A standard ruler is an

astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies ...

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 that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...

to determine its distance from

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

. 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 term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...

, 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 simultaneous increase in f ...

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

Relationship between angular size and distance

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

\theta \approx \frac{D}

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. The unit was formerly an SI supplementary unit (before that c ...

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

angular diameter distance In astronomy, angular diameter distance is a distance defined in terms of an object's physical size, x, and its angular size, \theta, as viewed from Earth: d_A= \frac Cosmology dependence The angular diameter distance depends on the assumed cos ...

. 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. F ...

Relationship between angular size and distance

See also