![]() Wilson found that while sunrise and sunset varied by season, wintertime predictions tended to run late, while summer predictions ran early. The site, which Wilson then fed into three separate refraction Most of these (about 600) came along with weather data for Records of 514 sunsets and 251 sunrises from 30 separate geographic ![]() Yet, simply using a standard value assumes the true conditions at these disparately different sites are the same. Air behaves very differently, say, on a still January morning over the Great Lakes versus a hot dusty July morning off the west coast of Africa. However, this value is an approximation, and does not account for local meteorological conditions. Wilson notes in the study that this value is cited as far back as 1865, and its use may go all the way back to that 17 th century master of optics, Isaac Newton. Most standard sunrise calculations assume a refraction angle of 34′ arcminutes, a little larger than the apparent diameter of the Sun. Of course, your actual horizon is probably cluttered with foreground objects that the Sun needs to clear, unless you live on a remote mountaintop or are lucky enough to observe sunrise and sunset from the beach. Most calculations assume local sunrise and sunset time as when the center of the Sun’s disk clears the horizon. ![]() This size also changes very slightly from perihelion in January to aphelion in July, as the Sun seems to grow then shrink from a value of 31.6′ 32.7′ arc minutes. Also, like the Moon, the Sun’s apparent diameter is about half a degree across, meaning you could line the local horizon with 720 Suns end to end, or 180 Suns from horizon to zenith. Along with the Moon, the Sun is one of the few celestial objects that is large and close enough to appear as more than a point of light to the naked eye. Air bends light, meaning we see the Sun slightly offset from its true position on the horizon due to the atmosphere. If we lived on an airless word, the calculated and observed moment of sunrise would be easy… but as air-breathing mammals, we’d have other problems to contend with. However, there is no point in giving sunrise and set times to any higher precision than a minute as atmospheric conditions each day can make the actual times vary slightly from the calculated times.The problem is one of refraction. If they were calculated to the nearest second then the curves calculated from them would be smoother. The probable explanation is that it is due to the rounding to the nearest minute in the calculation of sunrise and set times. The curve above is surprisingly messy and not the smooth curve that would be expected. At those times the changes day-to-day can be up to three minutes. There is more change at the time of the equinoxes – autumn and spring – in March and September respectively. This is not surprising as solstice means ‘the day the Sun stood still’, so at those two times of the year we expect little change from day-to-day. Similarly, there is little change from day-to-day at the time of the winter solstice in June. The change from one day to the next at the time of the summer solstice in late December is around zero. The time of sunrise has been becoming later by about a minute each day so that the length of the day has been shortening accordingly. Let us now ask what is the change in the day length from day-to-day? You may have noticed that the time of sunset since 2 January has not changed so far and will not change for a few more days until Friday 14 January 2011. ![]() At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year. Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. We have discussed in a previous post how that varies during the year. The length of the day is the interval between sunrise and sunset. The change from one day to the next in the length of daylight durind 2011. ![]()
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