/* This program uses the full VSOP87 theory to calculate the exact dates of the equinoxes and solstices to the nearest millisecond. While the sun.frink library has routines to calculate the solstices and equinoxes rather simply, these can be inaccurate up to several minutes or so. This program uses very high precision routines to calculate the solar longitude of earth for each season, and uses a secant method solver to obtain the exact time of the solstices and equinoxes to the nearest millisecond. The definition of the equinoxes and solstices are when earth's heliocentric *longitude* is equal to 180 degrees (spring), 270 degrees (summer), 0 degrees (autumn), and 90 degrees (winter.) The solstices are defined in terms of longitude, not latitude. Thus, you should be warned that the sun should be quite close to being over the equator at equinoxes, and close to being at max/min latitude at solstices, but these will not be exact. Beware anyone who tells you differently. */ use planets.frink use secant.frink // Let's calculate the longitude angle that corresponds to 1 millisecond of // time angleres = ms circle/solaryear timezone = "US/Mountain" // Function to use planets.frink to calculate the heliocentric longitude // at the specified time. longfunc = {|date| highAccuracySunApparentLongitude[date]} for yearnum = 1996 to 2020 { println[] // These functions use the low-precision equinox/solstice functions from // sun.frink to estimate a good starting point. springEquinox = secantInvert[longfunc, 180 degrees, springEquinox[yearnum] - 1 hour, springEquinox[yearnum] + 1 hour, angleres] println["Spring equinox is: " + (springEquinox -> timezone)] summerSolstice = secantInvert[longfunc, 270 degrees, summerSolstice[yearnum] - 1 hour, summerSolstice[yearnum] + 1 hour, angleres] println["Summer solstice is: " + (summerSolstice -> timezone)] autumnEquinox = secantInvert[longfunc, 0 degrees, autumnEquinox[yearnum] - 1 hour, autumnEquinox[yearnum] + 1 hour, angleres] println["Autumn equinox is: " + (autumnEquinox -> timezone)] winterSolstice = secantInvert[longfunc, 90 degrees, winterSolstice[yearnum] - 1 hour, winterSolstice[yearnum] + 1 hour, angleres] println["Winter solstice is: " + (winterSolstice -> timezone)] }