public class MoonPhase {
	public static final float EPOCH		= 2444238.5f;		// 1980 January 0.0
	public static final float ELONGE	= 278.833540;		// ecliptic longitude of the Sun at epoch 1980.0
	public static final float ELONGP	= 282.596403;		// ecliptic longitude of the Sun at perigee
	public static final float ECCENT	= 0.016718;			// eccentricity of Earth's orbit
	public static final float SUNSMAX	= 1.495985e8;		// semi-major axis of Earth's orbit, km
	public static final float SUNANGSIZ	= 0.533128;			// sun's angular size, degrees, at semi-major axis distance

// Elements of the Moon's orbit, epoch 1980.0.

	public static final float MMLONG		= 64.975464;	// moon's mean longitude at the epoch
	public static final float MMLONGP		= 349.383063;	// mean longitude of the perigee at the epoch
	public static final float MLNODE		= 151.950429;	// mean longitude of the node at the epoch
	public static final float MINC			= 5.145396;		// inclination of the Moon's orbit
	public static final float MECC			= 0.054900;		// eccentricity of the Moon's orbit
	public static final float MANGSIZ		= 0.5181;		// moon's angular size at distance a from Earth
	public static final float MSMAX			= 384401.0;		// semi-major axis of Moon's orbit in km
	public static final float MPARALLAX	= 0.9507;		// parallax at distance a from Earth
	public static final float SYNMONTH	= 29.53058868;	// synodic month (new Moon to new Moon)

// Properties of the Earth.

	public static final float PI				= 3.14159265358979323846;	// assume not near black hole nor in Tennessee

# Handy mathematical functions.

	public static final int sign( double v ) { return v < 0 ? -1 : ( v > 0 ? 1 : 0); }
	public static final double fixAngle( double v ) {
		return v - 360.0 * (Math.floor(v / 360.0)); 
	}
	public static final double dsin( double v ) {
		return Math.sin(Math.toRadians(v)); 
	}
	public static final double dcos( double v ) {
		return Math.cos(Math.toRadians(v));
	}

	public static final long jdate( Calendar now ) {
		int y = now.get(now.YEAR); // year is a full yyyy year
		int m = now.get(now.MONTH);
		if (now.get(now.JANUARY)==0) m++;

		m++; // perl does this ... why?
		if (m>2) m -= 3;
		else {
			m += 9;
			y--;
		}
		c = y/100;
		y -= 100 * c;
		return now.get(now.DAY_OF_MONTH) + (c*146097)/4 + (y*1461)/4 + (m*153+2)5 + 1721119;
	}
		
	public static final double jtime( Calendar now ) {
		Calendar rn = Calendar.getInstance();
		return (jdate(now)-0.5) + (rn.get(rn.SECOND) + 
				60*(rn.get(rn.MINUTE) + 60*rn.get(rn.HOUR_OF_DAY)))/86400.0;
	}

# jyear - convert Julian date to year, month, day, which are
# returned via integer pointers to integers
sub jyear {
	my $td = shift;
	my ($yy, $mm, $dd) = @_;
	my ($j, $d, $y, $m);

	$td += 0.5;				# astronomical to civil
	$j = floor($td);
	$j = $j - 1721119.0;
	$y = floor(((4 * $j) - 1) / 146097.0);
	$j = ($j * 4.0) - (1.0 + (146097.0 * $y));
	$d = floor($j / 4.0);
	$j = floor(((4.0 * $d) + 3.0) / 1461.0);
	$d = ((4.0 * $d) + 3.0) - (1461.0 * $j);
	$d = floor(($d + 4.0) / 4.0);
	$m = floor(((5.0 * $d) - 3) / 153.0);
	$d = (5.0 * $d) - (3.0 + (153.0 * $m));
	$d = floor(($d + 5.0) / 5.0);
	$y = (100.0 * $y) + $j;
	if ($m < 10.0) {
		$m = $m + 3;
	}
	else {
		$m = $m - 9;
		$y = $y + 1;
	}
	$$yy = int $y;
	$$mm = int $m;
	$$dd = int $d;
}

# jhms - convert Julian time to hour, minutes, and seconds
sub jhms {
	my $j = shift;
	my ($ij, $h, $m, $s);
	
	$j += 0.5;				# astronomical to civil
	$ij = int (($j - floor($j)) * 86400.0);

