Measuring Astronomical Distances: How Far Does Light Travel?

The vastness of space means that units of measurement that are convenient for everyday use become too large to be practical. For this reason, astronomers use light years to measure the distance that light travels. A light year is the distance that light travels in a year, which is about 6 trillion miles (9 trillion kilometres). This makes it easier to conceptualise the distance between objects in space. For example, Proxima Centauri, the closest star to the Sun, is 4.25 light years away, which is a more manageable figure than 24,000,000,000,000,000 miles.

Standard candles

Astronomers use a range of interconnected techniques, known as the 'cosmic distance ladder', to measure the distance between objects in space. One of the most prominent methods is the use of 'standard candles'.

Where m is the apparent magnitude of the object, M is the absolute magnitude of the object, and d is the distance to the object in parsecs.

The dimmer a standard candle appears compared to its true brightness, the further away it is.

The most commonly used standard candles are Cepheid Variable stars and RR Lyrae stars, where the absolute magnitude of the star can be determined from its variability period. Type Ia supernovae are also considered standard candles, although they are less standardised as they do not all have the same peak brightness. However, their differences in peak luminosities are correlated with how quickly the light curve declines after maximum light, and they can be standardised by correcting for this effect.

Cepheid Variable stars are a class of extremely bright variable stars. Their luminosity is related to the period of their pulsations: longer-period stars are brighter than shorter-period ones. The period-luminosity relation for Cepheids was discovered by Henrietta Leavitt in 1912, who found that the period of a Cepheid variable in the Small Magellanic Cloud is proportional to its average brightness. By measuring the period of a Cepheid, one can deduce its intrinsic brightness from the Leavitt period-luminosity relation, and then calculate its distance using its apparent brightness and the inverse-square law.

Type Ia supernovae are the result of the thermonuclear explosion of a white dwarf star. They are so bright that they can be seen at large distances, and their light curves have a very useful property: the dimmer the peak brightness of the supernova, the faster it drops in brightness in the following weeks. There is a linear relationship between the absolute magnitude of a Type Ia supernova and its drop in magnitude in the first 15 days after its maximum brightness, known as the Δm15(B) relationship. This allows astronomers to convert a simple timing measurement into a brightness measurement, and thus use Type Ia supernovae as standard candles.

Parallax measurements

Parallax is the observed displacement of an object caused by a change in the observer's viewpoint. In astronomy, it is used to measure the distances of far-off stars by using trigonometry.

Here's how it works: if you hold your hand out in front of you and close your right eye, placing your extended thumb over a distant object, then switch eyes so your left eye is closed and your right eye is open, your thumb will appear to shift slightly against the background. By measuring this small change and knowing the distance between your eyes, you can calculate the distance to your thumb.

Similarly, the orbit of the sun provides the baseline for measuring the distance to stars. Every six months, the Earth changes its position with respect to the surrounding universe by 186 million miles (300 million kilometres). We can theoretically observe this shift as tiny circles that stars perform in the sky every year. Due to the vast distances to even the nearest stars, these circles are barely noticeable, so detecting and measuring them is extremely difficult.

The first known astronomical measurement using parallax was done by the ancient Greek astronomer Hipparchus, who used observations of a solar eclipse from two different locations to calculate the distance of the moon.

The first person to succeed at measuring the distance to a star using the parallax method was German astronomer Friedrich Bessel in 1838. He calculated that the star 61 Cygni, in the Cygnus constellation, must be about 10 light-years away from Earth.

The European Space Agency's Gaia mission, launched in 2013, is expected to measure parallax angles to an accuracy of 10 microarcseconds for moderately bright stars, mapping nearby stars (and potentially planets) up to tens of thousands of light-years from Earth.

Redshift

In astronomy, redshift is used to measure the motion of cosmic objects by studying changes in their colour over time or how it differs from what is expected. If an object appears redder than expected, it indicates that it is moving away from the observer, whereas a bluer hue suggests motion towards the observer. This technique is particularly useful for discovering extrasolar planets and studying nearby objects.

The most accurate method to measure redshift is spectroscopy, which involves passing a beam of white light through a prism to separate it into its various components, creating a spectrum. Astronomers then compare the spectra of different elements with the spectra of stars. If the absorption or emission lines in the star's spectrum are shifted, it indicates that the object is in motion, either towards or away from the observer. For extremely distant objects that are too faint for spectroscopy, astronomers employ photometric redshifts, where they observe the peak brightness of the object through various filters.

Furthermore, redshift provides valuable insights into the expansion of the universe. As the universe expands, the space between galaxies also increases, causing distant galaxies to appear as if they are moving away from us at tremendous speeds. This expansion results in a shift of light towards longer wavelengths, known as "expansion redshifts". The concept of redshift is fundamental to our understanding of the cosmos and has far-reaching implications for cosmology and the Big Bang theory.

Astronomical units

The average distance between the Earth and the Sun is 149,597,870,700 metres or 149,597,870.7 kilometres. This definition was established by the International Astronomical Union (IAU) in 2012. The AU is also a fundamental component in defining another unit of astronomical length, the parsec.

For distances beyond the solar system, astronomers use light years and parsecs. One light year is the distance a photon of light travels in one year, which is about 6 trillion miles (9 trillion kilometres or 63,000 AU). Light years are used to measure interstellar distances.

Light years

The light-year was first measured by Friedrich Bessel in 1838, who made the first successful measurement of the distance to a star outside our solar system, 61 Cygni. Bessel mentioned that light takes 10.3 years to travel from 61 Cygni to Earth. However, he wasn't seriously suggesting the idea of light years as a unit of measurement. At that time, the speed of light had yet to be calculated accurately.

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