public static double CalcInterpolated(double year, double gregorianYear, double tidalAcceleration)
{
var B = TabStart - Tab2End;
var iy = (Tab2End - Tab2Start) / Tab2Step;
var dd = (year - Tab2End) / B;
var ans = dt2[iy] + dd * (dt[0] - dt2[iy]);
ans = TidalAcceleration.AdjustForTidalAcceleration(ans, gregorianYear, tidalAcceleration, TidalAccelerationMode.Const26, false);
return(ans / 86400.0);
}
/// <summary>
/// Stephenson & Morrison (2004)
/// </summary>
public static double Calc(JulianDayNumber tjd, double tid_acc)
{
double ans = 0, ans2, ans3;
double p, B, dd;
double tjd0;
int iy;
double Y = tjd.GetGregorianYear();
/* before -1000:
* formula by Stephenson & Morrison (2004; p. 335) but adjusted to fit the
* starting point of table dt2. */
if (Y < DeltaTTabulated.Tab2Start)
{
// before -1000
ans = DeltaTLongtermMorrisonStephenson.Calc(tjd);
ans = TidalAcceleration.AdjustForTidalAcceleration(ans, Y, tid_acc, TidalAccelerationMode.Const26, false);
/* transition from formula to table over 100 years */
if (Y >= DeltaTTabulated.Tab2Start - 100)
{
/* starting value of table dt2: */
ans2 = TidalAcceleration.AdjustForTidalAcceleration(DeltaTTabulated.dt2[0], DeltaTTabulated.Tab2Start, tid_acc, TidalAccelerationMode.Const26, false);
/* value of formula at epoch TAB2_START */
/* B = (TAB2_START - LTERM_EQUATION_YSTART) * 0.01;
* ans3 = -20 + LTERM_EQUATION_COEFF * B * B;*/
tjd0 = (DeltaTTabulated.Tab2Start - 2000) * 365.2425 + (double)JulianDayNumber.J2000;
ans3 = DeltaTLongtermMorrisonStephenson.Calc(JulianDayNumber.FromRaw(tjd0));
ans3 = TidalAcceleration.AdjustForTidalAcceleration(ans3, Y, tid_acc, TidalAccelerationMode.Const26, false);
dd = ans3 - ans2;
B = (Y - (DeltaTTabulated.Tab2Start - 100)) * 0.01;
/* fit to starting point of table dt2. */
ans -= dd * B;
}
}
/* between -1000 and 1600:
* linear interpolation between values of table dt2 (Stephenson & Morrison 2004) */
if (Y >= DeltaTTabulated.Tab2Start && Y < DeltaTTabulated.Tab2End)
{
double Yjul = tjd.GetJulianYear();
p = Math.Floor(Yjul);
iy = (int)((p - DeltaTTabulated.Tab2Start) / DeltaTTabulated.Tab2Step);
dd = (Yjul - (DeltaTTabulated.Tab2Start + DeltaTTabulated.Tab2Step * iy)) / DeltaTTabulated.Tab2Step;
ans = DeltaTTabulated.dt2[iy] + (DeltaTTabulated.dt2[iy + 1] - DeltaTTabulated.dt2[iy]) * dd;
/* correction for tidal acceleration used by our ephemeris */
ans = TidalAcceleration.AdjustForTidalAcceleration(ans, Y, tid_acc, TidalAccelerationMode.Const26, false);
}
ans /= 86400.0;
return(ans);
}
/// <summary>
/// Model used SE 1.77 - 2.05.01, for epochs before 1633:
/// Polynomials by Espenak & Meeus 2006, derived from Stephenson & Morrison 2004.
/// deltat_model == SEMOD_DELTAT_ESPENAK_MEEUS_2006:
/// This method is used only for epochs before 1633.
/// (For more recent epochs, we use the data provided by Astronomical Almanac K8-K9.)
