private static (double longitude, double obliquity) swi_nutation(JulianDayNumber tjd, SweData swed)
{
// from interpolation, with three data points in 1-day steps;
// maximum error is about 3 mas
if (swed.InterpolateNutation)
{
// precalculated data points available
if (swed.InterpolatedNutation != null && tjd < swed.InterpolatedNutation.Time2 && tjd > swed.InterpolatedNutation.Time0)
{
var dx = (tjd - swed.InterpolatedNutation.Time0).Raw - 1.0;
var longitude = quadratic_intp(swed.InterpolatedNutation.DPsi0, swed.InterpolatedNutation.DPsi1, swed.InterpolatedNutation.DPsi2, dx);
var obliquity = quadratic_intp(swed.InterpolatedNutation.DEps0, swed.InterpolatedNutation.DEps1, swed.InterpolatedNutation.DEps2, dx);
return(longitude, obliquity);
}
else
{
var interpol = new InterpolatedNutation
{
Time0 = tjd.AddDays(-1.0), // one day earlier
Time2 = tjd.AddDays(1.0) // one day later
};
(interpol.DPsi0, interpol.DEps0) = calc_nutation(interpol.Time0, swed);
(interpol.DPsi2, interpol.DEps2) = calc_nutation(interpol.Time2, swed);
(interpol.DPsi1, interpol.DEps1) = calc_nutation(tjd, swed);
swed.InterpolatedNutation = interpol;
return(interpol.DPsi1, interpol.DEps1);
}
}
return(calc_nutation(tjd, swed));
}
private (PlanetPosition position, PlanetPosition speed) CalcBySegment(JulianDayNumber tjd, SEFileSegment segment, bool calcSpeed = true)
{
var t = (tjd - segment.Start).Raw / segment.Size.Raw;
t = t * 2 - 1;
var position = new PlanetPosition(
longitude: echeb(t, segment.LongitudeCoefficients),
latitude: echeb(t, segment.LatitudeCoefficients),
distance: echeb(t, segment.DistanceCoefficients)
);
PlanetPosition speed = default;
if (calcSpeed)
{
speed = new PlanetPosition(
longitude: edcheb(t, segment.LongitudeCoefficients),
latitude: edcheb(t, segment.LatitudeCoefficients),
distance: edcheb(t, segment.DistanceCoefficients)
);
}
return(position, speed);
}
/// <summary>
/// <see cref="swi_check_nutation"/>
/// </summary>
internal static Nutation Calculate(JulianDayNumber tjd, SweData swed)
{
var(longitude, obliquity) = swi_nutation(tjd, swed);
var matrix = nut_matrix(longitude, obliquity, swed.oec);
return(new Nutation(tjd, longitude, obliquity, matrix));
}
private static (double longitude, double obliquity) calc_nutation(JulianDayNumber J, SweData swed)
{
int n;
double dpsi, deps;
double longitude = 0.0, obliquity = 0.0;
var jplhora_model = swed.JplHorizonsMode;
var nut_model = swed.NutationModel;
bool is_jplhor = false;
if (swed.Iflag.HasFlag(SEFLG.JPLHOR))
{
is_jplhor = true;
}
if (swed.Iflag.HasFlag(SEFLG.JPLHOR_APPROX) &&
jplhora_model == JplHorizonsMode.Three &&
J <= HORIZONS_TJD0_DPSI_DEPS_IAU1980)
{
is_jplhor = true;
}
if (is_jplhor)
{
(longitude, obliquity) = calc_nutation_iau1980(J, nut_model);
if (swed.Iflag.HasFlag(SEFLG.JPLHOR))
{
n = (int)(swed.Eop.EndDate.Raw - swed.Eop.BeginDate.Raw + 0.000001);
var J2 = J;
if (J < DPSI_DEPS_IAU1980_TJD0_HORIZONS)
{
J2 = DPSI_DEPS_IAU1980_TJD0_HORIZONS;
}
var t = (J2 - swed.Eop.BeginDate).Raw;
dpsi = bessel(swed.Eop.dPsi, n + 1, t);
deps = bessel(swed.Eop.dEps, n + 1, t);
longitude += dpsi / 3600.0 * DEGTORAD;
obliquity += deps / 3600.0 * DEGTORAD;
}
else
{
longitude += DPSI_IAU1980_TJD0 / 3600.0 * DEGTORAD;
