In this case on 2007 October 31, if you were at a longitude of 150-degrees East (the ‘standard meridian’ referred to), then the Sun would be due north but a clock would read 11h 43m 40s and the EOT is therefore 16m 20s. It varies slightly over long periods of time. The EOT is caused by Earth’s axial tilt (about 23.5-degrees) and Earth’s elliptical orbit about the Sun and it can be calculated, although there is no simple ‘formula’. But at the same instant a clock (which runs at a constant rate throughout the year) would read a time that is anything up to about 15-minutes before or after 12h 00m 00s, with the difference depending on the day of the year. If the Sun is due north it is 12h 00m 00s in solar time. The EOT is the difference between solar time (the time a sun dial would read) and mean time (the time a clock reads). Nguyen Thanh Trung, We know this from of the Equation of Time (EOT). 40 responses to “ How to calculate sunrise and set – a worked example” Within the rounding errors and the approximations involved that is close enough. Hence at Sydney the Sun is due north at 12h 38m 51” (TT)Ĭompare with values published in the 2007 (or almost any year) Australasian Sky Guide: sunrise 5:57 & sunset 19:22 On 31 October 2007 the Sun is due north at 11h 43m 40” at the standard meridianįor Sydney’s longitude subtract 4m 49” plus add 1h for daylight saving Sunrise and set for Sydney 31 October 2007 H is the hour angle, indicating how far east or west the Sun is from the overhead meridian. For anyone in the eastern standard time zone the standard meridian is 150°. To start the calculation we need from published tables the declination of the Sun on the day, that is how far north or south it is from the celestial equator, the projection of the equator into the sky.Īlso we need to know what time the Sun is due north, that is on the meridian, at the standard meridian. ![]() To follow the calculation you will need to know basic trigonometry. I calculated the times for tomorrow 31 October 2007. John asked for the formula to work out sunrise and set, as well as for a worked example. Sun rays as seen from Sydney Observatory on the late afternoon of 22 October 2007, image Nick Lomb
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