semidiameter

Semidiameter is a term used in geometry and astronomy to denote half of a circle’s diameter. In astronomy, it more commonly refers to the angular semidiameter, the angular radius of a celestial body’s disk as viewed from an observer on or near Earth.

In geometry, the semidiameter of a circle is simply its radius, the distance from the center to any point on the circumference. It is half of the circle’s diameter and defines many geometric relations and constructions.

In astronomical usage, the angular semidiameter is related to the angular diameter, which is the apparent size of the object on the sky. If an object has angular diameter δ, its angular semidiameter α is δ/2. For a distant spherical body with physical radius R at distance D, the exact angular semidiameter is α = arcsin(R/D). For small angles (common in astronomy), α ≈ R/D radians, so the angular diameter δ ≈ 2R/D.

Examples: the Moon has a mean distance of about 384,400 km and a mean radius of about 1,737 km, giving an angular semidiameter of roughly 0.25 degrees (about 16 arcminutes) and an angular diameter near 0.5 degrees. The Sun, with a similar apparent size, has an angular semidiameter of about 0.26 degrees as well, yielding an angular diameter of about 0.53 degrees.

Applications include estimating telescope resolution limits, planning observations of occultations or transits, and providing a convenient measure of an object’s apparent size in both professional and educational contexts. See also angular diameter, angular radius, and arcminute.