obliquity += DEPS_IAU1980_TJD0 / 3600.0 * DEGTORAD;
}
}
else if (nut_model == NutationModel.IAU_1980 || nut_model == NutationModel.IAU_CORR_1987)
{
(longitude, obliquity) = calc_nutation_iau1980(J, nut_model);
}
else if (nut_model == NutationModel.IAU_2000A || nut_model == NutationModel.IAU_2000B)
{
(longitude, obliquity) = calc_nutation_iau2000ab(J, nut_model);
if (swed.Iflag.HasFlag(SEFLG.JPLHOR_APPROX) && jplhora_model == JplHorizonsMode.Two)
{
longitude += -41.7750 / 3600.0 / 1000.0 * DEGTORAD;
obliquity += -6.8192 / 3600.0 / 1000.0 * DEGTORAD;
}
}
return(longitude, obliquity);
}
private EarthOrientationParameters(
JulianDayNumber beginDate, JulianDayNumber endDate,
IReadOnlyList <double> dPsi, IReadOnlyList <double> dEps)
{
BeginDate = beginDate;
EndDate = endDate;
BeginDateHorizons = JulianDayNumber.FromRaw(2437684.5);
this.dPsi = dPsi;
this.dEps = dEps;
}
internal SEFileData GetFile(int bodyNumber, JulianDayNumber jd)
{
if (_files.TryGetValue(bodyNumber, out var bag))
{
foreach (var item in bag)
{
if (item.StartDate <= jd && jd <= item.EndDate)
{
return(item);
}
}
}
throw new FileNotFoundException();
}
public Nutation(
JulianDayNumber date,
double longitude,
double obliquity,
double[,] matrix
)
{
Date = date;
Longitude = longitude;
Obliquity = obliquity;
Matrix = matrix;
Sin = Math.Sin(obliquity);
Cos = Math.Cos(obliquity);
}
public SweData(SEFLG iflag, DateTime dateTimeInUTC, EarthOrientationParameters eop, bool interpolateNutation = false)
{
Iflag = iflag;
CalculationDate = dateTimeInUTC;
Eop = eop;
InterpolateNutation = interpolateNutation;
CalculationJulianDayNumber = JulianDayNumber.FromDate(dateTimeInUTC);
TidalAcc = TidalAcceleration.Get(TidalAccelerationMode.Default);
IsManualTidalAcc = false;
LongtermPrecessionMode = PrecessionModel.Default;
ShorttermPrecessionMode = PrecessionModel.Default;
JplHorizonsMode = JplHorizonsMode.Default;
NutationModel = NutationModel.Default;
oec = Epsilon.Calc(CalculationJulianDayNumber, iflag, this);
oec2000 = Epsilon.Calc(JulianDayNumber.J2000, iflag, this);
}
/// <see cref="sweph"/>
private (PlanetPosition position, PlanetPosition speed) CalcBodyPositionAndSpeedInternal(int bodyNumber, DateTime dateTimeInUTC, bool calcSpeed)
{
var tjd = JulianDayNumber.FromDate(dateTimeInUTC);
var file = _storage.GetFile(bodyNumber, tjd);
var planet = bodyNumber > SEConsts.AseroidOffset
? InternalPlanets.AnyBody
: (InternalPlanets)bodyNumber;
var planetData = file.PlanetsData[planet];
var segment = file.ReadSegment(planetData, tjd, _sweData.oec2000);
var(position, speed) = CalcBySegment(tjd, segment, calcSpeed);
/* if planet wanted is barycentric sun:
* current sepl* files have do not have barycentric sun,
* but have heliocentric earth and barycentric earth.
* So barycentric sun and must be computed
* from heliocentric earth and barycentric earth: the
* computation above gives heliocentric earth, therefore we
* have to compute barycentric earth and subtract heliocentric
* earth from it. this may be necessary with calls from
* sweplan() and from app_pos_etc_sun() (light-time). */
if (bodyNumber == (int)InternalPlanets.BarycentricSun && planetData.Flags.HasFlag(PlanetFlags.EmbHeliocentric))
{
// sweph() calls sweph() !!! for EMB.
