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A minute of arc is π / 10 800 of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol ″, [2] is a unit of angular measurement equal to 1 / 60 of a minute of arc, 1 / 3600 of a degree, [1] 1 / 1 296 000 of a turn, and π / 648 000 (about 1 / 206 264.8 ...
An arcsecond is 1/3600th of one degree (1°) and a radian is 180/π degrees. So one radian equals 3,600 × 180/ arcseconds, which is about 206,265 arcseconds (1 rad ≈ 206,264.806247"). Therefore, the angular diameter of an object with physical diameter d at a distance D, expressed in arcseconds, is given by: [9]
provided the angle is measured in radians. Angles measured in degrees must first be converted to radians by multiplying them by / . These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.
Solid angles can also be measured in square degrees (1 sr = (180/ π) 2 square degrees), in square arc-minutes and square arc-seconds, or in fractions of the sphere (1 sr = 1 / 4 π fractional area), also known as spat (1 sp = 4 π sr). In spherical coordinates there is a formula for the differential,
A solid angle of one steradian subtends a cone aperture of approximately 1.144 radians or 65.54 degrees. In the SI, solid angle is considered to be a dimensionless quantity, the ratio of the area projected onto a surrounding sphere and the square of the sphere's radius. This is the number of square radians in the solid angle.
In Madhava's table, the entry corresponding to 22.50° is the measure in arcminutes, arcseconds and sixtieths of an arcsecond of the angle whose radian measure is the value of sin 22.50°, which is 0.3826834; multiply 0.3826834 radians by 180/ π to convert to 21.92614 degrees, which is
The resulting R is in radians. For example, in the case of yellow light with a wavelength of 580 nm, for a resolution of 0.1 arc second, we need D=1.2 m. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.
The constant term of this speed (5,028.796195 arcseconds per century in above equation) corresponds to one full precession circle in 25,771.57534 years (one full circle of 360 degrees divided by 50.28796195 arcseconds per year) [38] although some other sources put the value at 25771.4 years, leaving a small uncertainty.