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 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 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));
}
/// <summary>
/// Calculates ecliptical geocentric coordinates of Pluto for current epoch
/// </summary>
private CrdsEcliptical Pluto_Ecliptical(SkyContext c)
{
CrdsEcliptical plutoEcliptical = c.Get(Pluto_Equatorial0).ToEcliptical(c.Epsilon);
plutoEcliptical.Distance = c.Get(Pluto_EclipticalJ2000).Distance;
return(plutoEcliptical);
}
public void Phase_PhaseAngle_Elongation()
{
CrdsEquatorial eqSun = new CrdsEquatorial(20.6579, 8.6964);
CrdsEquatorial eqMoon = new CrdsEquatorial(134.6855, 13.7684);
const double epslion = 23.440636;
CrdsEcliptical sun = eqSun.ToEcliptical(epslion);
sun.Distance = 149971520;
CrdsEcliptical moon = eqMoon.ToEcliptical(epslion);
moon.Distance = 368410;
double psi = BasicEphem.Elongation(sun, moon);
Assert.AreEqual(110.79, psi, 1e-2);
double phaseAngle = BasicEphem.PhaseAngle(psi, sun.Distance, moon.Distance);
Assert.AreEqual(69.08, phaseAngle, 1e-2);
double phase = BasicEphem.Phase(phaseAngle);
Assert.AreEqual(0.68, phase, 1e-2);
}
public Sky()
{
// Ecliptic
LineEcliptic.FromHorizontal = (h) =>
{
var eq = h.ToEquatorial(GeoLocation, LocalSiderealTime);
var ec = eq.ToEcliptical(Epsilon);
return(new GridPoint(ec.Lambda, ec.Beta));
};
LineEcliptic.ToHorizontal = (c) =>
{
var ec = new CrdsEcliptical(c.Longitude, c.Latitude);
var eq = ec.ToEquatorial(Epsilon);
return(eq.ToHorizontal(GeoLocation, LocalSiderealTime));
};
// Horizontal grid
GridHorizontal.FromHorizontal = (h) => new GridPoint(h.Azimuth, h.Altitude);
GridHorizontal.ToHorizontal = (c) => new CrdsHorizontal(c.Longitude, c.Latitude);
// Equatorial grid
GridEquatorial.FromHorizontal = (h) =>
{
var eq = h.ToEquatorial(GeoLocation, LocalSiderealTime);
return(new GridPoint(eq.Alpha, eq.Delta));
};
GridEquatorial.ToHorizontal = (c) =>
{
var eq = new CrdsEquatorial(c.Longitude, c.Latitude);
return(eq.ToHorizontal(GeoLocation, LocalSiderealTime));
};
}
/// <summary>
/// Calculates ecliptical coordinates of Pluto for J2000.0 epoch
/// </summary>
private CrdsEcliptical Pluto_EclipticalJ2000(SkyContext c)
{
CrdsHeliocentrical plutoHeliocentrial = c.Get(Pluto_HeliocentricalJ2000);
CrdsHeliocentrical earthHeliocentrical = c.Get(Earth_HeliocentricalJ2000);
CrdsEcliptical plutoEcliptical = plutoHeliocentrial.ToRectangular(earthHeliocentrical).ToEcliptical();
return(plutoEcliptical);
}
public void EquatorialToEcliptical()
{
CrdsEquatorial eq = new CrdsEquatorial(new HMS("7h 45m 18.946s"), new DMS("+28* 01' 34.26''"));
CrdsEcliptical ecl = eq.ToEcliptical(23.4392911);
Assert.AreEqual(113.215630, ecl.Lambda, errorInDMS);
Assert.AreEqual(6.684170, ecl.Beta, errorInDMS);
}
public void EclipticalToRectangular()
{
CrdsEcliptical ecl = new CrdsEcliptical(199.907347, 0.62 / 3600.0, 0.99760775);
CrdsRectangular rect = ecl.ToRectangular(23.4402297);
Assert.AreEqual(-0.9379952, rect.X, 1e-7);
Assert.AreEqual(-0.3116544, rect.Y, 1e-7);
Assert.AreEqual(-0.1351215, rect.Z, 1e-7);
}
/// <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 void Libration()
{
double jd = 2448724.5;