// because we always call new calculation, warning about EARTH and EMB equality was omitted
var(embPos, embSpeed) = CalcBodyPositionAndSpeedInternal((int)InternalPlanets.EMB, dateTimeInUTC, calcSpeed);
position = new PlanetPosition(
embPos.Longitude - position.Longitude,
embPos.Latitude - position.Latitude,
embPos.Distance - position.Distance);
if (calcSpeed)
{
speed = new PlanetPosition(
embSpeed.Longitude - speed.Longitude,
embSpeed.Latitude - speed.Latitude,
embSpeed.Distance - speed.Distance);
}
}
// asteroids are heliocentric.
// if JPL or SWISSEPH, convert to barycentric - currently always
if (planet >= InternalPlanets.AnyBody)
{
(position, speed) = ConvertToBarycentric(position, speed, dateTimeInUTC, calcSpeed);
}
return(position, speed);
}
/// <see cref="swi_get_tid_acc"/>
public static double Calculate(EphemerisMode ephemerisMode, JulianDayNumber julianDay, JPLDENumber denum)
{
if (denum == JPLDENumber.Auto)
{
switch (ephemerisMode)
{
case EphemerisMode.Moshier:
denum = JPLDENumber.DE404;
break;
case EphemerisMode.JPL:
throw new NotImplementedException();
case EphemerisMode.SWISSEPH:
/*
* tjd_et = tjd_ut; // + swe_deltat_ex(tjd_ut, 0, NULL); we do not add delta t, because it would result in a recursive call of swi_set_tid_acc()
* if (swed.fidat[SEI_FILE_MOON].fptr == NULL ||
* tjd_et < swed.fidat[SEI_FILE_MOON].tfstart + 1 ||
* tjd_et > swed.fidat[SEI_FILE_MOON].tfend - 1)
* {
* iflag = SEFLG_SWIEPH | SEFLG_J2000 | SEFLG_TRUEPOS | SEFLG_ICRS;
* iflag = swe_calc(tjd_et, SE_MOON, iflag, xx, serr);
* }
* if (swed.fidat[SEI_FILE_MOON].fptr != NULL)
* {
* denum = swed.fidat[SEI_FILE_MOON].sweph_denum;
* }
* // Moon ephemeris file is not available, default to Moshier ephemeris
* else
*/
denum = JPLDENumber.DE404; // DE number of Moshier ephemeris
break;
}
}
return(Get(denum));
}
private static (double longitude, double obliquity) calc_nutation_iau2000ab(JulianDayNumber J, NutationModel nut_model)
{
int i, j, k, inls;
double M, SM, F, D, OM;
double AL, ALSU, AF, AD, AOM, APA;
double ALME, ALVE, ALEA, ALMA, ALJU, ALSA, ALUR, ALNE;
double darg, sinarg, cosarg;
double dpsi = 0, deps = 0;
double T = (J - JulianDayNumber.J2000).Raw / 36525.0;
/* luni-solar nutation */
/* Fundamental arguments, Simon & al. (1994) */
/* Mean anomaly of the Moon. */
M = swe_degnorm((485868.249036 +
T * (1717915923.2178 +
T * (31.8792 +
T * (0.051635 +
T * (-0.00024470))))) / 3600.0) * DEGTORAD;
/* Mean anomaly of the Sun */
SM = swe_degnorm((1287104.79305 +
T * (129596581.0481 +
T * (-0.5532 +
T * (0.000136 +
T * (-0.00001149))))) / 3600.0) * DEGTORAD;
/* Mean argument of the latitude of the Moon. */
F = swe_degnorm((335779.526232 +
T * (1739527262.8478 +
T * (-12.7512 +
T * (-0.001037 +
T * (0.00000417))))) / 3600.0) * DEGTORAD;
/* Mean elongation of the Moon from the Sun. */
D = swe_degnorm((1072260.70369 +
T * (1602961601.2090 +
T * (-6.3706 +
T * (0.006593 +
T * (-0.00003169))))) / 3600.0) * DEGTORAD;
/* Mean longitude of the ascending node of the Moon. */
OM = swe_degnorm((450160.398036 +
T * (-6962890.5431 +
T * (7.4722 +
T * (0.007702 +
T * (-0.00005939))))) / 3600.0) * DEGTORAD;
/* luni-solar nutation series, in reverse order, starting with small terms */
if (nut_model == NutationModel.IAU_2000B)
{
inls = NLS_2000B;
}
else
{
inls = NLS;
}
for (i = inls - 1; i >= 0; i--)
{
j = i * 5;
darg = swe_radnorm(
nls[j + 0] * M +
nls[j + 1] * SM +
nls[j + 2] * F +
nls[j + 3] * D +
nls[j + 4] * OM);
sinarg = Math.Sin(darg);
cosarg = Math.Cos(darg);
k = i * 6;
dpsi += (cls[k + 0] + cls[k + 1] * T) * sinarg + cls[k + 2] * cosarg;
