home
 
 
 
Code
<?php
											 
											/*
												Code
												© Charles Chandler
												http://qdl.scs-inc.us/?top=18881
											*/
											 
											/*
												See http://qdl.scs-inc.us/?top=18943 for the description.
											*/
											 
											function StefanBoltzmannLaw($emissivity, $meters2, $kelvins, $knownDepth = 1) {
											/*
												Stefan-Boltzmann Law
												--------------------
												P = eoAT^4
												where:
												P = total radiated power (watts)
												e = emissivity (=1 for BB radiators)
												o = Stefan's Constant
												A = radiating area (m^2)
												T = temperature (K)
											*/
											$stefansConstant = 5.670367 * pow(10, -8);
											/*
												Here's the correction for the effective depth of plasma BB
												radiators versus the classical BB surfaces ($knownDepth = 1).
											*/
											if (!$knownDepth) $knownDepth = pow($kelvins / 10000, 2.3219) * 4.905;
											return $emissivity * $stefansConstant * $meters2 * pow($kelvins, 4) * $knownDepth;
											}
											 
											function Acceleration($watts, $seconds, $kilograms) {
											/*
												Returns velocity of an object, in m/s, given the power
												used to accelerate it, the time, & the object's mass.
												 
												joules = .5 * kilograms * velocity^2
												watts * seconds = .5 * kilograms * velocity^2
												(watts * seconds) / (.5 * kilograms) = velocity^2
												sqrt((watts * seconds) / (.5 * kilograms)) = velocity
											*/
											return sqrt(($watts * $seconds) / (.5 * $kilograms));
											}
											//
											$mass_kg   = $solSys->sun->mass_kg;
											$area_m2   = $solSys->sun->area_m2;
											$begSpeed  = LU(11416, 'new_dp_velocity'); // imploding dusty plasma velocity: 258,961,135 m/s, or 86.38% c
											$nowSpeed  = $begSpeed;
											$secsInMY  = kSecsInYear * pow(10, 6);
											$imgFolder = '2ndParty/Images/Charles/LightCurve';
											$steps     = 10000; // number of iterations (max = 35000 before memory error)
											$sunAge    = 380.6611474853; // from a previous run of the 'sun' $mode, and used by the 'earth' mode
											//
											// which numbers to run...
											// last one set wins
											$mode =  '7500';
											$mode = '22000';
											$mode = '10000';
											$mode = 'solarFlares';
											$mode =   'sun';
											$mode = 'earth';
											$mode = 'earthFlares';
											 
											if     ($mode == '22000') {
											$title       = '';
											$maxMegaYear = 5778;
											$begKelvins  = 22000;
											$xPower      = -3;
											$yPower      = -3;
											}
											elseif ($mode == '10000') {
											$title       = 'percent of total population';
											$maxMegaYear = 5110;
											$begKelvins  = 10000;
											$xPower      = -3;
											$yPower      = -3;
											}
											elseif ($mode == '7500') {
											$title       = '';
											$maxMegaYear = 9400;
											$begKelvins  = 7500;
											$xPower      = -3;
											$yPower      = -3;
											}
											elseif ($mode == 'sun') {
											$title       = '';
											$maxMegaYear = 545;
											$begKelvins  = 10000;
											$xPower      =  0;
											$yPower      = -3;
											$sunTemp     = 5525;
											}
											elseif ($mode == 'solarFlares') {
											$title       = 'percent of total population';
											$maxMegaYear = 5110;
											$begKelvins  = 10000;
											$xPower      = -3;
											$yPower      = -3;
											}
											elseif ($mode == 'earth') {
											$title       = '';
											$maxMegaYear = 600;
											$begKelvins  = 10000;
											$mass_kg     = $solSys->earth->mass_kg;
											$area_m2     = $solSys->earth->area_km2 * 1000 * 1000;
											$xPower      =  0;
											$yPower      = -3;
											}
											elseif ($mode == 'earthFlares') {
											$title       = '';
											$maxMegaYear = 600;
											$begKelvins  = 10000;
											$mass_kg     = $solSys->earth->mass_kg;
											$area_m2     = $solSys->earth->area_km2 * 1000 * 1000;
											$xPower      =  0;
											$yPower      = -3;
											}
											//
											$xLabel = ($xPower == -3) ? 'billions of years' : 'millions of years';
											$yLabel = ($yPower == -3) ? 'thousands of kelvins' : 'kelvins';
											//
											$relRootName = $imgFolder.ucfirst($mode);
											$relTextFile = $relRootName.'.txt';
											if (file_exists($relTextFile)) {
											$pts = array();
											foreach(explode(kLF, file_get_contents($relTextFile)) as $line) {
											if (trim($line)) { // skip the blank line at the end
											list($nowMY, $nowKelvins) = explode(kTAB, $line);
											$pts[] = Pt($nowMY, $nowKelvins);
											// The last-assigned value of $nowKelvins is used later.
											}
											}
											}
											else {
											$pts   = array(Pt($xLabel, $yLabel)); // labels go in the first element
											$pts[] = Pt(0, $begKelvins); // add the initial temp at the 0 time step
											 