/// </summary>
/// <see cref="deltat_espenak_meeus_1620"/>
public static double Calc(JulianDayNumber tjd, double tidalAcceleration)
{
double ans = 0;
double u;
double Ygreg = tjd.GetGregorianYear();
if (Ygreg < -500)
{
ans = DeltaTLongtermMorrisonStephenson.Calc(tjd);
}
else if (Ygreg < 500)
{
u = Ygreg / 100.0;
ans = (((((0.0090316521 * u + 0.022174192) * u - 0.1798452) * u - 5.952053) * u + 33.78311) * u - 1014.41) * u + 10583.6;
}
else if (Ygreg < 1600)
{
u = (Ygreg - 1000) / 100.0;
ans = (((((0.0083572073 * u - 0.005050998) * u - 0.8503463) * u + 0.319781) * u + 71.23472) * u - 556.01) * u + 1574.2;
}
else if (Ygreg < 1700)
{
u = Ygreg - 1600;
ans = 120 - 0.9808 * u - 0.01532 * u * u + u * u * u / 7129.0;
}
else if (Ygreg < 1800)
{
u = Ygreg - 1700;
ans = (((-u / 1174000.0 + 0.00013336) * u - 0.0059285) * u + 0.1603) * u + 8.83;
}
else if (Ygreg < 1860)
{
u = Ygreg - 1800;
ans = ((((((0.000000000875 * u - 0.0000001699) * u + 0.0000121272) * u - 0.00037436) * u + 0.0041116) * u + 0.0068612) * u - 0.332447) * u + 13.72;
}
else if (Ygreg < 1900)
{
u = Ygreg - 1860;
ans = ((((u / 233174.0 - 0.0004473624) * u + 0.01680668) * u - 0.251754) * u + 0.5737) * u + 7.62;
}
else if (Ygreg < 1920)
{
u = Ygreg - 1900;
ans = (((-0.000197 * u + 0.0061966) * u - 0.0598939) * u + 1.494119) * u - 2.79;
}
else if (Ygreg < 1941)
{
u = Ygreg - 1920;
ans = 21.20 + 0.84493 * u - 0.076100 * u * u + 0.0020936 * u * u * u;
}
else if (Ygreg < 1961)
{
u = Ygreg - 1950;
ans = 29.07 + 0.407 * u - u * u / 233.0 + u * u * u / 2547.0;
}
else if (Ygreg < 1986)
{
u = Ygreg - 1975;
ans = 45.45 + 1.067 * u - u * u / 260.0 - u * u * u / 718.0;
}
else if (Ygreg < 2005)
{
u = Ygreg - 2000;
ans = ((((0.00002373599 * u + 0.000651814) * u + 0.0017275) * u - 0.060374) * u + 0.3345) * u + 63.86;
}
ans = TidalAcceleration.AdjustForTidalAcceleration(ans, Ygreg, tidalAcceleration, TidalAccelerationMode.Const26, false);
ans /= 86400.0;
return(ans);
}
/// <summary>
/// Calculate DeltaT
/// </summary>
/// <remarks>
/// delta t is adjusted to the tidal acceleration that is compatible
/// with the ephemeris mode contained in ephemerisMode and with the ephemeris
/// files made accessible through swe_set_ephe_path() or swe_set_jplfile().
/// If ephemerisMode is null, then the default tidal acceleration is ussed(i.e. that of DE431).
/// </remarks>
/// <see cref="calc_deltat"/>
/// <returns>DeltaT (ET - UT) in days</returns>
public static double Calc(JulianDayNumber julianDay, DeltaTMode deltaTMode, EphemerisMode?ephemerisMode)
{
var tidalAcceleration = ephemerisMode is null
? TidalAcceleration.Get(JPLDENumber.Default)
: TidalAcceleration.Calculate(ephemerisMode.Value, julianDay, JPLDENumber.Auto);
if (deltaTMode == DeltaTMode.Stephenson_Etc_2016 && julianDay < JulianDayNumber.J1955)
{
double deltaT = DeltaTStephensonEtc2016.Calc(julianDay, tidalAcceleration);
if (julianDay >= JulianDayNumber.J1952_05_04)
{
deltaT += (1.0 - (double)(JulianDayNumber.J1955 - julianDay) / 1000.0) * 0.6610218 / 86400.0;
}
return(deltaT);
}
if (deltaTMode == DeltaTMode.Espenak_Meeus_2006 && julianDay < J1633)
{
return(DeltaTEspenakMeeus1620.Calc(julianDay, tidalAcceleration));
}
var year = julianDay.GetYear();
// delta t model used in SE 1.72 - 1.76: Stephenson & Morrison 2004; before 1620
if (deltaTMode == DeltaTMode.Stephenson_Morrison_2004 && year < DeltaTTabulated.TabStart)
{
// before 1600:
if (year < DeltaTTabulated.Tab2End)
{
return(DeltaTStephensonMorrison2004_1600.Calc(julianDay, tidalAcceleration));
}
else
{
// between 1600 and 1620:
// linear interpolation between end of table dt2 and start of table dt
return(DeltaTTabulated.CalcInterpolated(year, julianDay.GetGregorianYear(), tidalAcceleration));
}
}
/* delta t model used before SE 1.64:
* Stephenson/Morrison 1984 with Borkowski 1988;
* before 1620 */
if (deltaTMode == DeltaTMode.Stephenson_Morrison_1984 && year < DeltaTTabulated.TabStart)
{
double B;
double ans;
if (year >= 948.0)
{
/* Stephenson and Morrison, stated domain is 948 to 1600:
* 25.5(centuries from 1800)^2 - 1.9159(centuries from 1955)^2 */
B = 0.01 * (year - 2000.0);
ans = (23.58 * B + 100.3) * B + 101.6;
}
else
{
/* Borkowski, before 948 and between 1600 and 1620 */
B = 0.01 * (year - 2000.0) + 3.75;
ans = 35.0 * B * B + 40.0;
}
return(ans / 86400.0);
}
/* 1620 - today + a few years (tabend):
* Tabulated values of deltaT from Astronomical Almanac
* (AA 1997etc., pp. K8-K9) and from IERS
* (http://maia.usno.navy.mil/ser7/deltat.data).
