/// <summary>
/// Gets equatorial coordinates of a star for current epoch
/// </summary>
public CrdsEquatorial Equatorial(SkyContext c, ushort hrNumber)
{
Star star = Stars.ElementAt(hrNumber - 1);
PrecessionalElements p = c.Get(GetPrecessionalElements);
double years = c.Get(YearsSince2000);
// Initial coodinates for J2000 epoch
CrdsEquatorial eq0 = new CrdsEquatorial(star.Equatorial0);
// Take into account effect of proper motion:
// now coordinates are for the mean equinox of J2000.0,
// but for epoch of the target date
eq0.Alpha += star.PmAlpha * years / 3600.0;
eq0.Delta += star.PmDelta * years / 3600.0;
// Equatorial coordinates for the mean equinox and epoch of the target date
CrdsEquatorial eq = Precession.GetEquatorialCoordinates(eq0, p);
// Nutation effect
var eq1 = Nutation.NutationEffect(eq, c.NutationElements, c.Epsilon);
// Aberration effect
var eq2 = Aberration.AberrationEffect(eq, c.AberrationElements, c.Epsilon);
// Apparent coordinates of the star
eq += eq1 + eq2;
return(eq);
}
public override void Calculate(SkyContext context)
{
// precessional elements
var p = Precession.ElementsFK5(Date.EPOCH_J2000, context.JulianDay);
foreach (var ds in DeepSkies)
{
ds.Equatorial = context.Get(Equatorial, ds);
ds.Horizontal = context.Get(Horizontal, ds);
if (ds.Outline != null)
{
foreach (var op in ds.Outline)
{
CrdsEquatorial eq0 = new CrdsEquatorial(op.Equatorial0);
// Equatorial coordinates for the mean equinox and epoch of the target date
var eq = Precession.GetEquatorialCoordinates(eq0, p);
// Nutation effect
var eq1 = Nutation.NutationEffect(eq, context.NutationElements, context.Epsilon);
// Aberration effect
var eq2 = Aberration.AberrationEffect(eq, context.AberrationElements, context.Epsilon);
// Apparent coordinates of the object
eq += eq1 + eq2;
// Apparent horizontal coordinates
op.Horizontal = eq.ToHorizontal(context.GeoLocation, context.SiderealTime);
}
}
}
}
public void CalculatePlanetApparentPlaceLP()
{
double jde = 2448976.5;
double tau = 0;
CrdsEcliptical ecl = null;
for (int i = 0; i < 2; i++)
{
CrdsHeliocentrical hEarth = PlanetPositions.GetPlanetCoordinates(3, jde - tau, highPrecision: false);
CrdsHeliocentrical hVenus = PlanetPositions.GetPlanetCoordinates(2, jde - tau, highPrecision: false);
var rect = hVenus.ToRectangular(hEarth);
ecl = rect.ToEcliptical();
tau = PlanetPositions.LightTimeEffect(ecl.Distance);
}
// Correction for FK5 system
CrdsEcliptical corr = PlanetPositions.CorrectionForFK5(jde, ecl);
ecl += corr;
ecl += Nutation.NutationEffect(16.749 / 3600.0);
CrdsEquatorial eq = ecl.ToEquatorial(23.439669);
Assert.AreEqual(new HMS("21h 04m 41.459s"), new HMS(eq.Alpha));
Assert.AreEqual(new DMS("-18* 53' 16.66''"), new DMS(eq.Delta));
}
public void HorizontalToEquatorial()
{
// Apparent local horizontal coordinates of Venus
var hor = new CrdsHorizontal(68.0337, 15.1249);
// Geographical coordinates of US Naval Observatory at Washington, DC
var geo = new CrdsGeographical(new DMS("+38* 55' 17''"), new DMS("+77* 03' 56''"));
// Date of observation
var jd = new Date(new DateTime(1987, 4, 10, 19, 21, 0, DateTimeKind.Utc)).ToJulianDay();
// Nutation elements
var nutation = Nutation.NutationElements(jd);
