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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 ) of a radian.
The daily arc path of an object on the celestial sphere, including the possible part below the horizon, has a length proportional to the cosine of the declination.Thus, the speed of the diurnal motion of a celestial object equals this cosine times 15° per hour, 15 arcminutes per minute, or 15 arcseconds per second.
Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars". [ 1 ] Viewed from the same location , a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day (also known as the sidereal ...
The rotation rate of the Earth (Ω = 7.2921 × 10 −5 rad/s) can be calculated as 2π / T radians per second, where T is the rotation period of the Earth which is one sidereal day (23 h 56 min 4.1 s). [2] In the midlatitudes, the typical value for is about 10 −4 rad/s.
The ancient Greek astronomer Hipparchus noted the apsidal precession of the Moon's orbit (as the revolution of the Moon's apogee with a period of approximately 8.85 years); [4] it is corrected for in the Antikythera Mechanism (circa 80 BCE) (with the supposed value of 8.88 years per full cycle, correct to within 0.34% of current measurements). [5]
(1) τ E = 1/ν E = A/(C − A) sidereal days ≈ 307 sidereal days ≈ 0.84 sidereal years ν E = 1.19 is the normalized Euler frequency (in units of reciprocal years), C = 8.04 × 10 37 kg m 2 is the polar moment of inertia of the Earth, A is its mean equatorial moment of inertia, and C − A = 2.61 × 10 35 kg m 2 .
The first is the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion is north, 90 degrees meaning the motion is east, (left on most sky maps and space telescope images) and so on), and the second is its magnitude, typically expressed in arcseconds per year (symbols: arcsec/yr, as/yr, ″/yr, ″ yr −1) or ...
At the time, a new standard epoch was accepted; followed later [7] [8] by a new reference system with fundamental catalogue , and expressions for precession of the equinoxes, and in 1979 by new expressions for the relation between Universal Time and sidereal time, [9] [10] [11] and in 1979 and 1980 by a theory of nutation.