Measuring Distance

Units of Distance

Astronomical Units (AU)

Astronomical units (AU or au) are a common unit to measure distances in space. These units are primarily used for measuring distances within the Solar System. The length of an astronomical unit is roughly the average distance from the Earth to the Sun. It is considered an average because Earth orbits around the Sun and throughout this orbit the distance between the Earth and the Sun varies by around 3% (“Astronomical Unit,” n.d.). The distance from Earth to the Sun is around 150 million kilometers.

Astronomical units are a convenient way of comparing distances of objects from the sun. For example, Jupiter is 5.2 AU from the Sun and Pluto is nearly 40 AU. With astronomical units we can easily tell that Pluto is roughly 7.5 times further away from the Sun compared to Jupiter. One way to find out the distance of the Earth to the Sun (AU) is by using the parallax method.

Parsecs (pc)

The parsec is defined as the distance to an object whose parallax angle is one arcsecond (Florida State College). An arcsecond is 1/3600 of a degree, or alternatively 1/60 or an arcminute. The relationship between the distance in parsecs, d, and the parallax angle in arcseconds, p, can be described in the formula . For example, an object with a parallax angle of 2 arcseconds would be 0.5 parsecs away. An object with a distance of 4 parsecs would have a parallax angle of 0.25 arcseconds.

Parsecs are used to measure the distances to objects outside our solar system. Though many people would prefer using light-years, most astronomers prefer use parsecs to describe distance, as the distance in parsecs can be easily determined using the parallax angle. One parsec is roughly 3.26 lightyears. Multiples of parsecs like the kiloparsec, 1000 pc; and megaparsec, 1 000 000 pc are used for larger distances.

Light-years (ly)

A light-year (ly) is the distance light travels in a vacuum in one year or how far it would travel in space in a year. A light-year is calculated using light’s accepted velocity of 299,792,458 m/s (186,282 miles per second). Thus, a light-year is about 9.46 trillion kilometres, 6 trillion miles or around 63,241 astronomical units. About 3.262 light-years equal one parsec.

A light-year is extremely useful as it allows us to get a rough estimate as to how long ago an event has happened. This is a reason why many use light-years when measuring in astronomy and why it is more commonly heard. Here the context of light-years is used to allow astronomers and others to know how far back in time they are viewing. So, if you are viewing something one light-year away, you are receiving the light emitted or reflected off the object one year ago.

Kilometres (km)

Sometimes we use metres and kilometres to describe the distances between objects in space. Metres and kilometres are a conventional way to show distances here on Earth, so referring to these terms may allow others with less astronomical knowledge to better grasp of the distance between objects.

Methods of Measuring Distance

Stellar Parallax

Not to scale. The parallax angle is half of the purple curve in this diagram. The blue dot represents Earth.

Stellar parallax is used to measure the distance between stars and our solar system. Parallax is the phenomenon where an object changes its apparent position relative to an observer, specifically as a result of the observer changing position while the object remains stationary. Organisms with binocular vision use parallax to sense depth from the two signals of two-dimensional images coming from their eyes. Stellar parallax is the same effect, but on the scale of celestial bodies. To determine depth, two perspectives must be compared. To get two distinct perspectives of the celestial object, two pictures are taken six months apart, so that the difference in the Earth’s position is the largest at approximately two AU. A line drawn from the Earth’s position to the Sun should be perpendicular to the object during these measurements. The greater the difference in the observer’s position, the easier parallax will be to decipher. With the Hubble Space Telescope, precise distance measurements can be taken up to 10,000 light-years away (9.5 x 10¹⁶ km) (Northon, 2014).

Cosmological Redshift and Blueshift

Redshift and blueshift describe how the wavelength of light from a luminous object changes depending on the velocity that the object is moving relative to the observer. It is a form of the Doppler Effect, a phenomenon in which the frequency of a wave is affected by the relative motion of a source to an observer, first described by physicist Christian Doppler (“Doppler effect,” n.d.).