// True obliquity
var epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// Apparent sidereal time at Greenwich
var theta0 = Date.ApparentSiderealTime(jd, nutation.deltaPsi, epsilon);
Assert.AreEqual(new HMS("8h 34m 56.853s"), new HMS(theta0));
// Expected apparent equatorial coordinates of Venus
var eqExpected = new CrdsEquatorial(new HMS("23h 09m 16.641s"), new DMS("-6* 43' 11.61''"));
// Tested value
var eqActual = hor.ToEquatorial(geo, theta0);
Assert.AreEqual(eqExpected.Alpha, eqActual.Alpha, errorInHMS);
Assert.AreEqual(eqExpected.Delta, eqActual.Delta, errorInDMS);
}
public void GetSolarCoordinatesLP()
{
double jde = 2448908.5;
// get Earth coordinates
CrdsHeliocentrical crds = PlanetPositions.GetPlanetCoordinates(Planet.Earth, jde, highPrecision: false);
Assert.AreEqual(19.907372, crds.L, 1e-6);
Assert.AreEqual(-0.644, crds.B * 3600, 1e-3);
Assert.AreEqual(0.99760775, crds.R, 1e-8);
// transform to ecliptical coordinates of the Sun
CrdsEcliptical ecl = new CrdsEcliptical(Angle.To360(crds.L + 180), -crds.B, crds.R);
// get FK5 system correction
CrdsEcliptical corr = PlanetPositions.CorrectionForFK5(jde, ecl);
Assert.AreEqual(-0.09033, corr.Lambda * 3600, 1e-5);
Assert.AreEqual(-0.023, corr.Beta * 3600, 1e-3);
// correct solar coordinates to FK5 system
ecl += corr;
Assert.AreEqual(199.907347, ecl.Lambda, 1e-6);
Assert.AreEqual(0.62, ecl.Beta * 3600, 1e-2);
Assert.AreEqual(0.99760775, ecl.Distance, 1e-8);
var nutation = Nutation.NutationElements(jde);
// True obliquity
double epsilon = Date.TrueObliquity(jde, nutation.deltaEpsilon);
// accuracy is 0.5"
Assert.AreEqual(15.908, nutation.deltaPsi * 3600, 0.5);
// accuracyis 0.1"
Assert.AreEqual(-0.308, nutation.deltaEpsilon * 3600, 0.1);
// accuracy is 0.1"
Assert.AreEqual(23.4401443, epsilon, 0.1 / 3600.0);
// add nutation effect
ecl += Nutation.NutationEffect(nutation.deltaPsi);
// calculate aberration effect
CrdsEcliptical aberration = Aberration.AberrationEffect(ecl.Distance);
Assert.AreEqual(-20.539, aberration.Lambda * 3600.0, 1e-3);
// add aberration effect
ecl += aberration;
// convert ecliptical to equatorial coordinates
CrdsEquatorial eq = ecl.ToEquatorial(epsilon);
// check apparent equatorial coordinates
// assume an accuracy of 0.5'' is sufficient
Assert.AreEqual(198.378178, eq.Alpha, 1.0 / 3600 * 0.5);
Assert.AreEqual(-7.783871, eq.Delta, 1.0 / 3600 * 0.5);
}
public void GetCoordinates()
{
double jd = 2448724.5;
// geocentrical coordinates
CrdsEcliptical ecl = LunarMotion.GetCoordinates(jd);
Assert.AreEqual(133.162655, ecl.Lambda, 1e-6);
Assert.AreEqual(-3.229126, ecl.Beta, 1e-6);
Assert.AreEqual(368409.7, ecl.Distance, 1e-1);
// get nutation elements
var nutation = Nutation.NutationElements(jd);
// apparent geocentrical ecliptical coordinates
ecl += Nutation.NutationEffect(nutation.deltaPsi);
// true obliquity of the Earth orbit
double epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// equatorial geocentrical coordinates
CrdsEquatorial eq = ecl.ToEquatorial(epsilon);
// Max error in Right Ascention is 0.1" of time
double errAlpha = new HMS("0h 0m 00.1s").ToDecimalAngle();
// Max error in Declination is 1" of arc
