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<?php
// 朮æ±åã®èšç®
function calculateTidalForce($G, $M, $d, $a, $theta) {
// æ°Žå¹³æå
$fTh = 3/2 * ($G * $M / pow($d, 3)) * $a * pow(sin($theta), 2);
// éçŽæå
$fTv = 3 * ($G * $M / pow($d, 3)) * $a * (pow(cos($theta), 2) - 1/3);
return ['horizontal' => $fTh, 'vertical' => $fTv];
}
// 朮æ±ããã³ã·ã£ã«ã®èšç®
function calculateTidalPotential($G, $M, $d, $a, $theta) {
return 3/2 * ($G * $M / pow($d, 3)) * pow($a, 2) * (pow(cos($theta), 2) - 1/3);
}
// 平衡朮æ±ã®èšç®
function calculateEquilibriumTide($g, $M, $E, $a, $c, $d, $theta) {
$D = 3/4 * $g * ($M / $E) * pow($a / $c, 3) * $a;
return 2 * $D * pow($c / $d, 3) * (pow(cos($theta), 2) - 1/3);
}
// 芳枬ç¹ã§ã®æœ®æ±ããã³ã·ã£ã«ã®èšç®
function calculateObservationPointPotential($D, $c, $d, $phi, $delta, $T) {
$cosTheta = cos($phi) * cos($delta) * cos($T) + sin($phi) * sin($delta);
return $D * pow($c / $d, 3) * (
pow(cos($phi), 2) * pow(cos($delta), 2) * pow(cos($T), 2) +
pow(sin($phi), 2) * pow(sin($delta), 2) * cos($T) +
3 * (pow(sin($phi), 2) - 1/3) * (pow(sin($delta), 2) - 1/3)
);
}
// 䜿çšäŸ
$G = 6.674e-11; // äžæåŒå宿°
$M = 7.34767309e22; // æã®è³ªé
$E = 5.97219e24; // å°çã®è³ªé
$d = 384400000; // å°çãšæã®å¹³åè·é¢
$a = 6371000; // å°çã®ååŸ
$g = 9.81; // éåå é床
$c = $d; // å°çãšæã®å¹³åè·é¢ïŒç°¡ç¥åã®ããåãå€ã䜿çšïŒ
$theta = deg2rad(45); // äŸãšããŠ45床ã䜿çš
$phi = deg2rad(35); // 芳枬ç¹ã®ç·¯åºŠïŒäŸïŒ35床ïŒ
$delta = deg2rad(5); // 倩äœã®èµ€ç·¯ïŒäŸïŒ5床ïŒ
$T = deg2rad(30); // æè§ïŒäŸïŒ30床ïŒ
$tidalForce = calculateTidalForce($G, $M, $d, $a, $theta);
$tidalPotential = calculateTidalPotential($G, $M, $d, $a, $theta);
$equilibriumTide = calculateEquilibriumTide($g, $M, $E, $a, $c, $d, $theta);
$observationPointPotential = calculateObservationPointPotential($D, $c, $d, $phi, $delta, $T);
echo "Tidal Force (Horizontal): " . $tidalForce['horizontal'] . " N\n";
echo "Tidal Force (Vertical): " . $tidalForce['vertical'] . " N\n";
echo "Tidal Potential: " . $tidalPotential . " J/kg\n";
echo "Equilibrium Tide: " . $equilibriumTide . " m\n";
echo "Observation Point Potential: " . $observationPointPotential . " J/kg\n";
<?php
/**
* æè§ãèšç®ãã
*
* @param int $year 幎
* @param int $month æ
* @param int $day æ¥
* @param int $hour æ
* @param int $minute å
* @param int $second ç§
* @param float $longitude çµåºŠïŒæ±çµã¯æ£ã西çµã¯è² ïŒ
* @return float æè§ïŒåºŠæ°æ³ïŒ
*/
function calculateHourAngle($year, $month, $day, $hour, $minute, $second, $longitude) {
// ä¿®æ£ãŠãªãŠã¹æ¥ãèšç®
$mjd = calculateModifiedJulianDate($year, $month, $day, $hour, $minute, $second);
// ã°ãªãããžæææãèšç®
$gst = calculateGreenwichSiderealTime($mjd);
// å°æ¹æææãèšç®
$lst = calculateLocalSiderealTime($gst, $longitude);
// æè§ãèšç®ïŒ0ãã360床ã®ç¯å²ã«æ£èŠåïŒ
$hourAngle = fmod($lst * 15, 360);
if ($hourAngle < 0) {
$hourAngle += 360;
}
return $hourAngle;
}
/**
* ä¿®æ£ãŠãªãŠã¹æ¥ãèšç®ãã
*/
function calculateModifiedJulianDate($y, $m, $d, $h, $mi, $s) {
if ($m <= 2) {
$y -= 1;
$m += 12;
}
$ret = (int)(365.25 * $y) + (int)($y / 400) - (int)($y / 100);
$ret += (int)(30.59 * ($m - 2)) + $d - 678912;
$ret += $h / 24 + $mi / 1440 + $s / 86400 - 0.375;
return $ret;
}
/**
* ã°ãªãããžæææãèšç®ãã
*/
function calculateGreenwichSiderealTime($mjd) {
$t = ($mjd - 51544.5) / 36525;
$gst = 280.46061837 + 360.98564736629 * ($mjd - 51544.5) + 0.000387933 * $t * $t - $t * $t * $t / 38710000;
return fmod($gst, 360) / 15; // æéåäœã«å€æ
}
/**
* å°æ¹æææãèšç®ãã
*/
function calculateLocalSiderealTime($gst, $longitude) {
$lst = $gst + $longitude / 15;
if ($lst < 0) {
$lst += 24;
} elseif ($lst >= 24) {
$lst -= 24;
}
return $lst;
}
// 䜿çšäŸ
$year = 2024;
$month = 9;
$day = 11;
$hour = 21;
$minute = 7;
$second = 0;
$longitude = 139.75; // æ±äº¬ã®çµåºŠ
$hourAngle = calculateHourAngle($year, $month, $day, $hour, $minute, $second, $longitude);
echo "æè§: " . $hourAngle . "床";
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