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torben |
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// Upgraded to Delphi 2009: Sebastian Zierer
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(* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is TurboPower SysTools
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*
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* The Initial Developer of the Original Code is
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* TurboPower Software
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*
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* Portions created by the Initial Developer are Copyright (C) 1996-2002
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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*
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* ***** END LICENSE BLOCK ***** *)
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{*********************************************************}
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{* SysTools: StEclpse.pas 4.04 *}
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{*********************************************************}
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{* SysTools: Lunar/Solar Eclipses *}
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{*********************************************************}
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{$I StDefine.inc}
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{ ************************************************************** }
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{ Sources: }
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{ 1. Astronomical Algorithms, Jean Meeus, Willmann-Bell, 1991. }
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{ }
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{ 2. Planetary and Lunar Coordinates (1984-2000), U.S. Govt, }
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{ 1983. }
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{ }
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{ 3. Supplement to the American Ephemeris and Nautical Almanac,}
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{ U.S. Govt, 1964. }
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{ }
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{ 4. MPO96-98 source files, Brian D. Warner, 1995-98. }
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{ }
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{ ************************************************************** }
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unit StEclpse;
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interface
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uses
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{$IFDEF UseMathUnit} Math, {$ENDIF}
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StBase, StList, StDate, StAstro, StMath;
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type
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TStEclipseType = (etLunarPenumbral, etLunarPartial, etLunarTotal,
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etSolarPartial, etSolarAnnular, etSolarTotal,
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etSolarAnnularTotal);
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TStHemisphereType = (htNone, htNorthern, htSouthern);
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TStContactTimes = packed record
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UT1, {start of lunar penumbral phase}
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UT2, {end of lunar penumbral phase}
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FirstContact, {start of partial eclipse}
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SecondContact, {start of totality}
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MidEclipse, {mid-eclipse}
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ThirdContact, {end of totality}
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FourthContact : TDateTime; {end of partial phase}
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end;
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TStLongLat = packed record
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JD : TDateTime;
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Longitude,
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Latitude,
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Duration : Double;
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end;
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PStLongLat = ^TStLongLat;
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TStEclipseRecord = packed record
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EType : TStEclipseType; {type of Eclipse}
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Magnitude : Double; {magnitude of eclipse}
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Hemisphere : TStHemisphereType; {favored hemisphere - solar}
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LContacts : TStContactTimes; {Universal Times of critical points}
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{ in lunar eclipses}
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Path : TStList; {longitude/latitude of moon's shadow}
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end; { during solar eclipse}
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PStEclipseRecord = ^TStEclipseRecord;
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TStBesselianRecord = packed record
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JD : TDateTime;
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Delta,