double errDelta = new DMS("0* 0' 01''").ToDecimalAngle();
Assert.AreEqual(new HMS("8h 58m 45.2s").ToDecimalAngle(), eq.Alpha, errAlpha);
Assert.AreEqual(new DMS("+13* 46' 06''").ToDecimalAngle(), eq.Delta, errDelta);
}
public void EquatorialToHorizontal()
{
// Apparent equatorial coordinates of Venus
var eq = new CrdsEquatorial(new HMS("23h 09m 16.641s"), new DMS("-6* 43' 11.61''"));
// Geographical coordinates of US Naval Observatory at Washington, DC
var geo = new CrdsGeographical(new DMS("+38* 55' 17''"), new DMS("+77* 03' 56''"));
// Date of observation
var jd = new Date(new DateTime(1987, 4, 10, 19, 21, 0, DateTimeKind.Utc)).ToJulianDay();
// Mean sidereal time at Greenwich
var theta0 = Date.MeanSiderealTime(jd);
Assert.AreEqual(new HMS("8h 34m 57.0896s"), new HMS(theta0));
// Nutation elements
var nutation = Nutation.NutationElements(jd);
// True obliquity
var epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// Apparent sidereal time at Greenwich
theta0 = Date.ApparentSiderealTime(jd, nutation.deltaPsi, epsilon);
Assert.AreEqual(new HMS("8h 34m 56.853s"), new HMS(theta0));
// Expected local horizontal coordinates of Venus
var hor = eq.ToHorizontal(geo, theta0);
Assert.AreEqual(15.1249, hor.Altitude, 1e-4);
Assert.AreEqual(68.0336, hor.Azimuth, 1e-4);
}
public void NutationElements()
{
var nutation = Nutation.NutationElements(jd);
var deltaPsi = nutation.deltaPsi * 3600;
var deltaEpsilon = nutation.deltaEpsilon * 3600;
Assert.AreEqual(-3.788, deltaPsi, 0.5);
Assert.AreEqual(9.443, deltaEpsilon, 0.1);
}
/// <summary>
/// Gets apparent geocentrical ecliptical coordinates of the Moon
/// </summary>
private CrdsEcliptical Ecliptical0(SkyContext c)
{
// geocentrical coordinates of the Moon
CrdsEcliptical ecliptical0 = LunarMotion.GetCoordinates(c.JulianDay);
// apparent geocentrical ecliptical coordinates
ecliptical0 += Nutation.NutationEffect(c.NutationElements.deltaPsi);
return(ecliptical0);
}
public static double ApparentEclipticLongitude(double julianDate, bool highPrecision)
{
var longitude = ConvertLongitudeToFK5(julianDate, highPrecision)
+ CoordinateTransformation.SetDMSToDegrees(0, 0, Nutation.NutationInLongitude(julianDate));
var radius = Earth.GetSunRadiusVector(julianDate);
return((highPrecision)
? longitude - (0.005775518 * radius * CoordinateTransformation.SetDMSToDegrees(0, 0, GetVariationEclipticLongitude(julianDate)))
: longitude - CoordinateTransformation.SetDMSToDegrees(0, 0, 20.4898 / radius));
}
private CrdsEcliptical UranusMoon_Ecliptical(SkyContext c, int m)
{
var ecliptical = c.Get(UranusMoons_Positions)[m - 1].ToEcliptical();
// Correction for FK5 system
ecliptical += PlanetPositions.CorrectionForFK5(c.JulianDay, ecliptical);
// Take nutation into account
ecliptical += Nutation.NutationEffect(c.NutationElements.deltaPsi);
return(ecliptical);
}
/// <summary>
/// Gets ecliptical coordinates of Sun
/// </summary>
public CrdsEcliptical Sun_Ecliptical(SkyContext c)
{
CrdsHeliocentrical hEarth = c.Get(Earth_Heliocentrial);
var sunEcliptical = new CrdsEcliptical(Angle.To360(hEarth.L + 180), -hEarth.B, hEarth.R);
// Corrected solar coordinates to FK5 system
