where:Z =LHA =6=a=azimuth of the sun measuredclockwise from northlocal hour angle of the sundeclination of the sunlatitude of the observerZ is normalized from 0° to 360°algebraically a correction as listed below.by addingThe above equation is derived using sphericaltrigonometry to solve the pole-zenith-star (PZS) trianglefor azimuthTime and DateTo calculate the LHA of the apparent sun at theinstant of observation, you must have accurate time thattakes into account the rotation of the earth. Time that isbased on the rotation of the earth can be obtained byadding a correction factor to Greenwich meantime.Coordinated universal time (UTC) is anothername for Greenwich mean time and is broadcast by theNational Bureau of Standards on radio station WWV.(Inexpensive receivers that are pretuned to WWV areavailable.) The correction factor (designated DUT) thatyou must add to the coordinated universal time is alsoobtained from WWV by counting the number of doubleticks following the minute tone. Each double tickrepresents a tenth-of-a-second correction and is positivethe frost 7 seconds (ticks). Beginning with the ninthsecond, each double tick is a negative correction. Thetotal correction, either positive or negative, will notexceed 0.7 second. By adding DUT to UTC, you gettime (designated UT1) that is based on the actualrotation of the earth.A stopwatch with a split (or lap) time feature is idealfor obtaining times of pointings. The stopwatch is set bystarting it on a WWV minute tone and then checking it1 minute later with a split time. If a significant differenceis observed, start and check the stopwatch again. Splittimes are taken for each pointing on the sun and addedto the beginning UTC time, corrected to UT1.To enter the ephemeris tables, you must know theGreenwich date for the time of observation. For anafternoon observation (local time) in the WesternHemisphere, if the UT1 is between 12 and 24 hours, theGreenwich date is the same as the local date. If the UT1time is between 0 and 12 hours, the Greenwich date isthe local date plus 1 day.For a morning observation (local time) in theEastern Hemisphere, if the UT1 time is between 0 and12, the Greenwich date is the same as the local date. Ifthe UT1 time is between 12 and 24 hours, the Greenwichdate is the local date minus 1 day.For a morning observation in the WesternHemisphere and an afternoon observation in the EasternHemisphere, Greenwich and local dates are the same.Latitude and LongitudeBoth the observer’s latitude and longitude arerequired for the hour angle method. Usually these valuescan be readily obtained by scaling from a map, such asa USGS 7.5-minute quadrangle sheet. For sunobservations, locating the observer’s position on themap and scaling must be performed to a reasonably highdegree of accuracy.Declination of the SunDeclination(6) of the sun is tabulated for O hoursuniversal time of each day (Greenwich date) in table15-5. You can interpolate for at the UT1 time ofobservation by using the following equation:A negative declination indicates that the sun is southof the equator, and a negative value must be used in theabove equation and in the azimuth (Z) equation.The Greenwich hour angle (GHA) of the sun istabulated for 0 hours universal time of each day(Greenwich date) in the ephemeris. Interpolation isrequired at the UT1 time of observation and can beaccomplished by using the following equation:NOTE: The value at the beginning of the day ofobservation is d’. The value 24 hours later at thebeginning of the next day is 24h.15-18

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