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Angle,
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XAxis,
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YAxis,
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L1,
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L2 : Double;
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end;
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TStEclipses = class(TStList)
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{.Z+}
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protected {private}
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FBesselianElements : array[1..25] of TStBesselianRecord;
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F0,
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FUPrime,
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FDPrime : Double;
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function GetEclipse(Idx : longint) : PStEclipseRecord;
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procedure CentralEclipseTime(JD, K, J2,
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SunAnom, MoonAnom,
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ArgLat, AscNode, EFac : Double;
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var F1, A1, CentralTime : Double);
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procedure CheckForEclipse(K : Double);
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procedure TotalLunarEclipse(CentralJD, MoonAnom, Mu,
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PMag, UMag, Gamma : Double);
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procedure PartialLunarEclipse(CentralJD, MoonAnom, Mu,
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PMag, UMag, Gamma : Double);
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procedure PenumbralLunarEclipse(CentralJD, MoonAnom, Mu,
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PMag, UMag, Gamma : Double);
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procedure GetBesselianElements(CentralJD : Double);
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procedure GetShadowPath(I1, I2 : Integer; Path : TStList);
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procedure NonPartialSolarEclipse(CentralJD, Mu, Gamma : Double);
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procedure PartialSolarEclipse(CentralJD, Mu, Gamma : Double);
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{.Z-}
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public
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constructor Create(NodeClass : TStNodeClass);
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override;
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procedure FindEclipses(Year : integer);
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property Eclipses[Idx : longint] : PStEclipseRecord
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read GetEclipse;
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end;
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implementation
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procedure DisposePathData(Data : Pointer); far;
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begin
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Dispose(PStLongLat(Data));
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end;
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procedure DisposeEclipseRecord(Data : Pointer); far;
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var
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EcData : TStEclipseRecord;
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begin
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EcData := TStEclipseRecord(Data^);
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if (Assigned(EcData.Path)) then
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EcData.Path.Free;
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Dispose(PStEclipseRecord(Data));
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end;
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constructor TStEclipses.Create(NodeClass : TStNodeClass);
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begin
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inherited Create(NodeClass);
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DisposeData := DisposeEclipseRecord;
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end;
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function TStEclipses.GetEclipse(Idx : longint) : PStEclipseRecord;
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begin
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if (Idx < 0) or (Idx > pred(Count)) then
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Result := nil
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else
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Result := PStEclipseRecord(Items[Idx].Data);
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end;
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procedure TStEclipses.FindEclipses(Year : integer);
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var
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K,
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MeanJD,
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JDofFirst,
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JDofLast : Double;
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begin
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JDofFirst := AstJulianDatePrim(Year, 1, 1, 0);
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JDofLast := AstJulianDatePrim(Year, 12, 31, pred(SecondsInDay));
