The Cosmic Distance Ladder - How to Measure Distances in Space

You might have heard before that the nearest star is 4.24 light-years from Earth. Or that the closest galaxy is 2.5 million light-years from the Milky Way. Or even that the most distant observed objects are 33.8 billion light-years away. But how do we measure these distances in space? After all, there’s no such thing as a cosmic ruler. That’s where the cosmic distance ladder comes in.

The cosmic distance ladder is a succession of various methods used to measure the distance to all sorts of objects in the universe. No single rung on this ladder is good enough to measure the distance to any given object, but when combined together, the universe becomes measurable. The distance ladder is built by measuring the distance of the closest objects and using them as points of reference to calibrate other measurement techniques for further objects, then using those methods to calibrate more methods for even more distant objects, and so on.

Direct Measurement

The very bottom rung of the ladder consists of objects to which we can directly measure the distance. The exact distance between the Earth and other objects in the Solar System, such as Venus, can be measured using radar. Then, using the known relationship between Earth, Venus, and the Sun from Kepler’s Third Law, we can determine the distance to the Sun from Earth. Using this known precise orbital distance, an astronomical unit, we can begin to work our way up the cosmic distance ladder.

In order to measure the distance to nearby stars, astronomers use the parallax method. By taking two images of a nearby star six months apart, that same star will be imaged as seen from two opposite sides of Earth’s orbit around the Sun, a known distance. When viewed from two different angles, closer objects will appear in a different location compared to further objects. This is what causes close buildings and trees to seem to pass by fast while driving, while distant mountains remain still. By knowing the distance between the two observations (the diameter of Earth's orbit) and measuring the shift in the star's position, you can use trigonometry to calculate the distance. With this method, we can determine the distance of stars up to tens of thousands of light-years away.

The effects of parallax. How one closer star appears relative to further stars depending on the location of the Earth around the Sun. Image Credit: NASA/ESA, A.Feild/STScI

Standard Candles

But the Milky Way galaxy stretches on for 100,000 light-years. We need to step further up the ladder to measure the more distant stars at the opposite edge and beyond. Now we need what are known as standard candles. A Cepheid variable star is a type of star that pulses brighter and dimmer with a specific period. More importantly, the period over which it pulses is directly related to how bright it is. Using this known relation, if we measure how long it takes a Cepheid to brighten fully from its dim state, then we know exactly how bright it should be at its most luminous. Knowing how bright it shines is what makes it a standard candle. The light we see from an object decreases with distance at a known rate, as dictated by the inverse-square law. By calculating the distance to a nearby Cepheid using parallax, we can determine how bright it would appear if we were right next to it. Since all Cepheid variables follow the same pattern, we can now look at any given Cepheid variable, measure how bright it looks to us, compare that to how bright it should be, and accurately calculate how far away it must be for us to see it as we do. Looking at Cepheid stars in the Andromeda galaxy is how we determined it’s 2.5 million light-years away.

But as the galaxies we observe get further and further, it gets difficult to make out the light of individual stars. We need an even brighter standard candle to measure the distance. That’s where supernovae come in. A supernova is an incredibly powerful explosion produced from a star. Most often, you’ll hear of supernovae that occur at the end of a star’s life. Those are called Type II supernovae. A different kind of supernova is the Type Ia, which occurs when a white dwarf, the stellar remains of a dead star, takes on material from a neighboring star and suddenly becomes massive enough at about 1.4 times the mass of the Sun to undergo a supernova. As this explosion always occurs to white dwarfs at roughly the same mass, they will always peak with roughly the same brightness. That means they can be used as a standard candle. By measuring the brightness of a Type Ia supernova, with distance known thanks to a Cepheid variable, we know exactly how bright such a supernova should be, and can determine the distance to even further out galaxies if we spot a Type Ia supernova within one of them. This allows us to measure the distances to galaxies up to about 10 billion light-years out.

The galaxy NGC 4526, a spiral galaxy approximately 55 million light-years away. While individual stars in it aren't visible, the bright light at the bottom left is a Type Ia supernova within the galaxy, helping to measure the galaxy's distance. Image Credit: NASA, ESA, The Hubble Key Project Team, and The High-Z Supernova Search Team

The Final Rung

The final rung on the cosmic distance ladder is redshift. The doppler effect is what causes sound waves to sound higher or lower pitch if an object is traveling towards or away from you. If you’ve heard a siren on an ambulance as it passes you, you might have noticed the siren starts off sounding high pitch when moving towards you, slowly becomes normal as it passes, and then gets lower pitch as it moves away from you. This occurs because sound is a wave, and the shorter the wavelength, the higher pitch it sounds. An object moving towards you will seem to have its wavelength condensed, while an object moving away will seem to have its wavelength stretched. As light is also a wave, an analogous process applies. Of visible light, red light has the longest wavelength, so an object moving away from you at extremely high velocities will seem to emit light that is closer to red than it would if it were standing still. This is called redshift.

The light of a galaxy shines at specific known wavelengths. If the wavelengths we actually see are longer than what we expect, then we know the galaxy is moving away from us. When Edwin Hubble, origin of the Hubble Space Telescope's name, was observing galaxies with known distances from earlier rungs on the ladder, he noticed that there was a relationship between the redshift of a galaxy and its distance from us. The further the galaxy was, the greater the redshift, meaning the faster it was moving away. This became known as Hubble’s Law, and is considered evidence of the Big Bang, as the galaxies all moving away would be the result of the expansion at the beginning of the universe. Since there was a constant correlation between distance and redshift, that means by measuring the redshift of galaxies too far away for even type Ia supernovae to be visible, we can determine the distance. This is how we’ve measured the distance to objects such as MoM-z14, the most distant currently known object.

Measuring our universe was like solving a puzzle. Every piece we fit into place allowed us an even deeper look into the cosmos. Climbing the cosmic distance ladder little by little has allowed us to measure objects at distances unfathomably far away from us and helped to make the universe just a little more comprehensible.