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**Method 1:**

function SunLongitude1($year, $month, $day, $hour, $min, $sec, $timeZone) { $jdn = gregoriantojd($month, $day, $year) + ($hour + $min / 60 + $sec / 3600) / 24; $T = ($jdn - 2451545.5 - $timeZone / 24) / 36525; // Time in Julian centuries from 2000-01-01 12:00:00 GMT $T2 = $T * $T; $dr = M_PI / 180; // degree to radian $M = 357.52910 + 35999.05030 * $T - 0.0001559 * $T2 - 0.00000048 * $T * $T2; // mean anomaly, degree $L0 = 280.46645 + 36000.76983 * $T + 0.0003032 * $T2; // mean longitude, degree $DL = (1.914600 - 0.004817 * $T - 0.000014 * $T2) * sin($dr * $M); $DL = $DL + (0.019993 - 0.000101 * $T) * sin($dr * 2 * $M) + 0.000290 * sin($dr * 3 * $M); $L = $L0 + $DL; // true longitude, degree // obtain apparent longitude by correcting for nutation and aberration $omega = 125.04 - 1934.136 * $T; $L = $L - 0.00569 - 0.00478 * sin($omega * $dr); $L = $L * $dr; return $L = ($L - M_PI * 2 * (floor($L / (M_PI * 2)))) / $dr; // Normalize to (0, 360) }

**Method 2:**

function SunLongitude2($year, $month, $day, $hour, $min, $sec, $timeZone) { // Get Julian date for date at noon $jd = gregoriantojd($month, $day, $year); //correct for half-day offset $dayfrac = $hour / 24 - .5; //now set the fraction of a day $frac = $dayfrac + $min / 60 / 24 + $sec / 3600 / 24 - $timeZone / 24; $jd = $jd + $frac; // The input to the Atronomer's almanach is the difference between // the Julian date and JD 2451545.0 (noon, 1 January 2000) $time = ($jd - 2451545); // Ecliptic coordinates // Mean longitude $mnlong = (280.460 + 0.9856474 * $time); $mnlong = fmod($mnlong, 360); if ($mnlong < 0) $mnlong = ($mnlong + 360); // Mean anomaly $mnanom = (357.528 + 0.9856003 * $time); $mnanom = fmod($mnanom, 360); if ($mnanom < 0) $mnanom = ($mnanom + 360); $mnanom = deg2rad($mnanom); // Ecliptic longitude and obliquity of ecliptic $eclong = ($mnlong + 1.915 * sin($mnanom) + 0.020 * sin(2 * $mnanom)); $eclong = fmod($eclong, 360); if ($eclong < 0) $eclong = ($eclong + 360); return $eclong; }

**Method 3:**

function SunLongitude3($year, $month, $day, $hour, $min, $sec, $timeZone) { $jd = gregoriantojd($month, $day, $year); $frac = $hour / 24 + $min / 60 / 24 + $sec / 3600 / 24 - $timeZone / 24; $jd = $jd + $frac; $d = ($jd - 2451544); $w = 282.9404 + 4.70935E-5 * $d; // (longitude of perihelion) $a = 1.000000; // (mean distance, a.u.) $e = 0.016709 - 1.151E-9 * $d; // (eccentricity) $M = 356.0470 + 0.9856002585 * $d; // (mean anomaly) $M = fmod($M, 360); // the obliquity of the ecliptic, oblecl: $oblecl = 23.4393 - 3.563E-7 * $d; //the Sun's mean longitude, L: $L = $w + $M; $L = fmod($L, 360); // the eccentric anomaly $E = $M + (180 / M_PI) * $e * sin(deg2rad($M)) * (1 + $e * cos(deg2rad($M))); $x = cos(deg2rad($E)) - $e; $y = sin(deg2rad($E)) * sqrt(1 - $e * $e); $r = sqrt($x * $x + $y * $y); $v = rad2deg(atan2($y, $x)); $lon = $v + $w; $lon = fmod($lon, 360); if ($lon < 0) $lon = ($lon + 360); return $lon; }

Compare the precision of these methods:

We can see in the website: http://www.usno.navy.mil/USNO/astronomical-applications/data-services/earth-seasons, at 03-20-2015 22:45 GMT, longitude of the sun is zero:

echo SunLongitude1(2015, 3, 20, 22, 45, 00, 0); //0.00357264073223 ~ 13'' echo SunLongitude2(2015, 3, 20, 22, 45, 00, 0); //0.00343733553098 ~ 13'' echo SunLongitude3(2015, 3, 20, 22, 45, 00, 0); //0.00785246612753 ~ 28''

Now, we can sort the precision of three methods:

SunLongitude2 > SunLongitude1 > SunLongitude3

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