Standard ruler

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A standard ruler is an astronomical object whose approximate size is known. By measuring its apparent angular diameter in the sky, one can determine its distance from Earth.

An object with a known diameter would look smaller at farther distances, the angular size being proportional to the inverse of the distance to the object. The distance to the object can therefore be estimated by knowing its actual diameter and measuring its angular size.

The angular diameter of a spiral galaxy, for instance can be easily measured by observation. The size of such galaxies are approximately known and do not differ very much. One can therefore use their size, and the angular size that is measured to estimate their distance. The relation of the angular diameter, actual diameter and distance is given by:

 \alpha = \frac{ 648000 }{ \pi } \frac{ D }{d }

where α is the angular diameter measured in arc seconds, D is the actual diameter of the galaxy and d is the distance of the galaxy to the observer.

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