sunEcliptical += PlanetPositions.CorrectionForFK5(c.JulianDay, sunEcliptical);
// Add nutation effect to ecliptical coordinates of the Sun
sunEcliptical += Nutation.NutationEffect(c.NutationElements.deltaPsi);
// Add aberration effect, so we have an final ecliptical coordinates of the Sun
sunEcliptical += Aberration.AberrationEffect(sunEcliptical.Distance);
return(sunEcliptical);
}
public void NutationEffect()
{
CrdsEquatorial eq = new CrdsEquatorial(41.5472, 49.3485);
NutationElements ne = new NutationElements()
{
deltaPsi = 14.861 / 3600,
deltaEpsilon = 2.705 / 3600
};
double epsilon = 23.436;
CrdsEquatorial correction = Nutation.NutationEffect(eq, ne, epsilon);
Assert.AreEqual(15.843, correction.Alpha * 3600, 1e-3);
Assert.AreEqual(6.218, correction.Delta * 3600, 1e-3);
}
public void TestEquinox()
{
JulianDate jd = new JulianDate(new DateTime(2003, 1, 1));
Nutation nut = new Nutation(jd);
Assert.That(nut.EquationOfEquinox, Is.EqualTo(-0.9381).Within(0.00005));
Assert.That(nut.DeltaPsi, Is.EqualTo(-15.340).Within(0.0005));
Assert.That(nut.DeltaEpsilon, Is.EqualTo(3.024).Within(0.0005));
Assert.That(nut.Epsilon.Seconds, Is.EqualTo(23.068));
jd = new JulianDate(new DateTime(2003, 2, 1));
nut = new Nutation(jd);
Assert.That(nut.EquationOfEquinox, Is.EqualTo(-0.8444).Within(0.00005));
Assert.That(nut.DeltaPsi, Is.EqualTo(-13.808).Within(0.0005));
Assert.That(nut.DeltaEpsilon, Is.EqualTo(3.782).Within(0.0005));
//Assert.That(nut.Epsilon, Is.EqualTo(Angle.FromDegrees(23, 26, 23.068)));
}
/// <summary>
/// Gets equatorial coordinates of deep sky object for current epoch
/// </summary>
private CrdsEquatorial Equatorial(SkyContext c, DeepSky ds)
{
PrecessionalElements p = c.Get(GetPrecessionalElements);
// Equatorial coordinates for the mean equinox and epoch of the target date
CrdsEquatorial eq = Precession.GetEquatorialCoordinates(ds.Equatorial0, p);
// Nutation effect
var eq1 = Nutation.NutationEffect(eq, c.NutationElements, c.Epsilon);
// Aberration effect
var eq2 = Aberration.AberrationEffect(eq, c.AberrationElements, c.Epsilon);
// Apparent coordinates of the object
eq += eq1 + eq2;
return(eq);
}
public void CalculatePlanetApparentPlaceHP()
{
double jde = 2448976.5;
// time taken by the light to reach the Earth
double tau = 0;
// previous value of tau to calculate the difference
double tau0 = 1;
// final difference to stop iteration process, 1 second of time
double deltaTau = TimeSpan.FromSeconds(1).TotalDays;
// Ecliptical coordinates of Venus
CrdsEcliptical ecl = null;
// Iterative process to find ecliptical coordinates of Venus
while (Math.Abs(tau - tau0) > deltaTau)
{
// Heliocentrical coordinates of Earth
var hEarth = PlanetPositions.GetPlanetCoordinates(3, jde - tau, highPrecision: true);
// Heliocentrical coordinates of Venus
var hVenus = PlanetPositions.GetPlanetCoordinates(2, jde - tau, highPrecision: true);
// Ecliptical coordinates of Venus
ecl = hVenus.ToRectangular(hEarth).ToEcliptical();
tau0 = tau;
tau = PlanetPositions.LightTimeEffect(ecl.Distance);
}
// Correction for FK5 system
ecl += PlanetPositions.CorrectionForFK5(jde, ecl);
// Take nutation into account
ecl += Nutation.NutationEffect(16.749 / 3600.0);
// Apparent equatorial coordinates of Venus