*/
if (year >= DeltaTTabulated.TabStart)
{
return(DeltaTTabulated.Calc(julianDay, tidalAcceleration, deltaTMode));
}
return(0);
}
/// <summary>
/// The tabulated values of deltaT, in hundredths of a second,
/// were taken from The Astronomical Almanac 1997etc., pp.K8-K9.
/// Some more recent values are taken from IERS
/// http://maia.usno.navy.mil/ser7/deltat.data .
/// </summary>
/// <remarks>
/// Bessel's interpolation formula is implemented to obtain fourth
/// order interpolated values at intermediate times.
/// The values are adjusted depending on the ephemeris used
/// and its inherent value of secular tidal acceleration ndot.
/// Note by Dieter Jan. 2017:
/// Bessel interpolation assumes equidistant sampling points. However the
/// sampling points are not equidistant, because they are for first January of
/// every year and years can have either 365 or 366 days.The interpolation uses
/// a step width of 365.25 days.As a consequence, in three out of four years
/// the interpolation does not reproduce the exact values of the sampling points
/// on the days they refer to.
/// </remarks>
/// <see cref="deltat_aa"/>
public static double Calc(JulianDayNumber tjd, double tid_acc, DeltaTMode mode)
{
double ans, ans2 = 0, ans3;
double p, B, B2, Y, dd;
double[] d = new double[6];
int i, iy, k;
Y = tjd.GetYear();
if (Y <= TabEnd)
{
// Index into the table.
p = Math.Floor(Y);
iy = (int)(p - TabStart);
/* Zeroth order estimate is value at start of year */
ans = dt[iy];
k = iy + 1;
if (k >= TabSize)
{
goto done; /* No data, can't go on. */
}
/* The fraction of tabulation interval */
p = Y - p;
/* First order interpolated value */
ans += p * (dt[k] - dt[iy]);
if ((iy - 1 < 0) || (iy + 2 >= TabSize))
{
goto done; /* can't do second differences */
}
/* Make table of first differences */
k = iy - 2;
for (i = 0; i < 5; i++)
{
if ((k < 0) || (k + 1 >= TabSize))
{
d[i] = 0;
}
else
{
d[i] = dt[k + 1] - dt[k];
}
k += 1;
}
/* Compute second differences */
for (i = 0; i < 4; i++)
{
d[i] = d[i + 1] - d[i];
}
B = 0.25 * p * (p - 1.0);
ans += B * (d[1] + d[2]);
if (iy + 2 >= TabSize)
{
goto done;
}
/* Compute third differences */
for (i = 0; i < 3; i++)
{
d[i] = d[i + 1] - d[i];
}
B = 2.0 * B / 3.0;
ans += (p - 0.5) * B * d[1];
if ((iy - 2 < 0) || (iy + 3 > TabSize))
{
goto done;
}
/* Compute fourth differences */
for (i = 0; i < 2; i++)
{
d[i] = d[i + 1] - d[i];
}
B = 0.125 * B * (p + 1.0) * (p - 2.0);
ans += B * (d[0] + d[1]);
done:
ans = TidalAcceleration.AdjustForTidalAcceleration(ans, Y, tid_acc, TidalAccelerationMode.Const26, false);
return(ans / 86400.0);
}
/* today - future:
* 3rd degree polynomial based on data given by
* Stephenson/Morrison/Hohenkerk 2016 here:
* http://astro.ukho.gov.uk/nao/lvm/
*/
if (mode == DeltaTMode.Stephenson_Etc_2016)
{
B = Y - 2000;
if (Y < 2500)
{
ans = B * B * B * 121.0 / 30000000.0 + B * B / 1250.0 + B * 521.0 / 3000.0 + 64.0;
/* for slow transition from tablulated data */
B2 = TabEnd - 2000;
ans2 = B2 * B2 * B2 * 121.0 / 30000000.0 + B2 * B2 / 1250.0 + B2 * 521.0 / 3000.0 + 64.0;
/* we use a parable after 2500 */
}
else
{
B = 0.01 * (Y - 2000);
ans = B * B * 32.5 + 42.5;
}
/*
* Formula Stephenson (1997; p. 507),
* with modification to avoid jump at end of AA table,
* similar to what Meeus 1998 had suggested.
* Slow transition within 100 years.
*/
}
else
{
B = 0.01 * (Y - 1820);
ans = -20 + 31 * B * B;
/* for slow transition from tablulated data */
B2 = 0.01 * (TabEnd - 1820);
ans2 = -20 + 31 * B2 * B2;
}
/* slow transition from tabulated values to Stephenson formula: */
if (Y <= TabEnd + 100)
{
ans3 = dt[TabSize - 1];
dd = (ans2 - ans3);
ans += dd * (Y - (TabEnd + 100)) * 0.01;
}
return(ans / 86400.0);
}