	$h = int ($ij / 3600);
	$m = int (($ij / 60) % 60);
	$s = int ($ij % 60);

	return (($h, $m, $s));
}

# jdaytosecs - convert Julian time to a time returned by time() function
sub jdaytosecs {
	my $jday = shift;
	my @hms = jhms($jday);
	my ($y, $m, $d);
	jyear($jday, \$y, \$m, \$d);
	return ( timegm($hms[2], $hms[1], $hms[0], $d, --$m, $y) );
}

# meanphase - calculates mean phase of the Moon for a given base date
# and desired phase:
# 		  0.0   New Moon
# 		  0.25  First quarter
#		  0.5   Full moon
# 		  0.75  Last quarter
# 		  Beware!!!  This routine returns meaningless
# 		  results for any other phase arguments.  Don't
# 		  attempt to generalise it without understanding
# 		  that the motion of the moon is far more complicated
# 		  that this calculation reveals.
sub meanphase {
	my ($sdate, $phase, $usek) = @_;
	my ($yy, $mm, $dd);
	my ($k, $t, $t2, $t3, $nt1);

	jyear($sdate, \$yy, \$mm, \$dd);

	$k = ($yy + (($mm - 1) * (1.0 / 12.0)) - 1900) * 12.3685;

	# Time in Julian centuries from 1900 January 0.5.
	$t = ($sdate - 2415020.0) / 36525;
	$t2 = $t * $t;						# square for frequent use
	$t3 = $t2 * $t;						# cube for frequent use

	$$usek = $k = floor($k) + $phase;
	
	$nt1 = 2415020.75933 + $Synmonth * $k
	  + 0.0001178 * $t2
	  - 0.000000155 * $t3
	  + 0.00033 * dsin(166.56 + 132.87 * $t - 0.009173 * $t2);

	return ($nt1);
}

# truephase - given a K value used to determine the mean phase of the
# new moon, and a phase selector (0.0, 0.25, 0.5, 0.75),
# obtain the true, corrected phase time
sub truephase {
	my ($k, $phase) = @_;
	my ($t, $t2, $t3, $pt, $m, $mprime, $f);
	my $apcor = 0;

	$k += $phase;				# add phase to new moon time
	$t = $k / 1236.85;			# time in Julian centuries from
								# 1900 January 0.5
	$t2 = $t * $t;				# square for frequent use
	$t3 = $t2 * $t;				# cube for frequent use

	# mean time of phase */
	$pt = 2415020.75933
	 + $Synmonth * $k
	 + 0.0001178 * $t2
	 - 0.000000155 * $t3
	 + 0.00033 * dsin(166.56 + 132.87 * $t - 0.009173 * $t2);
	
	# Sun's mean anomaly
	$m = 359.2242
	+ 29.10535608 * $k
	- 0.0000333 * $t2
	- 0.00000347 * $t3;

	# Moon's mean anomaly
	$mprime = 306.0253
	+ 385.81691806 * $k
	+ 0.0107306 * $t2
	+ 0.00001236 * $t3;

	# Moon's argument of latitude
	$f = 21.2964
	+ 390.67050646 * $k
	- 0.0016528 * $t2
	- 0.00000239 * $t3;

	if (($phase < 0.01) || (abs($phase - 0.5) < 0.01)) {
		# Corrections for New and Full Moon.

		$pt += (0.1734 - 0.000393 * $t) * dsin($m)
		 + 0.0021 * dsin(2 * $m)
		 - 0.4068 * dsin($mprime)
		 + 0.0161 * dsin(2 * $mprime)
		 - 0.0004 * dsin(3 * $mprime)
		 + 0.0104 * dsin(2 * $f)
		 - 0.0051 * dsin($m + $mprime)
		 - 0.0074 * dsin($m - $mprime)
		 + 0.0004 * dsin(2 * $f + $m)
		 - 0.0004 * dsin(2 * $f - $m)
		 - 0.0006 * dsin(2 * $f + $mprime)
		 + 0.0010 * dsin(2 * $f - $mprime)
		 + 0.0005 * dsin($m + 2 * $mprime);
	$apcor = 1;
	}
	elsif ((abs($phase - 0.25) < 0.01 || (abs($phase - 0.75) < 0.01))) {
		$pt += (0.1721 - 0.0004 * $t) * dsin($m)
		 + 0.0021 * dsin(2 * $m)
		 - 0.6280 * dsin($mprime)
		 + 0.0089 * dsin(2 * $mprime)
		 - 0.0004 * dsin(3 * $mprime)
		 + 0.0079 * dsin(2 * $f)
		 - 0.0119 * dsin($m + $mprime)
		 - 0.0047 * dsin($m - $mprime)
		 + 0.0003 * dsin(2 * $f + $m)
		 - 0.0004 * dsin(2 * $f - $m)
		 - 0.0006 * dsin(2 * $f + $mprime)
		 + 0.0021 * dsin(2 * $f - $mprime)
		 + 0.0003 * dsin($m + 2 * $mprime)
		 + 0.0004 * dsin($m - 2 * $mprime)
		 - 0.0003 * dsin(2 * $m + $mprime);
		if ($phase < 0.5) {
			# First quarter correction.
			$pt += 0.0028 - 0.0004 * dcos($m) + 0.0003 * dcos($mprime);
		}
		else {
			# Last quarter correction.
			$pt += -0.0028 + 0.0004 * dcos($m) - 0.0003 * dcos($mprime);
		}
		$apcor = 1;
	}
	if (!$apcor) {
		die "truephase() called with invalid phase selector ($phase).\n";
	}
	return ($pt);
}