CrdsEquatorial eq = ecl.ToEquatorial(23.439669);
Assert.AreEqual(new HMS("21h 04m 41.454s"), new HMS(eq.Alpha));
Assert.AreEqual(new DMS("-18* 53' 16.84''"), new DMS(eq.Delta));
}
/// <summary>
/// Gets ecliptical coordinates of planet
/// </summary>
public CrdsEcliptical Planet_Ecliptical(SkyContext c, int p)
{
// Heliocentrical coordinates of planet
CrdsHeliocentrical heliocentrical = c.Get(Planet_Heliocentrical, p);
// Heliocentrical coordinates of Earth
CrdsHeliocentrical hEarth = c.Get(Earth_Heliocentrial);
// Ecliptical coordinates of planet
var ecliptical = heliocentrical.ToRectangular(hEarth).ToEcliptical();
// Correction for FK5 system
ecliptical += PlanetPositions.CorrectionForFK5(c.JulianDay, ecliptical);
// Take nutation into account
ecliptical += Nutation.NutationEffect(c.NutationElements.deltaPsi);
return(ecliptical);
}
/// <summary>
/// Gets apparent geocentrical ecliptical coordinates of the Sun
/// </summary>
private CrdsEcliptical SunEcliptical(SkyContext c)
{
// get Earth coordinates
CrdsHeliocentrical hEarth = c.Get(EarthHeliocentrical);
// transform to ecliptical coordinates of the Sun
CrdsEcliptical sunEcliptical = new CrdsEcliptical(Angle.To360(hEarth.L + 180), -hEarth.B, hEarth.R);
// correct solar coordinates to FK5 system
sunEcliptical += PlanetPositions.CorrectionForFK5(c.JulianDay, sunEcliptical);
// add nutation effect to ecliptical coordinates of the Sun
sunEcliptical += Nutation.NutationEffect(c.NutationElements.deltaPsi);
// add aberration effect, so we have an final ecliptical coordinates of the Sun
sunEcliptical += Aberration.AberrationEffect(sunEcliptical.Distance);
return(sunEcliptical);
}
/// <summary>
/// Gets equatorial geocentrical coordinates for current epoch
/// </summary>
protected CrdsEquatorial EquatorialG(SkyContext c, T body)
{
// Precessinal elements to convert between epochs
var pe = c.Get(GetPrecessionalElements);
// Equatorial geocentrical coordinates for J2000 epoch
var eq0 = c.Get(EquatorialJ2000, body);
// Equatorial coordinates for the mean equinox and epoch of the target date
CrdsEquatorial eq = Precession.GetEquatorialCoordinates(eq0, pe);
// Nutation effect
var eq1 = Nutation.NutationEffect(eq, c.NutationElements, c.Epsilon);
// Aberration effect
var eq2 = Aberration.AberrationEffect(eq, c.AberrationElements, c.Epsilon);
// Apparent coordinates of the object
eq += eq1 + eq2;
return(eq);
}
/// <summary>
/// Gets equatorial coordinates of a star for current epoch
/// </summary>
public CrdsEquatorial Equatorial(SkyContext c, Nova n)
{
PrecessionalElements p = c.Get(GetPrecessionalElements);
double years = c.Get(YearsSince2000);
// Initial coodinates for J2000 epoch
CrdsEquatorial eq0 = new CrdsEquatorial(n.Equatorial0);
// Equatorial coordinates for the mean equinox and epoch of the target date
CrdsEquatorial eq = Precession.GetEquatorialCoordinates(eq0, p);
// Nutation effect
var eq1 = Nutation.NutationEffect(eq, c.NutationElements, c.Epsilon);
// Aberration effect
var eq2 = Aberration.AberrationEffect(eq, c.AberrationElements, c.Epsilon);
// Apparent coordinates of the star
eq += eq1 + eq2;
return(eq);
}
public CrdsEcliptical Ecliptical(SkyContext c)
