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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.
Animation showing equation of time and analemma path over one year.. The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative.
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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.
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Image source: Getty Images. 1. Your spouse must qualify for benefits. If your spouse is eligible for either retirement or disability benefits, you could receive up to 50% of their full benefit ...
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.