Astronomical parallax – How are distances measured in the universe?

“The space is big. Really big. I can’t believe how disproportionate, unimaginable, breathtaking it is. You might think the distance between your house and the pharmacy is long, but it’s nothing compared to the space.

This sentence in the introduction to The Hitchhiker’s Guide to the Galaxy by Douglas Adams shows in a very funny way how big our universe is. And when we talk about astronomical distances, we cannot use a measuring tape 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 apparent position of the same object as seen from two different points. From this measurement we can calculate the distance to it using very simple math.

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

[ Observação da paralaxe do dedo esticado em relação ao plano de fundo – Fonte: spot.pcc.edu ]

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

For example, if two astronomers observe the Moon at the same time from two distant locations on Earth, they will notice a slight difference in its position relative to the background stars. This difference can be measured in degrees because the observed directions form a triangle, with the Moon at one end and the observers at the other. Since the distance between the observers is known, we can use trigonometry to calculate the distance to the Moon.

This is a very simple and very effective method, but it has a problem: the further away the object is, the smaller the angle formed by the two aiming points, until the point where this angle tends to zero. In order to calculate larger measurements, we must therefore have a larger distance between the observers.

Fortunately, the Earth orbits 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 look at a star’s position today and compare it to its position in 6 months when Earth is on the other side of the solar system, we can measure the star’s parallax at a distance between observers twice the distance between Earth and the Earth’s Sun, or about 300 million kilometers.

1663150507 819 Astronomical parallax - How do we measure distances in the universe
[ Como é calculada a distância (d) de uma estrela próxima a partir da medida da paralaxe (p) tomada pela observação do astro em diferentes épocas do ano – Imagem: Marcelo Zurita ]

But even for nearby stars, the parallax is very small, measured on the order of milliseconds of an arc. Remember that 1 arcsecond is the sixtieth of 1 arcminute, which is the sixtieth 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 only 747 milliseconds of arc. From this measurement we can say that the distance to Alpha Centauri is 1.338 Parsec, where 1 Parsec is equal to the distance of an object with a parallax of 1 second of a degree, measured with observations that are at the same distance between Earth and the Earth’s Sun. 1 Parsec corresponds to 3.26 light years or approximately 30.9 trillion kilometers.

A curiosity in this regard is that astronomers began to measure the distance to stars using parallax even before they knew precisely the distance to the Sun, the basic measurement for this calculation. Finally, the measurements were calculated by Astronomical Units (AU)where an astronomical unit is equal to the distance between the Earth and the Sun, which was not originally known.

Later, when the astronomical unit has been calculated, we can finally know the distance to the stars in our universe. At least the closest ones. The distances of the most distant objects are calculated in a different way using the so-called Cepheid variables. But it is undoubtedly worth another case.

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