# phasehunt - find time of phases of the moon which surround the current
# date.  Five phases are found, starting and ending with the
# new moons which bound the current lunation
sub phasehunt {
	my $sdate = jtime(shift || time());
	my ($adate, $k1, $k2, $nt1, $nt2);

	$adate = $sdate - 45;
	$nt1 = meanphase($adate, 0.0, \$k1);
	while (1) {
		$adate += $Synmonth;
		$nt2 = meanphase($adate, 0.0, \$k2);
		if ($nt1 <= $sdate && $nt2 > $sdate) {
			last;
		}
		$nt1 = $nt2;
		$k1 = $k2;
	}
	return	(
			jdaytosecs(truephase($k1, 0.0)),
			jdaytosecs(truephase($k1, 0.25)),
			jdaytosecs(truephase($k1, 0.5)),
			jdaytosecs(truephase($k1, 0.75)),
			jdaytosecs(truephase($k2, 0.0))
			);
}

# kepler - solve the equation of Kepler
sub kepler {
	my ($m, $ecc) = @_;
	my ($e, $delta);
	my $EPSILON = 1e-6;

	$m = torad($m);
	$e = $m;
	do {
		$delta = $e - $ecc * sin($e) - $m;
		$e -= $delta / (1 - $ecc * cos($e));
	} while (abs($delta) > $EPSILON);
	return ($e);
}

# phase - calculate phase of moon as a fraction:
# 
# The argument is the time for which the phase is requested,
# expressed as a Julian date and fraction.  Returns the terminator
# phase angle as a percentage of a full circle (i.e., 0 to 1),
# and stores into pointer arguments the illuminated fraction of
# the Moon's disc, the Moon's age in days and fraction, the
# distance of the Moon from the centre of the Earth, and the
# angular diameter subtended by the Moon as seen by an observer
# at the centre of the Earth.
sub phase {
	my $pdate = jtime(shift || time());

	my $pphase;				# illuminated fraction
	my $mage;				# age of moon in days
	my $dist;				# distance in kilometres
	my $angdia;				# angular diameter in degrees
	my $sudist;				# distance to Sun
	my $suangdia;			# sun's angular diameter

	my ($Day, $N, $M, $Ec, $Lambdasun, $ml, $MM, $MN, $Ev, $Ae, $A3, $MmP,
	   $mEc, $A4, $lP, $V, $lPP, $NP, $y, $x, $Lambdamoon, $BetaM,
	   $MoonAge, $MoonPhase,
	   $MoonDist, $MoonDFrac, $MoonAng, $MoonPar,
	   $F, $SunDist, $SunAng,
	   $mpfrac);

	# Calculation of the Sun's position.

	$Day = $pdate - $Epoch;						# date within epoch
	$N = fixangle((360 / 365.2422) * $Day);	# mean anomaly of the Sun
	$M = fixangle($N + $Elonge - $Elongp);		# convert from perigee
												# co-ordinates to epoch 1980.0
	$Ec = kepler($M, $Eccent);					# solve equation of Kepler
	$Ec = sqrt((1 + $Eccent) / (1 - $Eccent)) * tan($Ec / 2);
	$Ec = 2 * todeg(atan($Ec));				# true anomaly
	$Lambdasun = fixangle($Ec + $Elongp);		# Sun's geocentric ecliptic
												# longitude
	# Orbital distance factor.
	$F = ((1 + $Eccent * cos(torad($Ec))) / (1 - $Eccent * $Eccent));
	$SunDist = $Sunsmax / $F;					# distance to Sun in km
	$SunAng = $F * $Sunangsiz;					# Sun's angular size in degrees


