standard ruler
{{Short description|Astronomical object of well-known physical size, used to determine distance via trigonometry}}
{{More citations|date=June 2025}}
A standard ruler is an astronomical object for which the actual physical size is known.{{cite web |last=Schirber |first=Michael |url=https://physics.aps.org/articles/v12/s110 |title=A Cosmic Ruler at 21 Centimeters |work=Physics |publisher=American Physical Society |date=26 September 2019 |access-date=4 June 2025}} By measuring its angular size in the sky, one can use simple trigonometry to determine its distance from Earth. 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, as the relationship between the distance and redshift 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.
Baryon acoustic oscillations are considered to be essential standard rulers for measuring large-scale structures in the universe.{{cite web |last=Young |first=Monica |url=https://skyandtelescope.org/astronomy-news/boss-a-ruler-to-measure-them-all-0108201423/ |title=BOSS: A Ruler to Measure Them All |work=Sky & Telescope |date=8 January 2015 |access-date=4 June 2025}}{{cite web |last=Percival |first=Will |url=https://phas.ubc.ca/making-cosmological-measurements-standard-rulers-and-standard-shapes |title=Making cosmological measurements with standard rulers and standard shapes |work=University of British Columbia |date=28 March 2019 |access-date=4 June 2025}}
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:
:
where θ is measured in radians.{{cite book |last=de Grijs |first=Richard |url=https://www.google.com/books/edition/An_Introduction_to_Distance_Measurement/yZCKld0KUeQC?hl=en&gbpv=1&pg=PA181 |title=An Introduction to Distance Measurement in Astronomy |publisher=Wiley |page=181 |date=2011 |access-date=4 June 2025 |isbn=978-1119979807}}
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. Standard candles measure another type of distance called the luminosity distance.
See also
- {{annotated link|Standard candle}}
- {{annotated link|Baryon acoustic oscillations#Standard ruler|Baryon acoustic oscillations}} - standard ruler
- {{annotated link|Standard siren}}
- {{annotated link|Angular diameter distance}}
- {{annotated link|Parallax}}
- {{annotated link|Cosmic distance ladder}}