CrdsEcliptical ecl = new CrdsEcliptical(133.167260, -3.229127);
double deltaPsi = 0.004610;
Libration le = LunarEphem.Libration(jd, ecl, deltaPsi);
Assert.AreEqual(-1.23, le.l, 1e-2);
Assert.AreEqual(4.20, le.b, 1e-2);
}
public void EclipticalToEquatorial()
{
CrdsEcliptical ecl = new CrdsEcliptical(113.215630, 6.684170);
CrdsEquatorial eq = ecl.ToEquatorial(23.4392911);
CrdsEquatorial eqExpected = new CrdsEquatorial(new HMS("7h 45m 18.946s"), new DMS("+28* 01' 34.26''"));
Assert.AreEqual(eqExpected.Alpha, eq.Alpha, errorInHMS);
Assert.AreEqual(eqExpected.Delta, eq.Delta, errorInDMS);
}
/// <summary>
/// Gets drawing rotation of image, measured clockwise from
/// a point oriented to top of the screen towards North ecliptic pole point
/// </summary>
/// <param name="ecl">Ecliptical coordinates of a central point of a body.</param>
/// <returns></returns>
public static float GetRotationTowardsEclipticPole(this IMapContext map, CrdsEcliptical ecl)
{
// Coordinates of center of a body (image) to be rotated
PointF p = map.Project(ecl.ToEquatorial(map.Epsilon).ToHorizontal(map.GeoLocation, map.SiderealTime));
// Point directed to North ecliptic pole
PointF pNorth = map.Project((ecl + new CrdsEcliptical(0, 1)).ToEquatorial(map.Epsilon).ToHorizontal(map.GeoLocation, map.SiderealTime));
// Clockwise rotation
return(LineInclinationY(p, pNorth));
}
public void PositionAngleOfAxis()
{
double jd = 2448724.5;
CrdsEcliptical ecl = new CrdsEcliptical(new DMS("133* 10' 00''"), new DMS("-3* 13' 45''"));
double epsilon = 23.440636;
double deltaPsi = 0.004610;
double P = LunarEphem.PositionAngleOfAxis(jd, ecl, epsilon, deltaPsi);
Assert.AreEqual(15.08, P, 1e-2);
}
private CrdsRectangular SunRectangular(double jd, double epsilon)
{
CrdsHeliocentrical hEarth = PlanetPositions.GetPlanetCoordinates(3, jd, true, false);
var eSun = new CrdsEcliptical(Angle.To360(hEarth.L + 180), -hEarth.B, hEarth.R);
// Corrected solar coordinates to FK5 system
// NO correction for nutation and aberration should be performed here (ch. 26, p. 171)
eSun += PlanetPositions.CorrectionForFK5(jd, eSun);
return(eSun.ToRectangular(epsilon));
}
/// <summary>
/// Gets ecliptical coordinates of Sun for J2000.0 epoch
/// </summary>
private CrdsEcliptical SunEcliptical(SkyContext c)
{
CrdsHeliocentrical hEarth = PlanetPositions.GetPlanetCoordinates(3, c.JulianDay, !c.PreferFastCalculation, false);
var eSun = new CrdsEcliptical(Angle.To360(hEarth.L + 180), -hEarth.B, hEarth.R);
// Corrected solar coordinates to FK5 system
// NO correction for nutation and aberration should be performed here (ch. 26, p. 171)
eSun += PlanetPositions.CorrectionForFK5(c.JulianDay, eSun);
return(eSun);
}
public override void Initialize()
{
// Ecliptic
LineEcliptic.FromHorizontal = (h, ctx) =>
{
var eq = h.ToEquatorial(ctx.GeoLocation, ctx.SiderealTime);
var ec = eq.ToEcliptical(ctx.Epsilon);
return(new GridPoint(ec.Lambda, ec.Beta));
};
LineEcliptic.ToHorizontal = (c, ctx) =>
{
var ec = new CrdsEcliptical(c.Longitude, c.Latitude);
var eq = ec.ToEquatorial(ctx.Epsilon);
return(eq.ToHorizontal(ctx.GeoLocation, ctx.SiderealTime));
};
// Galactic equator
LineGalactic.FromHorizontal = (h, ctx) =>
{