deps += (cls[k + 3] + cls[k + 4] * T) * cosarg + cls[k + 5] * sinarg;
}
var longitude = dpsi * O1MAS2DEG;
var obliquity = deps * O1MAS2DEG;
if (nut_model == NutationModel.IAU_2000A)
{
/* planetary nutation
* note: The MHB2000 code computes the luni-solar and planetary nutation
* in different routines, using slightly different Delaunay
* arguments in the two cases. This behaviour is faithfully
* reproduced here. Use of the Simon et al. expressions for both
* cases leads to negligible changes, well below 0.1 microarcsecond.*/
/* Mean anomaly of the Moon.*/
AL = swe_radnorm(2.35555598 + 8328.6914269554 * T);
/* Mean anomaly of the Sun.*/
ALSU = swe_radnorm(6.24006013 + 628.301955 * T);
/* Mean argument of the latitude of the Moon. */
AF = swe_radnorm(1.627905234 + 8433.466158131 * T);
/* Mean elongation of the Moon from the Sun. */
AD = swe_radnorm(5.198466741 + 7771.3771468121 * T);
/* Mean longitude of the ascending node of the Moon. */
AOM = swe_radnorm(2.18243920 - 33.757045 * T);
/* Planetary longitudes, Mercury through Neptune (Souchay et al. 1999). */
ALME = swe_radnorm(4.402608842 + 2608.7903141574 * T);
ALVE = swe_radnorm(3.176146697 + 1021.3285546211 * T);
ALEA = swe_radnorm(1.753470314 + 628.3075849991 * T);
ALMA = swe_radnorm(6.203480913 + 334.0612426700 * T);
ALJU = swe_radnorm(0.599546497 + 52.9690962641 * T);
ALSA = swe_radnorm(0.874016757 + 21.3299104960 * T);
ALUR = swe_radnorm(5.481293871 + 7.4781598567 * T);
ALNE = swe_radnorm(5.321159000 + 3.8127774000 * T);
/* General accumulated precession in longitude. */
APA = (0.02438175 + 0.00000538691 * T) * T;
/* planetary nutation series (in reverse order).*/
dpsi = 0;
deps = 0;
for (i = NPL - 1; i >= 0; i--)
{
j = i * 14;
darg = swe_radnorm(
npl[j + 0] * AL +
npl[j + 1] * ALSU +
npl[j + 2] * AF +
npl[j + 3] * AD +
npl[j + 4] * AOM +
npl[j + 5] * ALME +
npl[j + 6] * ALVE +
npl[j + 7] * ALEA +
npl[j + 8] * ALMA +
npl[j + 9] * ALJU +
npl[j + 10] * ALSA +
npl[j + 11] * ALUR +
npl[j + 12] * ALNE +
npl[j + 13] * APA);
k = i * 4;
sinarg = Math.Sin(darg);
cosarg = Math.Cos(darg);
dpsi += icpl[k + 0] * sinarg + icpl[k + 1] * cosarg;
deps += icpl[k + 2] * sinarg + icpl[k + 3] * cosarg;
}
longitude += dpsi * O1MAS2DEG;
obliquity += deps * O1MAS2DEG;
/* changes required by adoption of P03 precession
* according to Capitaine et al. A & A 412, 366 (2005) = IAU 2006 */
dpsi = -8.1 * Math.Sin(OM) - 0.6 * Math.Sin(2 * F - 2 * D + 2 * OM);
dpsi += T * (47.8 * Math.Sin(OM) + 3.7 * Math.Sin(2 * F - 2 * D + 2 * OM) + 0.6 * Math.Sin(2 * F + 2 * OM) - 0.6 * Math.Sin(2 * OM));
deps = T * (-25.6 * Math.Cos(OM) - 1.6 * Math.Cos(2 * F - 2 * D + 2 * OM));
longitude += dpsi / (3600.0 * 1000000.0);
obliquity += deps / (3600.0 * 1000000.0);
}
longitude *= DEGTORAD;
obliquity *= DEGTORAD;
return(longitude, obliquity);
}
internal static Nutation CalculateForSpeed(JulianDayNumber tjd, SweData swed) => Calculate(tjd.AddDays(-NUT_SPEED_INTV), swed);
private static (double longitude, double obliquity) calc_nutation_iau1980(JulianDayNumber J, NutationModel nut_model)
{
/* arrays to hold sines and cosines of multiple angles */
double[,] ss = new double[5, 8];
double[,] cc = new double[5, 8];
double arg;
double[] args = new double[5];
double f, g, T, T2;
double MM, MS, FF, DD, OM;
double cu, su, cv, sv, sw, s;
double C, D;
int i, j, k, k1, m, n;
int[] ns = new int[5];
/* Julian centuries from 2000 January 1.5,
* barycentric dynamical time
*/
T = (J - JulianDayNumber.J2000).Raw / 36525.0;
T2 = T * T;
/* Fundamental arguments in the FK5 reference system.