											// Use a logarithmic time step, with short steps at first, when the
											// temp is falling fast, and longer steps later, as it levels off.
											$logMaxSeconds = log($maxMegaYear * $secsInMY);
											 
											// If it's a star, 1/3 is nuclear power,
											// which doesn't diminish with power ouput.
											$nonNukePower = (BeginsWith($mode, 'earth')) ? 1 : (2 / 3);
											 
											// M A I N   L O O P
											$nowKelvins = $begKelvins;
											$oldSeconds = 0;
											for ($i = 1; $i <= $steps; $i++) {
											$nowWatts     = StefanBoltzmannLaw(1, $area_m2, $nowKelvins, false);
											$nowSeconds   = exp(($i / $steps) * $logMaxSeconds);
											$timeSpan     = $nowSeconds - $oldSeconds;
											$deceleration = Acceleration($nowWatts, $timeSpan, $mass_kg);
											$nowSpeed    -= $deceleration * $nonNukePower;
											$nowKelvins   = $begKelvins * ($nowSpeed / $begSpeed);
											$pts[]        = Pt($nowSeconds / $secsInMY, $nowKelvins);
											$oldSeconds   = $nowSeconds;
											// The last-assigned value of $nowKelvins is used later.
											 
											// Snag the age at which the Sun hits 5525 K.
											if (($mode == 'sun') and ($nowKelvins > $sunTemp)) $sunAge = $nowSeconds / $secsInMY;
											}
											//
											// Write the points to a text file.
											$str = '';
											foreach($pts as $pt) $str .= $pt['x'].kTAB.$pt['y'].kLF;
											file_put_contents($relTextFile, $str);
											}
											//
											// Add the offset curves for the discrepancy between the Stefan-Boltzman
											// prediction and the actual temperatures in the K class due to flares.
											if (($mode == '10000') or ($mode == 'solarFlares')) {
											$pts1 = $pts2 = $pts3 = array();
											$offY = 0;
											$begX = 650;
											$endX = 1200;
											$incX = ($endX - $begX) / 6;
											$incY = 850 / 6;
											$cnt  = 0;
											foreach($pts as $pt) {
											$x = $pt['x'];
											$y = $pt['y'];
											if ($y > 5200) { $pts1[] = Pt($x, $y); }
											else           { $pts4[] = Pt($x, $y);
											if (($x > $begX) and ($x < $endX)) {
											if ($x > $begX + ($incX * $cnt)) {
											$cnt++;
											$y += 4500;
											$offY += $incY;
											}
											}
											$pts3[] = Pt($x, $y - $offY);
											}
											if (($x > 1200) and ($y > $nowKelvins)) $pts2[] = Pt($x, $y - 850);
											}
											}
											elseif ($mode == 'earthFlares') {
											$pts1 = $pts2 = $pts3 = array();
											$offY = 0;
											$begX = 8.6542077541337;
											$endX = 51.139340047215;
											$incX = ($endX - $begX) / 6;
											$incY = 192 / 6;
											$cnt  = 0;
											foreach($pts as $pt) {
											$x = $pt['x'];
											$y = $pt['y'];
											if ($y > 5200) { $pts1[] = Pt($x, $y); }
											else           { $pts4[] = Pt($x, $y);
											if (($x > $begX) and ($x < $endX)) {
											if ($x > $begX + ($incX * $cnt)) {
											$cnt++;
											$y += 2700;
											$offY += $incY;
											}
											}
											$pts3[] = Pt($x, $y - $offY);
											}
											if (($x > $endX) and ($y > $nowKelvins)) $pts2[] = Pt($x, $y - 192);
											}
											}
											//
											// GraphPoints is just a QDL class for generating a PNG file, plotting
											// the points, labeling the axes, and adding annotations as specified.
											// Without it, you can still plot the points using the text file (above).
											$plotWide    = 640 * 2;
											$plotHigh    = 480 * 2;
											$marginLeft  =  52 * 2;
											$marginRight =  42 * 2;
											$marginUpper =  20 * 2; if ($title) $marginUpper = 90;
											$marginLower =  52 * 2;
											$gr          = 180; // gray
											//
											$img = new GraphPoints($title, $plotWide, $plotHigh, 255, 255, 255, true, 24);
											$img->SetTickLengths(8, 16, 20);
											$img->SetLineThickness(2);
											$img->Margins($marginLeft, $marginRight, $marginUpper, $marginLower);
											$img->SetPowers($xPower, $yPower);
											if     ($mode == '10000') {
											$img->xMin = 0;
											$img->xMax = $maxMegaYear * pow(10, $xPower);
											$img->yMin = 2400 * pow(10, $yPower);
											$img->yMax = $begKelvins * pow(10, $yPower);
											$img->AddPoints($pts4, true,   0,   0,   0);