Because light can be modeled as a wave (“Light as a Wave,” n.d.), it is affected by this shift. Luminous objects, such as stars and galaxies, moving towards or away from Earth will have their light received at a shorter or longer wavelength, respectively. Light emitted from a luminous object moving away from Earth will appear to be of a longer wavelength than if the object was still, relative to Earth, and vice versa. In the visible spectrum, light would appear more red or blue, hence the name. Using this knowledge, the velocity of luminous objects in space relative to Earth can be determined by comparing the expected spectrum with the measured spectrum. However, this relative motion can be used to determine distance. Due to the expansion of space as described by Hubble’s Law, light travelling through space will be lengthened in wavelength, or redshifted. Hubble’s Law describes the dominant motion of the universe as expansion, where the space between objects is increasing. More about Hubble’s Law can be read here. This velocity at which objects are appearing to move away from Earth increases with distance at a calculatable rate, so if the velocity is determined with redshift then the distance from Earth can be determined too.

Radar Astronomy

Radar astronomy is “the study of celestial bodies by examination of the radio-frequency energy they emit or reflect” ("Radio and radar astronomy", n.d.). Radio waves can pass through gases and planetary atmospheres, including the earth’s, with very little distortion. So, because of the minor distortions radio waves give astronomers a much clearer image of distant stars and galaxies. This is especially useful when distant objects are too far away for optical or visual observation. As our technology develops, the well-known radio telescopes will be able to detect fainter/weaker radio sources and receive or make out an image of better resolution or quality.

Receiving data and being able to make-out the details of a distant object also allows us to get a rough estimate of the distance between earth and the object.

Cepheids

Cepheids, also called Cepheid Variables, are stars which brighten and dim periodically. The reason behind this is that these special variables or stars increase and decrease in size. In other words, “the case of pulsating variables this is due to the periodic expansion and contraction of the surface layers of the stars” (“Pulsating Variable Stars”, n.d.). Each of these Cephids can be distinguished by their period of pulsation and the shape of their light curves the brighter the Cepheid, the longer its period. Aside from these outstanding aspects of a cephid they are also extremely bright and can be seen from “13 million light-years" away (“Cepheids”, n.d.).

We often use these Cepheids to determine the distance. For example, if an astronomer needed to find the distance from Earth to a galaxy their first step would be to look for a Cepheid in that galaxy. To find the distance from Earth to a Cepheid we need to know that the brighter the Cepheid the longer its period and that as light travels further its brightness decreases (“Cepheids”, n.d.). Precisely, the apparent brightness of a star is proportional to 1 divided by its distance squared. For example, if you took a star with an apparent brightness of X and doubled its distance its new apparent brightness would be .

Using the pulsation period of a Cepheid we can determine the brightness of a Cepheid. Thus using its brightness and its apparent brightness form earth we can determine the distance of the Cepheid to Earth.

References

Astronomical unit. (n.d.). Retrieved February 2, 2021, from https://www.britannica.com/science/astronomical-unit

Cepheids. (n.d.). Retrieved February 2, 2021, from https://starchild.gsfc.nasa.gov/docs/StarChild/questions/cepheids.html#:~:text=Cepheids,of%20millions%20of%20light%2Dyears.

Doppler effect. (n.d.). In Encyclopaedia Britannica. Retrieved from https://www.britannica.com/science/Doppler-effect

Light as a Wave. (n.d.). Retrieved from https://lco.global/spacebook/light/light-wave/

Northon, K. (2014, April 10). NASA's Hubble Extends Stellar Tape Measure 10 Times Farther Into Space. Retrieved from https://www.nasa.gov/press/2014/april/nasas-hubble-extends-stellar-tape-measure-10-times-farther-into-space/

Pulsating Variable Stars. (2020, November 17). Retrieved February 2, 2021, from https://www.atnf.csiro.au/outreach/education/senior/astrophysics/variable_pulsating.html

Radio and radar astronomy. (n.d.). Retrieved February 2, 2021, from https://www.britannica.com/science/radio-astronomy