* The coefficients, originally given to 0.001",
* are converted here to degrees.
*/
/* longitude of the mean ascending node of the lunar orbit
* on the ecliptic, measured from the mean equinox of date
*/
OM = -6962890.539 * T + 450160.280 + (0.008 * T + 7.455) * T2;
OM = swe_degnorm(OM / 3600) * DEGTORAD;
/* mean longitude of the Sun minus the
* mean longitude of the Sun's perigee
*/
MS = 129596581.224 * T + 1287099.804 - (0.012 * T + 0.577) * T2;
MS = swe_degnorm(MS / 3600) * DEGTORAD;
/* mean longitude of the Moon minus the
* mean longitude of the Moon's perigee
*/
MM = 1717915922.633 * T + 485866.733 + (0.064 * T + 31.310) * T2;
MM = swe_degnorm(MM / 3600) * DEGTORAD;
/* mean longitude of the Moon minus the
* mean longitude of the Moon's node
*/
FF = 1739527263.137 * T + 335778.877 + (0.011 * T - 13.257) * T2;
FF = swe_degnorm(FF / 3600) * DEGTORAD;
/* mean elongation of the Moon from the Sun.
*/
DD = 1602961601.328 * T + 1072261.307 + (0.019 * T - 6.891) * T2;
DD = swe_degnorm(DD / 3600) * DEGTORAD;
args[0] = MM;
ns[0] = 3;
args[1] = MS;
ns[1] = 2;
args[2] = FF;
ns[2] = 4;
args[3] = DD;
ns[3] = 4;
args[4] = OM;
ns[4] = 2;
/* Calculate Math.Sin( i*MM ), etc. for needed multiple angles
*/
for (k = 0; k <= 4; k++)
{
arg = args[k];
n = ns[k];
su = Math.Sin(arg);
cu = Math.Cos(arg);
ss[k, 0] = su; /* Math.Sin(L) */
cc[k, 0] = cu; /* Math.Cos(L) */
sv = 2.0 * su * cu;
cv = cu * cu - su * su;
ss[k, 1] = sv; /* Math.Sin(2L) */
cc[k, 1] = cv;
for (i = 2; i < n; i++)
{
s = su * cv + cu * sv;
cv = cu * cv - su * sv;
sv = s;
ss[k, i] = sv; /* Math.Sin( i+1 L ) */
cc[k, i] = cv;
}
}
/* first terms, not in table: */
C = (-0.01742 * T - 17.1996) * ss[4, 0]; /* Math.Sin(OM) */
D = (0.00089 * T + 9.2025) * cc[4, 0]; /* Math.Cos(OM) */
foreach (short[] p in nt)
{
if (nut_model != NutationModel.IAU_CORR_1987 && (p[0] == 101 || p[0] == 102))
{
continue;
}
/* argument of sine and cosine */
k1 = 0;
cv = 0.0;
sv = 0.0;
for (m = 0; m < 5; m++)
{
j = p[m];
if (j > 100)
{
j = 0; /* p[0] is a flag */
}
if (j > 0)
{
k = j;
if (j < 0)
{
k = -k;
}
su = ss[m, k - 1]; /* Math.Sin(k*angle) */
if (j < 0)
{
su = -su;
}
cu = cc[m, k - 1];
if (k1 == 0)
{ /* set first angle */
sv = su;
cv = cu;
k1 = 1;
}
else
{ /* combine angles */
sw = su * cv + cu * sv;
cv = cu * cv - su * sv;
sv = sw;
}
}
}
/* longitude coefficient, in 0.0001" */
f = p[5] * 0.0001;
if (p[6] != 0)
{
f += 0.00001 * T * p[6];
}
/* obliquity coefficient, in 0.0001" */
g = p[7] * 0.0001;
if (p[8] != 0)
{
g += 0.00001 * T * p[8];
}
if (p[0] >= 100)
{ /* coefficients in 0.00001" */
f *= 0.1;
g *= 0.1;
}
/* accumulate the terms */
