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lib/Astro/Coord/ECI/Moon.pm  view on Meta::CPAN

If called in scalar context, you get the phase.

This can be called as a class method, but if you do this the time
must be specified.

Jean Meeus' "Astronomical Algorithms", 2nd Edition, Chapter 49 page
349, defines the phases of the moon in terms of the difference between
the geocentric longitudes of the Moon and Sun - specifically, that
new, first quarter, full, and last quarter are the moments when this
difference is 0, 90, 180, and 270 degrees respectively.

Not quite above reproach, this module simply defines the phase of the
Moon as the difference between these two quantities, even if it is not
a multiple of 90 degrees. This is different than the "phase angle" of
the Moon, which Meeus defines as the elongation of the Earth from the
Sun, as seen from the Moon. Because we take the "phase angle" as just
pi - the phase (in radians), we introduce an error of about 0.3% in
the illumination calculation.

=cut

sub phase {
    my ($self, $time) = @_;

    (ref $self || $time) or croak <<eod;
Error - You must specify a time if you call phase() as a class method.
eod

    $self = $self->new () unless ref $self;

    $self->universal ($time) if $time;

    my $sun = $self->get( 'sun' )->universal( $self->universal() );

    my (undef, $longs) = $sun->ecliptic ();
    my (undef, $longm) = $self->ecliptic ();

    my $phase = mod2pi ($longm - $longs);
    return wantarray ? ($phase, (1 + cos ($self->PI - $phase)) / 2) : $phase;
}

=item $moon->time_set ()

This method sets coordinates of the object to the coordinates of the
Moon at the object's currently-set universal time.  The velocity
components are arbitrarily set to 0, since Meeus' algorithm does not
provide this information. The 'equinox_dynamical' attribute is set to
the currently-set dynamical time.

Although there's no reason this method can't be called directly, it
exists to take advantage of the hook in the B<Astro::Coord::ECI>
object, to allow the position of the Moon to be computed when the
object's time is set.

The computation comes from Jean Meeus' "Astronomical Algorithms", 2nd
Edition, Chapter 47, pages 337ff. Meeus gives the accuracy as 10
seconds of arc in latitude, and 4 seconds of arc in longitude. He
credits the algorithm to M. Chalpront-Touze and J. Chalpront, "The
Lunar Ephemeris ELP 2000" from I<Astronomy and Astrophysics> volume
124, pp 50-62 (1983), but the formulae for the mean arguments to
J. Chalpront, M. Chalpront-Touze, and G. Francou, I<Introduction dans
ELP 2000-82B de nouvelles valeurs des parametres orbitaux de la Lune
et du barycentre Terre-Lune>, Paris, January 1998.

=cut

sub time_set {
    my $self = shift;

    my $time = $self->dynamical;

    my $T = jcent2000 ($time);			# Meeus (22.1)

#	Moon's mean longitude.

    my $Lprime = mod2pi (deg2rad (			# Meeus (47.1)
	(((- ($T / 65_194_000) +
	1 / 538_841) * $T - 0.0015786) * $T +
	481267.88123421) * $T + 218.3164477));

#	Moon's mean elongation.

    my $D = mod2pi (deg2rad (((($T / 113_065_000 +	# Meeus (47.2)
	1 / 545_868) * $T - 0.0018819) * $T +
	445267.1114034) * $T + 297.8501921));

#	Sun's mean anomaly.

    my $M = mod2pi (deg2rad ((($T / 24_490_000 -		# Meeus (47.3)
	0.000_1536) * $T + 35999.050_2909) * $T +
	357.5291092));

#	Moon's mean anomaly.

    my $Mprime = mod2pi (deg2rad ((((- $T / 14_712_000 +	# Meeus (47.4)
	1 / 69_699) * $T + 0.008_7414) * $T +
	477198.867_5055) * $T + 134.963_3964));

#	Moon's argument of latitude (mean distance
#	from ascending node).

    my $F = mod2pi (deg2rad (((($T / 863_310_000 -	# Meeus (47.5)
	1 / 3_526_000) * $T - 0.003_6539) * $T +
	483202.017_5233) * $T + 93.272_0950));

#	Eccentricity correction factor.

    my $E = (- 0.000_0074 * $T - 0.002_516) * $T + 1;	# Meeus (47.6)
    my @efac = (1, $E, $E * $E);

#	Compute "further arguments".

    my $A1 = mod2pi (deg2rad (131.849 * $T + 119.75));		# Venus
    my $A2 = mod2pi (deg2rad (479264.290 * $T + 53.09));	# Jupiter
    my $A3 = mod2pi (deg2rad (481266.484 * $T + 313.45));	# undocumented

#	Compute periodic terms for longitude (sigma l) and
#	distance (sigma r).

    my ($sigmal, $sigmar) = (0, 0);