Sind totale Sonnenfinsternisse im Sommer häufiger?

$Arc = pi() / 180;
//==============================================
//Winkelfunktionen mit Argumenten in Grad
//==============================================
function gsin($phi){
    global $Arc;
    return sin($phi * $Arc);
}
function gcos($phi){
    global $Arc;
    return cos($phi * $Arc);
}
//==============================================
// Signum-, Fix-, Integer- und Cint-Funktion
//==============================================
function sgn($val){
    return $val == 0 ? 0 : ($val > 0 ? 1 : -1);
}
function fix($number){
    return sgn($number) * floor(abs($number));
}
function int($number){
    return floor($number);
}
function Cint($number){
    return round($number,0);
}    

//==============================================
//erzeugt ekliptikale Länge der Sonne in Grad
//==============================================
function Sonne_Laenge($JDatum){	
    $T = ($JDatum - 2415020) / 36525;
    $DLP = ((1.882 - 0.016 * $T) * gsin(57.24 + 150.27 * $T)
        + 6.4 * gsin(231.19 + 20.2 * $T)
        + 0.266 * gsin(31.8 + 119 * $T)) / 3600;
    $L0 = 279.6966778 + 36000.768925 * $T + 0.0003025 * $T * $T
        + 0.202 / 3600 * gsin(315.6 + 893.3 * $T) + $DLP;
    $g = 358.4758333 + 35999.04975 * $T - 0.00015 * $T * $T + $DLP; //mittl. Anomalie Sonne
    $G2 = 212.45 + 58517.493 * $T; //mittl. Anomalie Venus
    $G4 = 319.58 + 19139.977 * $T; //mittl. Anomalie Mars
    $G5 = 225.28 + 3034.583 * $T + 1300 / 3600 * gsin(133.775 + 39.804 * $T); //mittl. Anomalie Jupiter
    $D = 350.737486 + 445267.114217 * $T; //mittl. Winkel Sonne-Mond
    $DL = (1.919460278 - 0.004788888 * $T) * gsin($g)
        + (0.020093889 - 0.000100278 * $T) * gsin(2 * $g)
        + 0.000292778 * $T * gsin(3 * $g); //Sonne
    $DL2 = 4.838 * gcos(299.102 + $G2 - $g) +
        5.526 * gcos(148.313 + 2 * $G2 - 2 * $g) +
        2.497 * gcos(315.943 + 2 * $G2 - 3 * $g) +
        1.559 * gcos(345.253 + 3 * $G2 - 4 * $g) +
        1.024 * gcos(318.15 + 3 * $G2 - 5 * $g); //Venus
    $DL4 = 2.043 * gcos(343.888 - 2 * $G4 + 2 * $g) +
        1.77 * gcos(200.402 - 2 * $G4 + $g); //Mars
    $DL5 = 7.208 * gcos(179.532 - $G5 + $g) +
        2.6 * gcos(263.217 - $G5) +
        2.731 * gcos(87.145 - 2 * $G5 + 2 * $g); //Jupiter
    $DLM = 6.454 * gsin($D); //Mond
    $lamda = ($L0 + $DL + ($DL2 + $DL4 + $DL5 + $DLM) / 3600) / 360;
    $el = $lamda - int($lamda);
    If($el > 0.5) {$el = $el - 1;}
    return $el * 360;
}    

//==============================================
//erzeugt ekliptikale Länge des Mondes in Grad
//==============================================
function Mond_Laenge($JDatum){
	$T = ($JDatum - 2415020) / 36525;
	$T2 = $T * $T;
	$kl = 270.434164 + 481267.883142 * $T - 0.001133 * $T2;
	$M = 296.104608 + 477198.849108 * $T + 0.009192 * $T2;
	$O = 259.183275 - 1934.142008 * $T + 0.002078 * $T2;
	$l = 279.696678 + 36000.768925 * $T + 0.000303 * $T2;
	$n = 358.475833 + 35999.04975 * $T - 0.00015 * $T2;
	$L1 = 22640 * gsin($M) + 769 * gsin(2 * $M) + 36 * gsin(3 * $M);
	$L2 = -125 * gsin($kl - $l) + 2370 * gsin(2 * ($kl - $l));
	$l3 = -668 * gsin($n) - 412 * gsin(2 * ($kl - $O));
	$l4 = 212 * gsin(2 * ($kl - $l - $M)) + 4586 * gsin(2 * ($kl - $l) - $M);
	$l5 = 192 * gsin(2 * ($kl - $l) + $M) + 165 * gsin(2 * ($kl - $l) - $n);
	$l6 = 206 * gsin(2 * ($kl - $l) - $M - $n) - 110 * gsin($M + $n) + 148 * gsin($M - $n);
	$lamda = ($kl + ($L1 + $L2 + $l3 + $l4 + $l5 + $l6) / 3600) / 360;
	$el = $lamda - int($lamda);
        if($el > 0.5) {$el = $el - 1;}
	return $el * 360;
}    