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K := Int((Year - 2000) * 12.3685 - 1);
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repeat
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MeanJD := 2451550.09765 + 29.530588853 * K;
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if (MeanJD < JDofFirst) then
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K := K + 0.5;
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until (MeanJD >= JDofFirst);
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while (MeanJD < JDofLast) do begin
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CheckForEclipse(K);
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K := K + 0.5;
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MeanJD := 2451550.09765 + 29.530588853 * K;
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end;
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end;
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procedure TStEclipses.CentralEclipseTime(JD, K, J2,
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SunAnom, MoonAnom,
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ArgLat, AscNode, EFac : Double;
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var F1, A1, CentralTime : Double);
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{the mean error of this routine is 0.36 minutes in a test between}
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{1951 through 2050 with a maximum of 1.1 - Meeus}
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begin
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F1 := ArgLat - (0.02665/radcor) * sin(AscNode);
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A1 := (299.77/radcor)
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+ (0.107408/radcor) * K
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- (0.009173/radcor) * J2;
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if (Frac(K) > 0.1) then
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{correction at Full Moon - Lunar eclipse}
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CentralTime := JD
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- 0.4065 * sin(MoonAnom)
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+ 0.1727 * EFac * sin(SunAnom)
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else
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{correction at New Moon - solar eclipse}
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CentralTime := JD
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- 0.4075 * sin(MoonAnom)
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+ 0.1721 * EFac * sin(SunAnom);
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CentralTime := CentralTime
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+ 0.0161 * sin(2 * MoonAnom)
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- 0.0097 * sin(2 * F1)
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+ 0.0073 * sin(MoonAnom - SunAnom) * EFac
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- 0.0050 * sin(MoonAnom + SunAnom) * EFac
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- 0.0023 * sin(MoonAnom - 2*F1)
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+ 0.0021 * sin(2*SunAnom) * EFac
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+ 0.0012 * sin(MoonAnom + 2*F1)
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+ 0.0006 * sin(2*MoonAnom + SunAnom) * EFac
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- 0.0004 * sin(3*MoonAnom)
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- 0.0003 * sin(SunAnom + 2*F1) * EFac
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+ 0.0003 * sin(A1)
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- 0.0002 * sin(SunAnom - 2*F1) * EFac
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- 0.0002 * sin(2*MoonAnom - SunAnom) * EFac
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- 0.0002 * sin(AscNode);
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end;
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procedure TStEclipses.CheckForEclipse(K : Double);
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var
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MeanJD,
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J1, J2, J3,
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PMag, UMag,
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CentralJD,
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SunAnom,
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MoonAnom,
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ArgLat,
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AscNode,
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EFac,
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DeltaT,
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F1, A1,
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P, Q, W,
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Gamma, Mu : Double;
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begin
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{compute Julian Centuries}
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J1 := K / 1236.85;
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J2 := Sqr(J1);
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J3 := J2 * J1;
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{mean Julian Date for phase}
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MeanJD := 2451550.09765
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+ 29.530588853 * K
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+ 0.0001337 * J2
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- 0.000000150 * J3