{
// get Earth coordinates
CrdsHeliocentrical crds = PlanetPositions.GetPlanetCoordinates(Planet.EARTH, c.JulianDay, highPrecision: true);
// transform to ecliptical coordinates of the Sun
var ecl = new CrdsEcliptical(Angle.To360(crds.L + 180), -crds.B, crds.R);
// get FK5 system correction
CrdsEcliptical corr = PlanetPositions.CorrectionForFK5(c.JulianDay, ecl);
// correct solar coordinates to FK5 system
ecl += corr;
// add nutation effect
ecl += Nutation.NutationEffect(c.NutationElements.deltaPsi);
// add aberration effect
ecl += Aberration.AberrationEffect(ecl.Distance);
return(ecl);
}
public void GetSolarCoordinatesLP()
{
double jde = 2448908.5;
// get Earth coordinates
CrdsHeliocentrical crds = PlanetPositions.GetPlanetCoordinates(3, jde, highPrecision: false);
// transform to ecliptical coordinates of the Sun
CrdsEcliptical ecl = new CrdsEcliptical(Angle.To360(crds.L + 180), -crds.B, crds.R);
// get FK5 system correction
CrdsEcliptical corr = PlanetPositions.CorrectionForFK5(jde, ecl);
// correct solar coordinates to FK5 system
ecl += corr;
var nutation = Nutation.NutationElements(jde);
// True obliquity
double epsilon = Date.TrueObliquity(jde, nutation.deltaEpsilon);
// add nutation effect
ecl += Nutation.NutationEffect(nutation.deltaPsi);
// calculate aberration effect
CrdsEcliptical aberration = Aberration.AberrationEffect(ecl.Distance);
// add aberration effect
ecl += aberration;
// convert ecliptical to equatorial coordinates
CrdsEquatorial eq = ecl.ToEquatorial(epsilon);
// check apparent equatorial coordinates
// assume an accuracy of 0.5'' is sufficient
Assert.AreEqual(198.378178, eq.Alpha, 1.0 / 3600 * 0.5);
Assert.AreEqual(-7.783871, eq.Delta, 1.0 / 3600 * 0.5);
}
/// <summary>
/// Gets equatorial coordinates of a star for current epoch
/// </summary>
private CrdsEquatorial Equatorial(SkyContext context, Tycho2Star star)
{
PrecessionalElements p = context.Get(PrecessionalElements);
double years = context.Get(YearsSince2000);
// Take into account effect of proper motion:
// now coordinates are for the mean equinox of J2000.0,
// but for epoch of the target date
var eq0 = star.Equatorial0 + new CrdsEquatorial(star.PmRA * years / 3600000, star.PmDec * years / 3600000);
// Equatorial coordinates for the mean equinox and epoch of the target date
CrdsEquatorial eq = Precession.GetEquatorialCoordinates(eq0, p);
// Nutation effect
var eqN = Nutation.NutationEffect(eq, context.NutationElements, context.Epsilon);
// Aberration effect
var eqA = Aberration.AberrationEffect(eq, context.AberrationElements, context.Epsilon);
// Apparent coordinates of the star
eq += eqN + eqA;
return(eq);
}
public void Positions()
{
// Test data is obtained from NASA JPL Ephemeris tool
// https://ssd.jpl.nasa.gov/horizons.cgi
List <TestData> testDatas = new List <TestData>()
{
// Triton
// 2020-Jan-07 13:00 2458856.041666667 -0.964 12.797
new TestData()
{
MoonNumber = 1,
Neptune = new CrdsEcliptical(new DMS("346* 24' 16.12''"), new DMS("-1* 01' 26.26''"), 30.416),
JulianDay = 2458856.041666667,
X = -0.964,
Y = 12.797
},
// Triton
// 2025-Jan-22 19:00 2460698.291666667 1.086 -12.382
new TestData()
{
MoonNumber = 1,