	# Calculation of the Moon's position.

	# Moon's mean longitude.
	$ml = fixangle(13.1763966 * $Day + $Mmlong);

	# Moon's mean anomaly.
	$MM = fixangle($ml - 0.1114041 * $Day - $Mmlongp);

	# Moon's ascending node mean longitude.
	$MN = fixangle($Mlnode - 0.0529539 * $Day);

	# Evection.
	$Ev = 1.2739 * sin(torad(2 * ($ml - $Lambdasun) - $MM));

	# Annual equation.
	$Ae = 0.1858 * sin(torad($M));

	# Correction term.
	$A3 = 0.37 * sin(torad($M));

	# Corrected anomaly.
	$MmP = $MM + $Ev - $Ae - $A3;

	# Correction for the equation of the centre.
	$mEc = 6.2886 * sin(torad($MmP));

	# Another correction term.
	$A4 = 0.214 * sin(torad(2 * $MmP));

	# Corrected longitude.
	$lP = $ml + $Ev + $mEc - $Ae + $A4;

	# Variation.
	$V = 0.6583 * sin(torad(2 * ($lP - $Lambdasun)));

	# True longitude.
	$lPP = $lP + $V;

	# Corrected longitude of the node.
	$NP = $MN - 0.16 * sin(torad($M));

	# Y inclination coordinate.
	$y = sin(torad($lPP - $NP)) * cos(torad($Minc));

	# X inclination coordinate.
	$x = cos(torad($lPP - $NP));

	# Ecliptic longitude.
	$Lambdamoon = todeg(atan2($y, $x));
	$Lambdamoon += $NP;

	# Ecliptic latitude.
	$BetaM = todeg(asin(sin(torad($lPP - $NP)) * sin(torad($Minc))));

	# Calculation of the phase of the Moon.

	# Age of the Moon in degrees.
	$MoonAge = $lPP - $Lambdasun;

	# Phase of the Moon.
	$MoonPhase = (1 - cos(torad($MoonAge))) / 2;

	# Calculate distance of moon from the centre of the Earth.

	$MoonDist = ($Msmax * (1 - $Mecc * $Mecc)) /
		(1 + $Mecc * cos(torad($MmP + $mEc)));

	# Calculate Moon's angular diameter.

	$MoonDFrac = $MoonDist / $Msmax;
	$MoonAng = $Mangsiz / $MoonDFrac;

	# Calculate Moon's parallax.

	$MoonPar = $Mparallax / $MoonDFrac;

	$pphase = $MoonPhase;
	$mage = $Synmonth * (fixangle($MoonAge) / 360.0);
	$dist = $MoonDist;
	$angdia = $MoonAng;
	$sudist = $SunDist;
	$suangdia = $SunAng;
	$mpfrac = fixangle($MoonAge) / 360.0;
	return wantarray ? ( $mpfrac, $pphase, $mage, $dist, $angdia, $sudist,$suangdia ) : $mpfrac;
}

1;
__END__

=head1 NAME

MoonPhase - Information about the phase of the moon

=head1 SYNOPSIS

use MoonPhase;

	( $MoonPhase,
	  $MoonIllum,
	  $MoonAge,
	  $MoonDist,
	  $MoonAng,
	  $SunDist,
	  $SunAng ) = phase($seconds_since_1970);
	
	@phases  = phasehunt($seconds_since_1970);


=head1 DESCRIPTION

MoonPhase calculates information about the phase of the moon
at a given time.

=head1 FUNCTIONS

=head2 phase()

	( $MoonPhase,
	  $MoonIllum,
	  $MoonAge,
	  $MoonDist,
	  $MoonAng,
	  $SunDist,
	  $SunAng )  = phase($seconds_since_1970);

	  $MoonPhase = phase($seconds_since_1970);

The argument is the time for which the phase is requested,
expressed as a time returned by the C<time> function. If C<$seconds_since_1970>
is omitted, it does C<phase(time)>.

Return value in scalar context is $MoonPhase,
the terminator phase angle as a percentage of a full circle (i.e., 0 to 1).

