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This plot was created using the simple sunrise equation, approximating the sun as a single point and does not take into account effects caused by the atmosphere or the diameter of the Sun. The sunrise equation or sunset equation can be used to derive the time of sunrise or sunset for any solar declination and latitude in terms of local solar ...
Sunrise seen over the Atlantic Ocean through cirrus clouds on the Jersey Shore at Spring Lake, New Jersey, U.S. Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning, [1] at the start of the Sun path. The term can also refer to the entire process of the solar disk crossing the horizon.
The following formulas assume the north-clockwise convention. The solar azimuth angle can be calculated to a good approximation with the following formula, however angles should be interpreted with care because the inverse sine, i.e. x = sin −1 y or x = arcsin y, has multiple solutions, only one of which will be correct.
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
While the formula can be derived by applying the cosine law to the zenith-pole-Sun spherical triangle, the spherical trigonometry is a relatively esoteric subject.. By introducing the coordinates of the subsolar point and using vector analysis, the formula can be obtained straightforward without incurring the use of spherical trigonometry.
Analemma: Equation of time vs. declination of the Sun. Calculated for the year 2020 using the formulas from The Astronomical Almanac for the Year 2019. As often seen on a globe, the analemma is also often plotted as a two-dimensional figure of equation of time vs. declination of the Sun.
Similar equations are coded into a Fortran 90 routine in Ref. [3] and are used to calculate the solar zenith angle and solar azimuth angle as observed from the surface of the Earth. Start by calculating n , the number of days (positive or negative, including fractional days) since Greenwich noon, Terrestrial Time, on 1 January 2000 ( J2000.0 ).
In Solar Transit, I replaced J* with j2000 - (Longitude/360)/1.0027. The basic idea here is that sidereal time = sideral time at 0h + hours since 0h*1.0027. Equation of time should also be converted in UT time. Staubinr 08:52, 14 October 2018 (UTC) After 3 to 4 pages of mathematics equations, I was able to prove that I was right.