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+ 0.00000000073 * J2 * J2;
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{solar mean anomaly}
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SunAnom := 2.5534
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+ 29.1053569 * K
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- 0.0000218 * J2
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- 0.00000011 * J3;
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SunAnom := Frac(SunAnom / 360.0) * 360;
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if (SunAnom < 0) then
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SunAnom := SunAnom + 360.0;
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{lunar mean anomaly}
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MoonAnom := 201.5643
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+ 385.81693528 * K
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+ 0.0107438 * J2
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+ 0.00001239 * J3
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- 0.000000058 * J2 * J2;
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MoonAnom := Frac(MoonAnom / 360.0) * 360;
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if (MoonAnom < 0) then
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MoonAnom := MoonAnom + 360.0;
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{lunar argument of latitude}
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ArgLat := 160.7108
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+ 390.67050274 * K
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- 0.0016341 * J2
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- 0.00000227 * J3
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+ 0.000000011 * J2 * J2;
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ArgLat := Frac(ArgLat / 360.0) * 360;
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if (ArgLat < 0) then
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ArgLat := ArgLat + 360.0;
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{lunar ascending node}
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AscNode := 124.7746
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- 1.56375580 * K
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+ 0.0020691 * J2
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+ 0.00000215 * J3;
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AscNode := Frac(AscNode / 360.0) * 360;
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if (AscNode < 0) then
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AscNode := AscNode + 360.0;
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{convert to radians}
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SunAnom := SunAnom/radcor;
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MoonAnom := MoonAnom/radcor;
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ArgLat := ArgLat/radcor;
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AscNode := AscNode/radcor;
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{correction factor}
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EFac := 1.0 - 0.002516 * J1 - 0.0000074 * J2;
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{if AscNode > 21 deg. from 0 or 180 then no eclipse}
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if (abs(sin(ArgLat)) > (sin(21.0/radcor))) then Exit;
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{there is probably an eclipse - what kind? when?}
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CentralEclipseTime(MeanJD, K, J2, SunAnom, MoonAnom,
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ArgLat, AscNode, EFac,
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F1, A1, CentralJD);
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{Central JD is in Dynamical Time. Sun/Moon Positions are based on UT}
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{An APPROXIMATE conversion is made to UT. This has limited accuracy}
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DeltaT := (-15 + (sqr(CentralJD - 2382148) / 41048480)) / 86400;
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CentralJD := CentralJD - DeltaT;
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P := 0.2070 * sin(SunAnom) * EFac
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+ 0.0024 * sin(2*SunAnom) * EFac
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- 0.0392 * sin(MoonAnom)
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+ 0.0116 * sin(2*MoonAnom)
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- 0.0073 * sin(SunAnom + MoonAnom) * EFac
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+ 0.0067 * sin(MoonAnom - SunAnom) * EFac
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+ 0.0118 * sin(2*F1);
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Q := 5.2207
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- 0.0048 * cos(SunAnom) * EFac
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+ 0.0020 * cos(2*SunAnom) * EFac
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- 0.3299 * cos(MoonAnom)
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- 0.0060 * cos(SunAnom + MoonAnom) * EFac
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|
|
+ 0.0041 * cos(MoonAnom - SunAnom) * EFac;
|
| 340 |
|
|
|
| 341 |
|
|
W := abs(cos(F1));
|
| 342 |
|
|
|
| 343 |
|
|
Gamma := (P * cos(F1) + Q * sin(F1)) * (1 - 0.0048 * W);
|
| 344 |
|
|
|
| 345 |
|
|
Mu := 0.0059
|
| 346 |
|
|
+ 0.0046 * cos(SunAnom) * EFac
|
| 347 |
|
|
- 0.0182 * cos(MoonAnom)
|
| 348 |
|
|
+ 0.0004 * cos(2*MoonAnom)
|
| 349 |
|
|
- 0.0005 * cos(SunAnom + MoonAnom);
|
| 350 |
|
|
|
| 351 |
|
|
if (Frac(abs(K)) > 0.1) then begin
|
| 352 |
|
|