//==============================================
//erzeugt ekliptikale Breite des Mondes in Grad
//==============================================
function Mond_Breite($JDatum){
	$T = ($JDatum - 2415020) / 36525;
	$T2 = $T * $T;
	$kl = 270.434164 + 481267.883142 * $T - 0.001133 * $T2;
	$M = 296.104608 + 477198.849108 * $T + 0.009192 * $T2;
	$O = 259.183275 - 1934.142008 * $T + 0.002078 * $T2;
	$l = 279.696678 + 36000.768925 * $T + 0.000303 * $T2;
	$n = 358.475833 + 35999.04975 * $T - 0.00015 * $T2;
	$L1 = 22640 * gsin($M) + 769 * gsin(2 * $M) + 36 * gsin(3 * $M);
	$L2 = -125 * gsin($kl - $l) + 2370 * gsin(2 * ($kl - $l));
	$L3 = -668 * gsin($n) - 412 * gsin(2 * ($kl - $O));
	$L4 = 212 * gsin(2 * ($kl - $l - $M)) + 4586 * gsin(2 * ($kl - $l) - $M);
	$L5 = 192 * gsin(2 * ($kl - $l) + $M) + 165 * gsin(2 * ($kl - $l) - $n);
	$L6 = 206 * gsin(2 * ($kl - $l) - $M - $n) - 110 * gsin($M + $n) + 148 * gsin($M - $n);
	$lamda = $kl + ($L1 + $L2 + $L3 + $L4 + $L5 + $L6) / 3600;
	$b1 = 18520 * gsin($lamda - $O + 412 / 3600 * gsin(2 * ($kl - $O)) + 541 / 3600 * gsin($n));
	$b2 = -526 * gsin(2 * $l - $kl - $O);
	$b3 = 44 * gsin(2 * $l - $kl - $O + $M);
	$b4 = -31 * gsin(2 * $l - $kl - $O - $M);
	$b5 = -23 * gsin(2 * $l - $kl - $O + $n);
	$b6 = 11 * gsin(2 * $l - $kl - $O - $n);
	$b7 = -25 * gsin($kl - $O - 2 * $M);
	$b8 = 21 * gsin($kl - $O - $M);
	$beta = ($b1 + $b2 + $b3 + $b4 + $b5 + $b6 + $b7 + $b8) / 3600 / 360;
	return ($beta - Cint($beta)) * 360;
}    

//==============================================
//  erzeugt Zeitpunkt der Mondphase als Julianisches Datum
//  Phase = 0 ist Neumond, Phase = 90 ist letztes Viertel usw.
//  move ist optional: 1 = nächster, 0 = vorheriger
//==============================================
function Mondphase_nach($JDatum, $Phase, $move = 1){
    $JDatum = $JDatum + 0.000005;
    $M = 29.530589;
    $p = (Sonne_Laenge($JDatum) - Mond_Laenge($JDatum) - $Phase) / 360;
    if($move==1) {$p = $p-int($p);} else {$p = $p-fix($p)+$move;}
    $z = $p * $M + $JDatum;
    do{
        $p = (Sonne_Laenge($z) - Mond_Laenge($z) - $Phase) / 360;
        If($p < -0.5) {$p = $p + 1;}
        If($p > 0.5) {$p = $p - 1;}
        $z += ($p - fix($p)) * $M;
    }
    while (abs($p) > 0.000001);
    return  $z;
}    

//==============================================
// Sonnenabstand in Astronomische Einheiten
// für den Abstand in km mit 149597870.7 multiplizieren
//==============================================
function Sonnenabstand($JDatum){
    $T = ($JDatum - 2415020) / 36525;

    $DLP = (1.882 / 3600 - 0.016 / 3600 * $T) * gsin(57.24 + 150.27 * $T)
	 + 6.4 / 3600 * gsin(231.19 + 20.2 * $T) + 0.266 / 3600 * gsin(31.8 + 119 * $T);

    $g = 358.4758333 + 35999.04975 * $T - 0.00015 * $T * $T + $DLP;
    $G2 = 212.45 + 58517.493 * $T;
    $G4 = 319.58 + 19139.977 * $T;
    $G5 = 225.28 + 3034.583 * $T + 1300 / 3600 * gsin(133.775 + 39.804 * $T);
    $G6 = 175.6 + 1221.794 * $T;