var eq = h.ToEquatorial(ctx.GeoLocation, ctx.SiderealTime);
var eq1950 = Precession.GetEquatorialCoordinates(eq, peTo1950);
var gal = eq1950.ToGalactical();
return(new GridPoint(gal.l, gal.b));
};
LineGalactic.ToHorizontal = (c, ctx) =>
{
var gal = new CrdsGalactical(c.Longitude, c.Latitude);
var eq1950 = gal.ToEquatorial();
var eq = Precession.GetEquatorialCoordinates(eq1950, peFrom1950);
return(eq.ToHorizontal(ctx.GeoLocation, ctx.SiderealTime));
};
// Meridian line
LineMeridian.FromHorizontal = (h, ctx) => new GridPoint(0, h.Azimuth - 180);
LineMeridian.ToHorizontal = (c, context) => new CrdsHorizontal(0, c.Longitude - 180);
// Horizontal grid
GridHorizontal.FromHorizontal = (h, ctx) => new GridPoint(h.Azimuth, h.Altitude);
GridHorizontal.ToHorizontal = (c, context) => new CrdsHorizontal(c.Longitude, c.Latitude);
// Equatorial grid
GridEquatorial.FromHorizontal = (h, ctx) =>
{
var eq = h.ToEquatorial(ctx.GeoLocation, ctx.SiderealTime);
return(new GridPoint(eq.Alpha, eq.Delta));
};
GridEquatorial.ToHorizontal = (c, ctx) =>
{
var eq = new CrdsEquatorial(c.Longitude, c.Latitude);
return(eq.ToHorizontal(ctx.GeoLocation, ctx.SiderealTime));
};
}
/// <summary>
/// Calculates Sun rectangular coordinates for J2000 epoch
/// </summary>
private CrdsRectangular Sun_RectangularJ2000(SkyContext c)
{
// Heliocentrical coordinates of Earth
CrdsHeliocentrical hEarth = c.Get(Earth_HeliocentricalJ2000);
// transform to ecliptical coordinates of the Sun
CrdsEcliptical eclSun = new CrdsEcliptical(Angle.To360(hEarth.L + 180), -hEarth.B, hEarth.R);
// Sun rectangular coordinates, J2000.0 epoch
CrdsRectangular rSun = eclSun.ToRectangular(epsilonJ2000);
return(rSun);
}
/// <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);
}
/// <summary>
/// Gets horizontal topocentrical coordinates of Earth Shadow
/// </summary>
private CrdsHorizontal EarthShadowCoordinates(SkyContext c)
{
// Ecliptical coordinates of Sun
var eclSun = c.Get(SunEcliptical);
// Coordinates of Earth shadow is an opposite point on the celestial sphere
var eclShadow = new CrdsEcliptical(eclSun.Lambda + 180, -eclSun.Beta);
// Equatorial geocentrical coordinates of the shadow center
var eq0 = eclShadow.ToEquatorial(c.Epsilon);
// Topocentrical equatorial coordinates
var eq = eq0.ToTopocentric(c.GeoLocation, c.SiderealTime, c.Get(Parallax));
// finally get the horizontal coordinates
return(eq.ToHorizontal(c.GeoLocation, c.SiderealTime));
}
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 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);
}
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);
}
private CrdsRectangular NeptuneMoon_Rectangular(SkyContext c, int m)
{
CrdsEquatorial moonEq = c.Get(NeptuneMoon_Equatorial, m);
CrdsEcliptical moonEcl = c.Get(NeptuneMoon_Ecliptical, m);
CrdsEquatorial neptuneEq = c.Get(Planet_Equatorial, Planet.NEPTUNE);
CrdsEcliptical neptuneEcl = c.Get(Planet_Ecliptical, Planet.NEPTUNE);
double sd = c.Get(Planet_Semidiameter, Planet.NEPTUNE) / 3600;
double P = c.Get(Planet_Appearance, Planet.NEPTUNE).P;
double[] alpha = new double[] { moonEq.Alpha, neptuneEq.Alpha };
Angle.Align(alpha);
double[] delta = new double[] { moonEq.Delta, neptuneEq.Delta };