											$img->AddPoints($pts1, true,   0,   0,   0);
											$img->AddPoints($pts2, true, 255,   0,   0);
											$img->AddText(2000, 4200, 'stefan-boltzmann prediction', 'left');
											$img->AddText(1300, 2550, 'required for ~76.45% in M class', 'left', 255,   0,   0);
											}
											elseif ($mode == 'solarFlares') {
											$img->xMin = 0;
											$img->xMax = $maxMegaYear * pow(10, $xPower);
											$img->yMin = 2400 * pow(10, $yPower);
											$img->yMax = $begKelvins * pow(10, $yPower);
											$img->AddPoints($pts4, true, $gr, $gr, $gr);
											$img->AddPoints($pts1, true,   0,   0,   0);
											$img->AddPoints($pts3, true,   0,   0, 255);
											$img->AddPoints($pts2, true, 255,   0,   0);
											$img->AddText(2000, 4200, 'stefan-boltzmann prediction', 'left', $gr, $gr, $gr);
											$img->AddText(1300, 2550, 'after energy loss to flares', 'left', 255,   0,   0);
											$img->AddText( 710, 9600, 'flares',                      'left',   0,   0, 255);
											}
											elseif ($mode == 'earthFlares') {
											$img->xMin = 0;
											$img->xMax = $maxMegaYear * pow(10, $xPower);
											$img->yMin = 1500 * pow(10, $yPower);
											$img->yMax = $begKelvins * pow(10, $yPower);
											$img->AddPoints($pts4, true, $gr, $gr, $gr);
											$img->AddPoints($pts1, true,   0,   0,   0);
											$img->AddPoints($pts3, true,   0,   0, 255);
											$img->AddPoints($pts2, true, 255,   0,   0);
											$img->AddText(150, 3100, 'stefan-boltzmann prediction', 'left', $gr, $gr, $gr);
											$img->AddText(150, 1900, 'after energy loss to flares', 'left', 255,   0,   0);
											$img->AddText( 10, 8200, 'flares',                      'left',   0,   0, 255);
											}
											elseif ($mode == 'earth') {
											$img->xMin = 0;
											$img->xMax = $maxMegaYear * pow(10, $xPower);
											$img->yMin = 1500 * pow(10, $yPower);
											$img->yMax = $begKelvins * pow(10, $yPower);
											$img->AddPoints($pts, true, 0, 0, 0);
											$img->AddText(150, 3100, 'stefan-boltzmann prediction', 'left');
											$img->AddLine($sunAge, 10000, $sunAge, $img->yMin / pow(10, $yPower));
											}
											else {
											$img->AddPoints($pts, true, 0, 0, 0);
											}
											//
											// horizontal lines for stellar classes
											if ($mode == 'sun') {
											$img->AddLine(0,  7500, $maxMegaYear,  7500); $img->AddText($maxMegaYear * .97, ( 7500 + 10000) / 2, 'A');
											$img->AddLine(0,  6000, $maxMegaYear,  6000); $img->AddText($maxMegaYear * .97, ( 6000 +  7500) / 2, 'F');
											$img->AddLine(0,  5200, $maxMegaYear,  5200); $img->AddText($maxMegaYear * .97, ( 5200 +  6000) / 2, 'G');
											$img->AddLine($sunAge - 11, 5525,      $sunAge + 11, 5525,      1, 2);
											$img->AddLine($sunAge, $sunTemp - 120, $sunAge, $sunTemp + 120, 1, 2);
											echo 'sun age: '.$sunAge.'<br />';
											}
											else {
											if (($mode != '10000') and ($mode != 'solarFlares') and (!BeginsWith($mode, 'earth')))
											$img->AddLine(0, 10000, $maxMegaYear, 10000); $img->AddText($maxMegaYear * .97, (10000 + 30000) / 2, 'B');
											$img->AddLine(0,  7500, $maxMegaYear,  7500); $img->AddText($maxMegaYear * .97, ( 7500 + 10000) / 2, 'A');
											$img->AddLine(0,  6000, $maxMegaYear,  6000); $img->AddText($maxMegaYear * .97, ( 6000 +  7500) / 2, 'F');
											$img->AddLine(0,  5200, $maxMegaYear,  5200); $img->AddText($maxMegaYear * .97, ( 5200 +  6000) / 2, 'G');
											$img->AddLine(0,  3700, $maxMegaYear,  3700); $img->AddText($maxMegaYear * .97, ( 3700 +  5200) / 2, 'K');
											$img->AddLine(0,  2400, $maxMegaYear,  2400); $img->AddText($maxMegaYear * .97, ( 2400 +  3700) / 2, 'M');
											if ($mode == 'earthFlares')
											$img->AddLine($sunAge, 10000, $sunAge, $img->yMin / pow(10, $yPower));
											}
											//
											// Hash marks for known star population percentages.
											if (($mode == '10000') or ($mode == 'solarFlares')) {
											$h = (($img->yMax - $img->yMin) / pow(10, $yPower)) * .015;
											$x1 = $maxMegaYear;
											$x2 = $x1 - ((76.45 / 100) * $maxMegaYear);
											$x3 = $x2 - ((12.10 / 100) * $maxMegaYear);
											$x4 = $x3 - (( 7.60 / 100) * $maxMegaYear);
											$x5 = $x4 - (( 3.00 / 100) * $maxMegaYear);
											 