    $D = 350.737486 + 445267.114217 * $T;

    $A = 296.104608 + 477198.849108 * $T;

    $U = 11.250889 + 483202.02515 * $T;

    $DL = (1.919460278 - 0.004788888 * $T) * gsin($g)
	 + (0.020093889 - 0.000100278 * $T) * gsin(2 * $g)
	 + 0.000292778 * $T * gsin(3 * $g);

    $R0 = (0.00003057 - 0.00000015 * $T)
	 + (-0.00727412 + 0.00001814 * $T) * gcos($g)
	 + (-0.00009138 + 0.00000046 * $T) * gcos(2 * $g)
	 - 0.00000145 * gcos(3 * $g);

    $DR2 = (2359 * gcos(209.08 + $G2 - $g) + 160 * gcos(58.4 + 2 * $G2 - $g)
        + 6842 * gcos(58.318 + 2 * $G2 - 2 * $g) + 869 * gcos(226.7 + 2 * $G2 - 3 * $g)
        + 1045 * gcos(87.57 + 3 * $G2 - 3 * $g) + 1497 * gcos(255.25 + 3 * $G2 - 4 * $g)
        + 194 * gcos(49.5 + 3 * $G2 - 5 * $g) + 376 * gcos(116.28 + 4 * $G2 - 4 * $g)
        + 196 * gcos(105.2 + 4 * $G2 - 5 * $g) + 163 * gcos(145.4 + 5 * $G2 - 5 * $g)
        + 141 * gcos(105.4 + 5 * $G2 - 7 * $g)) / pow(10, 9);

    $DR4 = (150 * gcos(127.7 - $G4 + $g) + 2057 * gcos(253.828 - 2 * $G4 + 2 * $g)
        + 151 * gcos(295 - 2 * $G4 + $g) + 168 * gcos(203.5 - 3 * $G4 + 3 * $g)
        + 215 * gcos(249 - 3 * $G4 + 2 * $g) + 478 * gcos(15.17 - 4 * $G4 + 3 * $g)
        + 105 * gcos(65.9 - 4 * $G4 + 2 * $g) + 107 * gcos(324.6 - 5 * $G4 + 4 * $g)
        + 139 * gcos(137.3 - 6 * $G4 + 4 * $g)) / pow(10, 9);

    $DR5 = (208 * gcos(112 - $G5 + 2 * $g) + 7067 * gcos(89.545 - $G5 + $g)
        + 244 * gcos(338.6 - $G5) + 103 * gcos(350.5 - 2 * $G5 + 3 * $g)
        + 4026 * gcos(357.108 - 2 * $G5 + 2 * $g) + 1459 * gcos(19.467 - 2 * $G5 + $g)
        + 281 * gcos(81.2 - 3 * $G5 + 3 * $g) + 803 * gcos(352.56 - 3 * $G5 + 2 * $g)
        + 174 * gcos(8.6 - 3 * $G5 + $g) + 113 * gcos(347.7 - 4 * $G5 + 2 * $g)) / pow(10, 9);

    $DR6 = (429 * gcos(10.6 - $G6 + $g) + 162 * gcos(200.6 - 2 * $G6 + 2 * $g)
        + 112 * gcos(203.1 - 2 * $G6 + $g)) / pow(10, 9);

    $DRM = (13360 * gcos($D) + 370 * gcos($D + $A) - 1330 * gcos($D - $A) - 140 * gcos($D + $g) + 360 * gcos($D - $g)) / pow(10, 9);

    return  pow(10, $R0 + $DR2 + $DR4 + $DR5 + $DR6 + $DRM);
}    

//==============================================
// Mondabstand in Kilometer
//==============================================
function Mondabstand($JDatum){
    return 6378.14 / gsin(MondHP($JDatum));
}

//==============================================
// Mond-Horizontal-Paralaxe
//==============================================
function MondHP($JDatum){
    $T = ($JDatum - 2415020) / 36525;

    $M = 296.104608 + 477198.849108 * $T + 0.009192 * $T * $T;
    $kl = 270.434164 + 481267.883142 * $T - 0.001133 * $T * $T;
    $l = 279.696678 + 36000.768925 * $T + 0.000303 * $T * $T;

    return 3423 / 3600 + 187 / 3600 * gcos($M) + 10 / 3600 * gcos(2 * $M)
	+ 34 / 3600 * gcos(2 * ($kl - $l) - $M)
	+ 28 / 3600 * gcos(2 * ($kl - $l))
	+ 3 / 3600 * gcos(2 * ($kl - $l) + $M);
}