double x = (alpha[0] - alpha[1]) * Math.Cos(Angle.ToRadians(neptuneEq.Delta)) / sd;
double y = (delta[0] - delta[1]) / sd;
// radius-vector of moon, in planet's equatorial radii
double r = Math.Sqrt(x * x + y * y);
// rotation angle
double theta = Angle.ToDegrees(Math.Atan2(x, y));
// rotate with position angle of the planet
theta -= P;
// convert back to rectangular coordinates, but rotated with P angle:
y = r * Math.Cos(Angle.ToRadians(theta));
x = -r *Math.Sin(Angle.ToRadians(theta));
const double NEPTUNE_RADIUS = 24622;
const double AU = 149597870;
// z is expressed in Uranus equatorial radii
double z = (moonEcl.Distance - neptuneEcl.Distance) / (2 * NEPTUNE_RADIUS / AU);
return(new CrdsRectangular(x, y, z));
}
public static void Rotate(this IMapContext map, PointF p, CrdsEcliptical ecl)
{
// Point directed to North ecliptic pole
PointF pNorth = map.Project((ecl + new CrdsEcliptical(0, 1)).ToEquatorial(map.Epsilon).ToHorizontal(map.GeoLocation, map.SiderealTime));
// Clockwise rotation
float inc = LineInclinationY(p, pNorth);
if (map.IsInverted)
{
inc = -90 - inc;
}
float rotation = (float)inc;
if (map.IsInverted)
{
rotation = 90 - rotation;
}
map.Graphics.TranslateTransform(p.X, p.Y);
map.Graphics.RotateTransform(rotation);
}
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>
/// Calculates heliocentrical coordinates of Pluto for J2000 epoch
/// </summary>
private CrdsHeliocentrical Pluto_HeliocentricalJ2000(SkyContext c)
{
// 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;
// Sun rectangular coordinates, J2000.0 epoch
CrdsRectangular rSun = c.Get(Sun_RectangularJ2000);
// Heliocentrical coordinates of Pluto
CrdsHeliocentrical plutoHeliocentrial = null;
// Iterative process to find heliocentrical coordinates of planet
while (Math.Abs(tau - tau0) > deltaTau)
{
// Heliocentrical coordinates of Pluto
plutoHeliocentrial = PlutoPosition.Position(c.JulianDay - tau);
// Rectangular heliocentrical coordinates of Pluto
CrdsRectangular rPluto = new CrdsEcliptical(plutoHeliocentrial.L, plutoHeliocentrial.B, plutoHeliocentrial.R).ToRectangular(epsilonJ2000);
double x = rPluto.X + rSun.X;
double y = rPluto.Y + rSun.Y;
double z = rPluto.Z + rSun.Z;
double dist = Math.Sqrt(x * x + y * y + z * z);
tau0 = tau;
tau = PlanetPositions.LightTimeEffect(dist);
}
return(plutoHeliocentrial);
}
public void Separation()
{
// Example 17.a, AA(II)
{
var c1 = new CrdsEquatorial(213.9154, 19.1825);
var c2 = new CrdsEquatorial(201.2983, -11.1614);
Assert.AreEqual(32.7930, Angle.Separation(c1, c2), 1e-4);
}
{
var c1 = new CrdsEcliptical(213.9154, 19.1825);
var c2 = new CrdsEcliptical(201.2983, -11.1614);
Assert.AreEqual(32.7930, Angle.Separation(c1, c2), 1e-4);
}
{
var c1 = new CrdsGeographical(213.9154, 19.1825);
var c2 = new CrdsGeographical(201.2983, -11.1614);
Assert.AreEqual(32.7930, Angle.Separation(c1, c2), 1e-4);
}
{
var c1 = new CrdsHorizontal(213.9154, 19.1825);
var c2 = new CrdsHorizontal(201.2983, -11.1614);
Assert.AreEqual(32.7930, Angle.Separation(c1, c2), 1e-4);
}
}
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);
}
}
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);
}
}
