Tuesday, March 22, 2011

A Check on the Amount of Daylight

I live in an agricultural community and information on sunrise and sunset is published daily in the local newspaper on the weather page. The hours of daylight listed for the last few days differs from that computed using the formula for a local latitude of 37° and the declination of the Sun computed for midday in our time zone.

There are two main reasons for the discrepancy. The first is the astronomical definition of the time of sunrise which is taken to be the time at which the Sun first appears on the horizon. At this time the center of the Sun is half its diameter below the horizon. The second correction needed is for the refraction of the Sun's rays by the Earth's atmosphere usually taken to be 34 minutes of arc*. These two corrections combine to add an additional Δt equal to 6 minutes 40 seconds to the amount of daylight. The differences between the published lengths of time and corrected formula times is about one minute.

*see P. Kenneth Seidelmann, ed., Explanatory Supplement to the Astronomical Almanac, 1992, p.483

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