunately, the Earth is in orbit around the Sun and this allows us to calculate the distance to nearby stars by measuring their position at different times of the year. If we observe the position of a star today and compare it with its position in 6 months, when the Earth will be on the other side of the Solar System, we can measure the parallax of the star with a distance between observers equal to twice the distance between Earth. and Terra Sole, that is about 300 million kilometers.

But even for nearby stars, the parallax is very small, measured in the order of milliseconds of arc. Remember that 1 second of arc is the sixtieth part of 1 minute of arc, which is the sixtieth part of 1 degree. That is, in 1 degree, there are 3600 seconds of arc.

Alpha Centauri, for example, is the closest star system to Earth and its parallax measures just 747 milliseconds of arc. From this measurement we can say that the distance from Alpha Centauri is 1.338 Parsec, where 1 Parsec is equivalent to the distance to an object with a parallax of 1 second of degree, measured with observations that are the same distance between the Earth and the Earth, the Sun. 1 Parsec equals 3.26 light years or about 30.9 trillion kilometers.

A curiosity about it is that astronomers have begun to measure the distance from the stars using parallax, even before knowing the distance from the Sun, the basic measure for this calculation. Finally, the measures were calculated in where an Astronomical Unit is equivalent to the distance between the Earth and the Sun, which was initially not known.

Later, when the Astronomical Unit has been calculated, we can finally know the distances of the stars in our Universe. At least the closest. The distances of the most distant objects are calculated in another way using the so-called Cepheid variables. But this, undoubtedly, is worth something else.

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Source: Olhar Digital