A standard ruler is an

astronomical Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include ...

object for which the actual physical size is known. By measuring its angular size in the sky, one can use simple

trigonometry Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The fiel ...

to determine its distance from

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

. In simple terms, this is because objects of a fixed size appear smaller the further away they are. Measuring distances is of great importance in

cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...

, as the relationship between the distance and

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...

of an object can be used to measure the expansion rate and geometry of the Universe. Distances can also be measured using

standard candles The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible ...

; many different types of standard candles and rulers are needed to construct the

cosmic distance ladder The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible ...

. Baryon acoustic oscillations are considered to be essential standard rulers for measuring large-scale structures in the universe.

Relationship between angular size and distance

The relation between the angular diameter (θ), actual (physical) size (r), and distance (D) of an object from the observer is given by: :

D \approx \frac

where θ is measured in

radians The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

. Because space is expanding, there is no single unique way of measuring the distance between source and observer. The distance measured by a standard ruler is known as the

angular diameter distance Angular may refer to: Anatomy * Angular artery, the terminal part of the facial artery * Angular bone, a large bone in the lower jaw of amphibians and reptiles * Angular incisure, a small anatomical notch on the stomach * Angular gyrus, a regi ...

. Standard candles measure another type of distance called the

luminosity distance Luminosity distance ''DL'' is defined in terms of the relationship between the absolute magnitude ''M'' and apparent magnitude ''m'' of an astronomical object. : M = m - 5 \log_\!\, which gives: : D_L = 10^ where ''DL'' is measured in parsecs. ...

References

{{Reflist Astrometry Length, distance, or range measuring devices

Relationship between angular size and distance

See also

References