Neptune = new CrdsEcliptical(new DMS("357° 43' 31.73''"), new DMS("-1° 16' 24.69''"), 30.416),
JulianDay = 2460698.291666667,
X = 1.086,
Y = -12.382
},
// Nereid
// 2020-Feb-27 00:00 2458906.500000000 5.124 10.556
new TestData()
{
MoonNumber = 2,
Neptune = new CrdsEcliptical(new DMS("348* 00' 11.97''"), new DMS("-1* 00' 54.27''"), 30.906),
JulianDay = 2458906.5,
X = 5.124,
Y = 10.556
},
// Nereid
// 2020-Jul-13 00:00 2459043.500000000 384.491 206.269
new TestData()
{
MoonNumber = 2,
Neptune = new CrdsEcliptical(new DMS("350* 51' 10.8''"), new DMS("-1* 05' 15.56''"), 29.405),
JulianDay = 2459043.5,
X = 384.491,
Y = 206.269
},
// Nereid
// 1980-Jan-01 00:00 2444239.500000000 135.407 32.771
new TestData()
{
MoonNumber = 2,
Neptune = new CrdsEcliptical(new DMS("260* 55' 41.93''"), new DMS("+1* 20' 26.28''"), 31.209),
JulianDay = 2444239.5,
X = 135.407,
Y = 32.771
}
};
// possible error in coordinates is 1 arcsecond
const double error = 1;
foreach (var testData in testDatas)
{
NutationElements ne = Nutation.NutationElements(testData.JulianDay);
double epsilon = Date.TrueObliquity(testData.JulianDay, ne.deltaEpsilon);
CrdsEcliptical eclSatellite = NeptunianMoons.Position(testData.JulianDay, testData.Neptune, testData.MoonNumber);
CrdsEquatorial eqNeptune = testData.Neptune.ToEquatorial(epsilon);
CrdsEquatorial eqSatellite = eclSatellite.ToEquatorial(epsilon);
double X = (eqSatellite.Alpha - eqNeptune.Alpha) * Math.Cos(Angle.ToRadians(eqNeptune.Delta)) * 3600;
double Y = (eqSatellite.Delta - eqNeptune.Delta) * 3600;
Assert.AreEqual(testData.X, X, error);
Assert.AreEqual(testData.Y, Y, error);
}
}
public void Noumenia()
{
// Example are taken from
// http://www.makkahcalendar.org/en/islamicCalendarArticle4.php
// IX.4 Example of Makkah
{
// 17 Nov 2009, "best time" is 14:48 UTC
double jd = new Date(new DateTime(2009, 11, 17, 14, 48, 0, DateTimeKind.Utc)).ToJulianEphemerisDay();
// Nutation elements
var nutation = Nutation.NutationElements(jd);
// True obliquity
var epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// Sidereal time at Greenwich
double siderealTime = Date.ApparentSiderealTime(jd, nutation.deltaPsi, epsilon);
// Ecliptical coordinates of the Sun, taken from the example (see ref.)
CrdsEcliptical eclSun = new CrdsEcliptical(235.39, 0);
// Ecliptical coordinates of the Moon, taken from the example (see ref.)
CrdsEcliptical eclMoon = new CrdsEcliptical(245.01, -3.76);
// Geograhical coordinates of Makkah
CrdsGeographical geo = new CrdsGeographical(-39.82563, 21.42664);
double q = LunarEphem.CrescentQ(eclMoon, eclSun, 0.2539 * 3600, epsilon, siderealTime, geo);
Assert.AreEqual(-0.465, q, 0.001);
}
// IX.5 Example of intermediate horizon 30°W, 30°S at 21:04
{
// 17 Nov 2009, 21:04 UTC
double jd = new Date(new DateTime(2009, 11, 17, 21, 04, 0, DateTimeKind.Utc)).ToJulianEphemerisDay();
// Nutation elements
var nutation = Nutation.NutationElements(jd);
// True obliquity
var epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// Sidereal time at Greenwich
double siderealTime = Date.ApparentSiderealTime(jd, nutation.deltaPsi, epsilon);
// Ecliptical coordinates of the Sun, taken from the example (see ref.)