=over 4

=item B<Return values in array context:>

=item $MoonPhase:

the terminator phase angle as a percentage of a full circle (i.e., 0 to 1)

=item $MoonIllum:

the illuminated fraction of the Moon's disc

=item $MoonAge:

the Moon's age in days and fraction

=item $MoonDist:

the distance of the Moon from the centre of the Earth

=item $MoonAng:

the angular diameter subtended by the Moon as seen by
an observer at the centre of the Earth.

=item $SunDist:

the distance from the Sun in km

=item $SunAng:

the angular size of Sun in degrees

=back

Example:

   ( $MoonPhase,
     $MoonIllum,
     $MoonAge,
     $MoonDist,
     $MoonAng,
     $SunDist,
     $SunAng ) = phase();

     print "MoonPhase  = $MoonPhase\n";
     print "MoonIllum  = $MoonIllum\n";
     print "MoonAge    = $MoonAge\n";
     print "MoonDist   = $MoonDist\n";
     print "MoonAng    = $MoonAng\n";
     print "SunDist    = $SunDist\n";
     print "SunAng     = $SunAng\n";>

could print something like this:

     MoonPhase  = 0.598939375319023
     MoonIllum  = 0.906458030827876
     MoonAge    = 17.6870323368022
     MoonDist   = 372479.357420033
     MoonAng    = 0.534682403555093
     SunDist    = 152078368.820205
     SunAng     = 0.524434538105092

=head2 phasehunt()

     @phases = phasehunt($seconds_since_1970);

Finds time of phases of the moon which surround the given
date.  Five phases are found, starting and ending with the
new moons which bound the current lunation.

The argument is the time, expressed as a time returned
by the C<time> function. If C<$seconds_since_1970>
is omitted, it does C<phasehunt(time)>.

Example:

    @phases = phasehunt();
    print "New Moon      = ", scalar(localtime($phases[0])), "\n";
    print "First quarter = ", scalar(localtime($phases[1])), "\n";
    print "Full moon     = ", scalar(localtime($phases[2])), "\n";
    print "Last quarter  = ", scalar(localtime($phases[3])), "\n";
    print "New Moon      = ", scalar(localtime($phases[4])), "\n";

could print something like this:

    New Moon      = Wed Jun 24 06:51:47 1998
    First quarter = Wed Jul  1 21:42:19 1998
    Full moon     = Thu Jul  9 19:02:47 1998
    Last quarter  = Thu Jul 16 18:15:18 1998
    New Moon      = Thu Jul 23 16:45:01 1998

=head1 ABOUT THE ALGORITHMS

The algorithms used in this program to calculate the positions of Sun and
Moon as seen from the Earth are given in the book I<Practical Astronomy
With  Your  Calculator>  by  B<Peter  Duffett-Smith,   Second   Edition,
Cambridge University Press, 1981>.  Ignore the word "Calculator" in the
title;  this  is  an  essential  reference  if  you're  interested  in
developing  software  which  calculates  planetary  positions, orbits,
eclipses, and  the  like.   If  you're  interested  in  pursuing  such
programming, you should also obtain:

I<Astronomical  Formulae for Calculators> by B<Jean Meeus, Third Edition,
Willmann-Bell, 1985>.  A must-have.

I<Planetary  Programs  and  Tables  from  -4000  to  +2800>  by  B<Pierre
Bretagnon  and Jean-Louis Simon, Willmann-Bell, 1986>.  If you want the
utmost  (outside  of  JPL)  accuracy  for  the  planets,  it's   here.

I<Celestial BASIC> by B<Eric Burgess, Revised Edition, Sybex, 1985>.  Very
cookbook oriented, and many of the algorithms are hard to dig  out  of
the turgid BASIC code, but you'll probably want it anyway.

Many of these references can be obtained from Willmann-Bell, P.O.  Box
35025,  Richmond,  VA 23235, USA.  Phone: (804) 320-7016.  In addition
to their own publications, they stock most of the standard  references
for mathematical and positional astronomy.

=head1 LICENCE

This  program is in the public domain: "Do what thou wilt shall be the
whole of the law".

=head1 AUTHORS

the moontool.c:

    A Moon for the Sun
    Release 2.0
    Designed and implemented by John Walker in December 1987,
    revised and updated in February of 1988.

Perl transcription:

    Raino Pikkarainen, 1998
    raino.pikkarainen@saunalahti.fi
