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 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 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));
};
}
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 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>
/// 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));
}
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);
}
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);
}
}