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The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos(h) = 1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
More exactly, sidereal time is the angle, measured along the celestial equator, from the observer's meridian to the great circle that passes through the March equinox (the northern hemisphere's vernal equinox) and both celestial poles, and is usually expressed in hours, minutes, and seconds.
For example, if a star with RA = 1 h 30 m 00 s is at its meridian, then a star with RA = 20 h 00 m 00 s will be on the/at its meridian (at its apparent highest point) 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation , is similar to right ascension but increases westward rather than eastward.
According to the definitions of the angles on the celestial sphere GHA = GAST − α (see hour angle) where: GAST is the Greenwich apparent sidereal time (the angle between the apparent vernal equinox and the meridian in the plane of the equator). This is a known function of UT. [29]
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.
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 ...
In the star chart to the right, declination is shown by the radial coordinate, starting at 90° north in the center and decreasing to 30° north at the outer edge. Sidereal hour angle is shown as the angular coordinate, starting at 0° at the left of the chart, and increasing counter-clockwise.
An object's right ascension and the local sidereal time can be used to determine the time of its culmination (see hour angle). The term meridian comes from the Latin meridies , which means both "midday" and "south", as the celestial equator appears to tilt southward from the Northern Hemisphere .