/**
* Finds the mean obliquity of the ecliptic (ε0) for a given date by using the
* coefficients provided by Laskar.
*
* By using this method the accuracy is estimated to be at 0".01 after 1000
* years and a few arc seconds after 10,000 years on either side of the
* epoch J2000. Also, this method is only valid over a period of 10,000 years
* on either side of J2000 and will throe an exception if attempted on out
* of range dates
*
* @param AstroDate $date Date to find ε0 for
* @return Angle Mean obliquity (ε0)
* @throws Exception Occurs with an out of range date, |year| > 10,000
*
* @see Meeus, Jean. Astronomical Algorithms. Richmond, Virg.: Willmann-Bell,
* 2009. 147. Print.
*/
public static function meanObliquityLaskar(AstroDate $date)
{
// Time factor
$t = ($date->copy()->toUTC()->jd - 2451545.0) / 36525;
// Check for out of range date
if (abs($t) >= 1) {
$msg = "The Laskar method is not valid for the year {$date->year}.";
throw new Exception($msg);
}
$ε0TermsLaskar = [Angle::dms(23, 26, 21.448)->rad, Angle::dms(0, 0, -4680.93)->rad, Angle::dms(0, 0, -1.55)->rad, Angle::dms(0, 0, 1999.25)->rad, Angle::dms(0, 0, -51.38)->rad, Angle::dms(0, 0, -249.67)->rad, Angle::dms(0, 0, -39.05)->rad, Angle::dms(0, 0, 7.12)->rad, Angle::dms(0, 0, 27.87)->rad, Angle::dms(0, 0, 5.79)->rad, Angle::dms(0, 0, 2.45)->rad];
$ε0 = static::Horner($t, $ε0TermsLaskar);
return Angle::rad($ε0);
}
/**
* Creates a new geographic location from values expressed as radians
*
* @param float $lat Latitude, radians
* @param float $lon Longitude, radians West negative
*
* @return static
*/
public static function rad($lat, $lon)
{
return new static(Angle::rad($lat), Angle::rad($lon));
}
/**
* Converts this instance to an equatorial coordinate
*
* @return Equat
*/
public function toEquat()
{
// Cartesian -> spherical
IAU::C2s([$this->x->au, $this->y->au, $this->z->au], $theta, $phi);
// Create RA and Declination components from radians
$ra = Angle::rad($theta)->norm()->toTime();
$dec = Angle::rad($phi);
// Return new equatorial instance using same frame and epoch
return new Equat($this->frame, $this->epoch, $ra, $dec, $this->r);
}
/**
* Performs a [IRCS -> observed] coordinate transformation for the parameters
* of this instance
* @param string $type Coordintate type, 'e' for equat 'h' for horiz
* @return static|Horiz
*/
protected function ICRStoObserved($type = 'e', Pressure $pressure = null, Temperature $temp = null, $humidity = null)
{
// Instance initial properties
$rc = $this->ra->toAngle()->rad;
$dc = $this->dec->rad;
$date1 = $this->epoch->toDate()->toTDB()->toJD();
$pr = 0;
$pd = 0;
$rv = 0;
$px = $this->dist->au > 0 ? 8.794 / 3600 / $this->dist->au : 0;
$utc1 = $this->epoch->toDate()->toUTC()->toJD();
$dut1 = IERS::jd($utc1)->dut1();
$elong = $this->topo ? $this->topo->lon->rad : 0;
$phi = $this->topo ? $this->topo->lat->rad : 0;
$hm = 0;
//$this->obsrv->height->m;
$xp = IERS::jd($utc1)->x() / 3600 * pi() / 180;
$yp = IERS::jd($utc1)->y() / 3600 * pi() / 180;
$phpa = $pressure ? $pressure->mbar : 0;
$tc = $temp ? $temp->c : 0;
$rh = $humidity ? $humidity : 0;
$wl = 0.55;
// ICRS -> CIRS (geocentric observer)
IAU::Atci13($rc, $dc, $pr, $pd, $px, $rv, $date1, 0, $ri, $di, $eo);
// CIRS -> ICRS (astrometric)
//IAU::Atic13($ri, $di, $date1, 0, $rca, $dca, $eo);
// ICRS (astrometric) -> CIRS (geocentric observer)
//IAU::Atci13($rca, $dca, $pr, $pd, $px, $rv, $date1, 0, $ri, $di, $eo);
// Apparent place ?
//$ri = $ri - $eo;
//$di = $di;
//
// CIRS -> topocentric
IAU::Atio13($ri, $di, $utc1, 0, $dut1, $elong, $phi, $hm, $xp, $yp, $phpa, $tc, $rh, $wl, $aob, $zob, $hob, $dob, $rob);
if ($type == 'e') {
// Copy this instance, and override the apparent RA and Decl
$topocentric = $this->copy();
$topocentric->ra = Angle::rad($rob)->toTime();
$topocentric->dec = Angle::rad($dob);
$topocentric->apparent = true;
// Return apparent coordinates
return $topocentric;
} else {
// Prepare new horizontal instance
$horiz = new Horiz(Angle::rad(deg2rad(90) - $zob), Angle::rad($aob), $this->dist);
return $horiz;
}
}
/**
* Finds the sidereal time of this intsance
*
* @param type $mode Type of sidereal time... (a = apparent, m = mean)
* @param Angle $lon If a longitude is supplied, finds local sidereal time,
* otherwise returns sidereal time at Greenwich
*/
public function sidereal($mode = 'a', Angle $lon = null)
{
// Get UT1 time
$ut = $this->copy()->toUT1();
$uta = $ut->jd;
$utb = $ut->dayFrac;
$ut = null;
// Get TT time
$tt = $this->copy()->toTT();
$tta = $tt->jd;
$ttb = $tt->dayFrac;
$tt = null;
// Compute either GMST or GAST
$st;
if ($mode == 'a') {
$strad = IAU::Gst06a($uta, $utb, $tta, $ttb);
} else {
$strad = IAU::Gmst06($uta, $utb, $tta, $ttb);
}
// Add longitude if relevant
if ($lon) {
$st = Angle::rad($strad)->add($lon)->norm()->toTime();
} else {
$st = Angle::rad($strad)->toTime();
}
// Return as hours
return $st->setUnit('hours');
}
public function testSign()
{
$this->assertEquals('-', Angle::deg(-10)->sign);
$this->assertEquals('-', Angle::rad(-10)->sign);
$this->assertEquals('-', Angle::asec(-10)->sign);
$this->assertEquals('-', Angle::amin(-10)->sign);
$this->assertEquals('-', Angle::mas(-10)->sign);
$this->assertEquals('-', Angle::dms(-10, 0, 0, 0)->sign);
$this->assertEquals('-', Angle::dms(0, -10, 0, 0)->sign);
$this->assertEquals('-', Angle::dms(0, 0, -10, 0)->sign);
$this->assertEquals('-', Angle::dms(0, 0, 0, -10)->sign);
$this->assertEquals('+', Angle::dms(10, 0, 0, 0)->sign);
$this->assertEquals('+', Angle::dms(1, -10, 0, 0)->sign);
$this->assertEquals('+', Angle::dms(1, 0, -10, 0)->sign);
$this->assertEquals('+', Angle::dms(1, 0, 0, -10)->sign);
$this->assertEquals('+', Angle::deg(10)->sign);
$this->assertEquals('+', Angle::rad(10)->sign);
$this->assertEquals('+', Angle::asec(10)->sign);
$this->assertEquals('+', Angle::amin(10)->sign);
$this->assertEquals('+', Angle::mas(10)->sign);
}