CrdsEcliptical eclSun = new CrdsEcliptical(235.65, 0);
// Ecliptical coordinates of the Moon, taken from the example (see ref.)
CrdsEcliptical eclMoon = new CrdsEcliptical(248.32, -3.55);
// Geograhical coordinates of Makkah
CrdsGeographical geo = new CrdsGeographical(30, -30);
double q = LunarEphem.CrescentQ(eclMoon, eclSun, 0.2536 * 3600, epsilon, siderealTime, geo);
Assert.AreEqual(0.367, q, 0.001);
}
}
private void DoTest(CrdsGeographical location, OrbitalElements oe, string testData, double errorR, double errorEq)
{
Regex regex = new Regex("^(\\S+)\\s+(\\S+)\\s+(\\S+)\\s+(\\S+)\\s+(\\S+ \\S+ \\S+) (\\S+ \\S+ \\S+)$");
string[] lines = testData.Split('\n');
foreach (string line in lines)
{
string dataLine = line.Trim();
if (!string.IsNullOrEmpty(dataLine))
{
var match = regex.Match(dataLine);
double jd = double.Parse(match.Groups[1].Value, CultureInfo.InvariantCulture);
double X = double.Parse(match.Groups[2].Value, CultureInfo.InvariantCulture);
double Y = double.Parse(match.Groups[3].Value, CultureInfo.InvariantCulture);
double Z = double.Parse(match.Groups[4].Value, CultureInfo.InvariantCulture);
string ra = match.Groups[5].Value;
string dec = match.Groups[6].Value;
var eqTest = new CrdsEquatorial(new HMS(ra), new DMS(dec));
var nutation = Nutation.NutationElements(jd);
var aberration = Aberration.AberrationElements(jd);
// True obliquity
double epsilon = Date.TrueObliquity(jd, nutation.deltaEpsilon);
// final difference to stop iteration process, 1 second of time
double deltaTau = TimeSpan.FromSeconds(1).TotalDays;
// time taken by the light to reach the Earth
double tau = 0;
// previous value of tau to calculate the difference
double tau0 = 1;
// Rectangular coordinates of minor body
CrdsRectangular r = null;
// Rectangular coordinates of the Sun
var sun = SunRectangular(jd, epsilon);
// Distance to the Earth
double Delta = 0;
// Iterative process to find rectangular coordinates of minor body
while (Math.Abs(tau - tau0) > deltaTau)
{
// Rectangular coordinates of minor body
r = MinorBodyPositions.GetRectangularCoordinates(oe, jd - tau, epsilon);
double ksi = sun.X + r.X;
double eta = sun.Y + r.Y;
double zeta = sun.Z + r.Z;
// Distance to the Earth
Delta = Math.Sqrt(ksi * ksi + eta * eta + zeta * zeta);
tau0 = tau;
tau = PlanetPositions.LightTimeEffect(Delta);
}
// Test heliocentric rectangular coordinates
Assert.AreEqual(X, r.X, errorR);
Assert.AreEqual(Y, r.Y, errorR);
Assert.AreEqual(Z, r.Z, errorR);
double x = sun.X + r.X;
double y = sun.Y + r.Y;
double z = sun.Z + r.Z;
double alpha = Angle.ToDegrees(Math.Atan2(y, x));
double delta = Angle.ToDegrees(Math.Asin(z / Delta));
var eq0 = new CrdsEquatorial(alpha, delta);
var theta0 = Date.ApparentSiderealTime(jd, nutation.deltaPsi, epsilon);
var parallax = PlanetEphem.Parallax(Delta);
var eq = eq0.ToTopocentric(location, theta0, parallax);
// Test equatorial coordinates
Assert.AreEqual(eqTest.Alpha, eq.Alpha, errorEq / 3600.0);
Assert.AreEqual(eqTest.Delta, eq.Delta, errorEq / 3600.0);
}
}
}