if (p[0] != 102)
{
C += f * sv;
D += g * cv;
}
else
{ /* Math.Cos for nutl and Math.Sin for nuto */
C += f * cv;
D += g * sv;
}
}
/* Save answers, expressed in radians */
var longitude = DEGTORAD * C / 3600.0;
var obliquity = DEGTORAD * D / 3600.0;
return(longitude, obliquity);
}
/// <summary>
/// Load from EOP files
/// <parameter name="eopC04File">File from https://datacenter.iers.org/data/latestVersion/EOP_14_C04_IAU1980_one_file_1962-now.txt</parameter>
/// <parameter name="eopFinalsFile">File from https://datacenter.iers.org/data/latestVersion/finals.all.iau1980.txt</parameter>
/// </summary>
public static EarthOrientationParameters LoadFrom(
Stream eopC04File,
Stream?eopFinalsFile)
{
const double TJDOFS = 2400000.5;
string s;
JulianDayNumber beginDate = default;
var dpsi = new List <double>();
var deps = new List <double>();
int mjdsv = 0;
using (var reader = new StreamReader(eopC04File))
{
while ((s = reader.ReadLine()) != null)
{
if (!s.StartsWith("1962"))
{
continue;
}
var values = s.Split(' ', StringSplitOptions.RemoveEmptyEntries);
var mjd = int.Parse(values[3]);
// is file in one-day steps?
if (mjdsv > 0 && mjd - mjdsv != 1)
{
throw new FormatException("File must be in one-day steps");
}
if (mjdsv == 0)
{
beginDate = JulianDayNumber.FromRaw(mjd + TJDOFS);
}
dpsi.Add(double.Parse(values[8], CultureInfo.InvariantCulture));
deps.Add(double.Parse(values[9], CultureInfo.InvariantCulture));
mjdsv = mjd;
}
}
var endDate = JulianDayNumber.FromRaw(mjdsv + TJDOFS);
// file finals.all may have some more data, and especially estimations for the near future
if (eopFinalsFile != null)
{
mjdsv = 0;
using var reader = new StreamReader(eopFinalsFile);
while ((s = reader.ReadLine()) != null)
{
var mjd = int.Parse(GetDigits(s, 7));
var jd = JulianDayNumber.FromRaw(mjd + TJDOFS);
if (jd <= endDate)
{
continue;
}
// are data in one-day steps?
if (mjdsv > 0 && mjd - mjdsv != 1)
{
throw new FormatException("File must be in one-day steps");
}
// dpsi, deps Bulletin B
var dPsi = GetDoubleFromStr(s, 168);
var dEps = GetDoubleFromStr(s, 178);
if (dPsi == 0.0)
{
// try dpsi, deps Bulletin A
dPsi = GetDoubleFromStr(s, 99);
dEps = GetDoubleFromStr(s, 118);
}
if (dPsi == 0.0)
{
break;
}
dpsi.Add(dPsi / 1000.0);
deps.Add(dEps / 1000.0);
mjdsv = mjd;
}
}
return(new EarthOrientationParameters(beginDate, endDate, dpsi, deps));
}
public bool IsPlanetHeliocentric(int bodyNumber, DateTime dateTimeInUTC) => _storage .GetFile(bodyNumber, JulianDayNumber.FromDate(dateTimeInUTC)) .PlanetsData[(InternalPlanets)bodyNumber] .Flags .HasFlag(PlanetFlags.Heliocentric);
