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Although ERA is intended to replace sidereal time, there is a need to maintain definitions for sidereal time during the transition, and when working with older data and documents. Similarly to mean solar time, every location on Earth has its own local sidereal time (LST), depending on the longitude of the point.
The local hour angle (LHA) of an object in the observer's sky is = or = + where LHA object is the local hour angle of the object, LST is the local sidereal time, is the object's right ascension, GST is Greenwich sidereal time and is the observer's longitude (positive east from the prime meridian). [3]
The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. [2] [3]: 14
On a prograde planet like the Earth, the sidereal day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). More simply, 1→2 is a complete ...
As seen from above the Earth's north pole, a star's local hour angle (LHA) for an observer near New York. Also depicted are the star's right ascension and Greenwich hour angle (GHA), the local mean sidereal time (LMST) and Greenwich mean sidereal time (GMST). The symbol ♈︎ identifies the March equinox direction.
The equation of time — above the axis a sundial will appear fast relative to a clock showing local mean time, and below the axis a sundial will appear slow.. Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude.
The equation can also be derived from the Ascendant at the equator (=0º). Longitude of East Point as function of Local Sidereal Time Angles in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure must be converted to decimal before calculations are performed.
The observer position vector (in Equatorial coordinate system) of the observation points can be determined from the latitude and local sidereal time (from Topocentric coordinate system) at the surface of the focal body of the orbiting body (for example, the Earth) via either: