# How do we measure the distances to stars?

The tools and techniques we use to measure even the largest distances on earth are almost completely useless in space. The stars, galaxies and other objects we see in the night sky are simply too far away from us for these methods to work. Measuring these immense distances therefore often comes down to calculations and deductions. It is perhaps better to say that we calculate or compute the distance to a star, than to say we measure it.

# Parallax

The first technique we can use to calculate the distance to a celestial body relies on parallax, which is the apparent change in the position of a stationary object due to a change in the position of the observer. We experience this in a car, where trees on the side of the road seem to move due to our motion. You may have noticed however that the farther away an object is from us, the less it seems to move, to the point where very distant objects like stars appear completely unaffected by parallax. This is because the distance required to cause a significant change in the viewing angle is proportional to the distance between us and the object. Although no amount of distance we travel on the earth could ever be enough to produce a noticeable parallax in stars, we can utilize the motion of the earth itself to do so.

The earth’s orbit has a massive diameter of nearly 300 million kilometres. So, by clicking two pictures, one at any given day, and the second exactly six months after the first one, we essentially get two viewpoints 300 million kilometres away from each other. This is enough to make the parallax noticeable for some of the nearer objects when they are viewed against more distance stars.

Since we know the distance between the earth and the sun** and can calculate the parallax angle from the two images, we can use some basic trigonometry to calculate the distance between the earth and the star.

The parallax method requires viewing nearer stars against more distant background stars, and thus only works for stars within a range of around 1000 light-years from the earth. Although a 1000 light-years is a tiny tiny fraction of the observable universe, there are a lot of stars in this region around us which we can study in great detail.

## Beyond the parallax

Deducing distances beyond a 1000 light years requires measuring the brightness and luminosity of stars accurately. The luminosity of an object is its absolute brightness, or a measure of how much energy the object radiates in a given time. The brightness, or more accurately the apparent brightness, is how bright the object appears to us, which changes with a change in distance, with farther objects appearing dimmer.

By studying the stars close to us, we have been able to classify stars into many different types depending on their color, temperature, size and (apparent) brightness. For example, hot blue stars, as their name suggests, are blue in color, with temperatures exceeding 10000 kelvin, while yellow stars, like our sun, burn at around 6000 Kelvin with a yellow light.

Similar stars have similar luminosities, or in other words, they put out the same amount of energy in a given time, but their apparent brightness differs based on how far each one is from us. The apparent or observed brightness is inversely proportional to the square of the distance.

Apparent brightness = Luminosity / 4𝛑d2

A star that is twice as far away will appear four times as dimmer.

Using parallax, we can calculate the distance to some of the closer stars as we have already seen. If we compare such a star with a star of the same type but much farther away, we can compare their brightness to deduce the distance to the second star using the equation highlighted above.

This method is only limited to stars however, and only those in our own galaxy. Calculating distances to other cosmic objects, like nebulae or black holes often involves approximations in relation to nearby stars, and involves a variety of techniques including photometry.

Measuring distances to other galaxies requires different methods, many of which rely on measuring smaller distances accurately. These methods collectively form the Cosmic Distance Ladder, where each successive rung is based on the previous rung. I think this is a fairly common theme in physics, and science in general, which is probably why many advanced concepts and ideas seem so absurd at first glance. It really makes you wonder about how vast the expanse of our collective knowledge really is.

**Here’s a great article on how we calculated the Earth-Sun distance:

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## More from Ayush Gurule

Hey! I write about astrophysics and science and a bunch of other stuff I like!

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## Ayush Gurule

Hey! I write about astrophysics and science and a bunch of other stuff I like!