/// <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 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 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);
}
}
}
}
/// <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 AberrationElements()
{
// AA(II) example 25.a
{
AberrationElements ae = Aberration.AberrationElements(2448908.5);
Assert.AreEqual(0.016711668, ae.e, 1e-9);
Assert.AreEqual(199.90988, ae.lambda, 1e-5);
}
// AA(II) example 23.a
{
AberrationElements ae = Aberration.AberrationElements(Date.JulianDay(2028, 11, 13.19));
Assert.AreEqual(0.01669649, ae.e, 1e-8);
Assert.AreEqual(231.328, ae.lambda, 1e-3);
Assert.AreEqual(103.434, ae.pi, 1e-3);
}
}
/// <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);
}
/// <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);
}
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);
}
}
}
void ShowAberration()
{
Aberration v = new Aberration();
ShowParameterView(v, TestChart.getCorrectPhoto());
}