											$above = 450;
											$img->AddLine(  0, 2400,   0, $begKelvins - $h + $above);
											$img->AddLine($x1, 2400, $x1, $begKelvins - $h + $above);
											$img->AddLine($x2, 2400, $x2, $begKelvins - $h + $above);
											$img->AddLine($x3, 2400, $x3, $begKelvins - $h + $above);
											$img->AddLine($x4, 2400, $x4, $begKelvins - $h + $above);
											$img->AddLine($x5, 2400, $x5, $begKelvins - $h + $above);
											 
											$img->AddText(             .5, $begKelvins + $h + 400, '.6'   ); // A
											$img->AddText(($x4 + $x5) / 2, $begKelvins + $h +  80, '3'    ); // F
											$img->AddText(($x3 + $x4) / 2, $begKelvins + $h +  80, '7.6'  ); // G
											$img->AddText(($x2 + $x3) / 2, $begKelvins + $h +  80, '12.1' ); // K
											$img->AddText(($x1 + $x2) / 2, $begKelvins + $h +  80, '76.45'); // M
											}
											//
											// white background
											$img->Indexed(true, 255);
											$img->Create($relRootName.'_wbg.png');
											$img->DeIndex();
											//
											// black background
											$img->Invert();
											$img->Brighten(50);
											$img->Indexed(true, 255);
											$img->Create($relRootName.'_bbg.png');
											$img->Destroy();
											//
											// preview
											echo '<img src="'.$relRootName.'_bbg.png" width="640" height="480" />';
											 
										?>

← PREV Powered by Quick Disclosure Lite®
© 2010~2017 SCS-INC.US
NEXT →