{Check for Lunar Eclipse possibilities}
|
| 353 |
|
|
PMag := (1.5573 + Mu - abs(Gamma)) / 0.5450;
|
| 354 |
|
|
UMag := (1.0128 - Mu - abs(Gamma)) / 0.5450;
|
| 355 |
|
|
|
| 356 |
|
|
if (UMag >= 1.0) then
|
| 357 |
|
|
TotalLunarEclipse(CentralJD, MoonAnom, Mu, PMag, UMag, Gamma)
|
| 358 |
|
|
else if (UMag > 0) then
|
| 359 |
|
|
PartialLunarEclipse(CentralJD, MoonAnom, Mu, PMag, UMag, Gamma)
|
| 360 |
|
|
else if ((UMag < 0) and (PMag > 0)) then
|
| 361 |
|
|
PenumbralLunarEclipse(CentralJD, MoonAnom, Mu, PMag, UMag, Gamma);
|
| 362 |
|
|
end else begin
|
| 363 |
|
|
{Check for Solar Eclipse possibilities}
|
| 364 |
|
|
{
|
| 365 |
|
|
Non-partial eclipses
|
| 366 |
|
|
--------------------
|
| 367 |
|
|
central Axis of moon's umbral shadow touches earth's surface
|
| 368 |
|
|
Can be total, annular, or both
|
| 369 |
|
|
|
| 370 |
|
|
non-central Axis of moon's umbral shadow does not touch earth's surface
|
| 371 |
|
|
Eclipse is usually partial but can be one of possibilities
|
| 372 |
|
|
for central eclipse if very near one of the earth's poles
|
| 373 |
|
|
|
| 374 |
|
|
Partial eclipses
|
| 375 |
|
|
----------------
|
| 376 |
|
|
partial None of the moon's umbral shadow touches the earth's surface
|
| 377 |
|
|
}
|
| 378 |
|
|
|
| 379 |
|
|
if (abs(Gamma) <= (0.9972 + abs(Mu))) then
|
| 380 |
|
|
NonPartialSolarEclipse(CentralJD, Mu, Gamma)
|
| 381 |
|
|
else begin
|
| 382 |
|
|
if (abs(Gamma) < 1.5433 + Mu) then
|
| 383 |
|
|
PartialSolarEclipse(CentralJD, Mu, Gamma);
|
| 384 |
|
|
end;
|
| 385 |
|
|
end;
|
| 386 |
|
|
end;
|
| 387 |
|
|
|
| 388 |
|
|
procedure TStEclipses.TotalLunarEclipse(CentralJD, MoonAnom, Mu,
|
| 389 |
|
|
PMag, UMag, Gamma : Double);
|
| 390 |
|
|
var
|
| 391 |
|
|
TLE : PStEclipseRecord;
|
| 392 |
|
|
PartialSemiDur,
|
| 393 |
|
|
TotalSemiDur,
|
| 394 |
|
|
Dbl1 : Double;
|
| 395 |
|
|
begin
|
| 396 |
|
|
New(TLE);
|
| 397 |
|
|
TLE^.Magnitude := UMag;
|
| 398 |
|
|
TLE^.Hemisphere := htNone;
|
| 399 |
|
|
TLE^.EType := etLunarTotal;
|
| 400 |
|
|
TLE^.Path := nil;
|
| 401 |
|
|
CentralJD := AJDToDateTime(CentralJD);
|
| 402 |
|
|
|
| 403 |
|
|
PartialSemiDur := 1.0128 - Mu;
|
| 404 |
|
|
TotalSemiDur := 0.4678 - Mu;
|
| 405 |
|
|
Dbl1 := 0.5458 + 0.0400 * cos(MoonAnom);
|
| 406 |
|
|
|
| 407 |
|
|
PartialSemiDur := 60/Dbl1 * sqrt(sqr(PartialSemiDur) - sqr(Gamma)) / 1440;
|
| 408 |
|
|
TotalSemiDur := 60/Dbl1 * sqrt(sqr(TotalSemiDur) - sqr(Gamma)) / 1440;
|
| 409 |
|
|
|
| 410 |
|
|
TLE^.LContacts.FirstContact := CentralJD - PartialSemiDur;
|
| 411 |
|
|
TLE^.LContacts.SecondContact := CentralJD - TotalSemiDur;
|
| 412 |
|
|
TLE^.LContacts.MidEclipse := CentralJD;
|
| 413 |
|
|
TLE^.LContacts.ThirdContact := CentralJD + TotalSemiDur;
|
| 414 |
|
|
TLE^.LContacts.FourthContact := CentralJD + PartialSemiDur;
|
| 415 |
|
|
|
| 416 |
|
|
PartialSemiDur := 60/Dbl1 * sqrt(sqr(1.5573 + Mu) - sqr(Gamma)) / 1440;
|
| 417 |
|
|
TLE^.LContacts.UT1 := CentralJD - PartialSemiDur;
|
| 418 |
|
|
TLE^.LContacts.UT2 := CentralJD + PartialSemiDur;
|
| 419 |
|
|
|
| 420 |
|
|
Self.Append(TLE);
|
| 421 |
|
|
end;
|
| 422 |
|
|
|
| 423 |
|
|
procedure TStEclipses.PartialLunarEclipse(CentralJD, MoonAnom, Mu,
|
| 424 |
|
|
PMag, UMag, Gamma : Double);
|
| 425 |
|
|
var
|
| 426 |
|
|
TLE : PStEclipseRecord;
|
| 427 |
|
|
PartialSemiDur,
|
| 428 |
|
|
Dbl1 : Double;
|
| 429 |
|
|
begin
|
| 430 |
|
|
New(TLE);
|
| 431 |
|
|
TLE^.Magnitude := UMag;
|
| 432 |
|
|
TLE^.Hemisphere := htNone;
|
| 433 |
|
|
TLE^.EType := etLunarPartial;
|
| 434 |
|
|
TLE^.Path := nil;
|
| 435 |
|
|
CentralJD := AJDToDateTime(CentralJD);
|
| 436 |
|
|
|
| 437 |
|
|
PartialSemiDur := 1.0128 - Mu;
|
| 438 |
|
|
Dbl1 := 0.5458 + 0.0400 * cos(MoonAnom);
|
| 439 |
|
|
|
| 440 |
|
|
PartialSemiDur := 60/Dbl1 * sqrt(sqr(PartialSemiDur) - sqr(Gamma)) / 1440;
|
| 441 |
|
|
|
| 442 |
|
|
TLE^.LContacts.FirstContact := CentralJD - PartialSemiDur;
|
| 443 |
|
|
TLE^.LContacts.SecondContact := 0;
|
| 444 |
|
|
TLE^.LContacts.MidEclipse := CentralJD;
|
| 445 |
|
|
TLE^.LContacts.ThirdContact := 0;
|
| 446 |
|
|
TLE^.LContacts.FourthContact := CentralJD + PartialSemiDur;
|
| 447 |
|
|
|
| 448 |
|
|
PartialSemiDur := 60/Dbl1 * sqrt(sqr(1.5573 + Mu) - sqr(Gamma)) / 1440;
|
| 449 |
|
|
TLE^.LContacts.UT1 := CentralJD - PartialSemiDur;
|
| 450 |
|
|
TLE^.LContacts.UT2 := CentralJD + PartialSemiDur;
|
| 451 |
|
|
|
| 452 |
|
|
Self.Append(TLE);
|
| 453 |
|
|
end;
|
| 454 |
|
|
|
| 455 |
|
|
procedure TStEclipses.PenumbralLunarEclipse(CentralJD, MoonAnom, Mu,
|
| 456 |
|
|
PMag, UMag, Gamma : Double);
|
| 457 |
|
|
var
|
| 458 |
|
|
TLE : PStEclipseRecord;
|
| 459 |
|
|
PartialSemiDur,
|
| 460 |
|
|
Dbl1 : Double;
|
| 461 |
|
|
begin
|
| 462 |
|
|
New(TLE);
|
| 463 |
|
|
TLE^.Magnitude := PMag;
|
| 464 |
|
|
TLE^.Hemisphere := htNone;
|
| 465 |
|
|
TLE^.EType := etLunarPenumbral;
|
| 466 |
|
|
TLE^.Path := nil;
|
| 467 |
|
|
CentralJD := AJDToDateTime(CentralJD);
|
| 468 |
|
|
|
| 469 |
|
|
TLE^.LContacts.FirstContact := 0;
|
| 470 |
|
|
TLE^.LContacts.SecondContact := 0;
|
| 471 |
|
|
TLE^.LContacts.MidEclipse := CentralJD;
|
| 472 |
|
|
TLE^.LContacts.ThirdContact := 0;
|
| 473 |
|
|
TLE^.LContacts.FourthContact := 0;
|
| 474 |
|
|
|
| 475 |
|
|
Dbl1 := 0.5458 + 0.0400 * cos(MoonAnom);
|
| 476 |
|
|
PartialSemiDur := 60/Dbl1 * sqrt(sqr(1.5573 + Mu) - sqr(Gamma)) / 1440;
|
| 477 |
|
|
TLE^.LContacts.UT1 := CentralJD - PartialSemiDur;
|
| 478 |
|
|
TLE^.LContacts.UT2 := CentralJD + PartialSemiDur;
|
| 479 |
|
|
|
| 480 |
|
|
Self.Append(TLE);
|
| 481 |
|
|
end;
|
| 482 |
|
|
|
| 483 |
|
|
procedure TStEclipses.GetBesselianElements(CentralJD : Double);
|
| 484 |
|
|
var
|
| 485 |
|
|
I,
|
| 486 |
|
|
Mins : LongInt;
|
| 487 |
|
|
CurJD,
|
| 488 |
|
|
SidTime,
|
| 489 |
|
|
SunDist,
|
| 490 |
|
|
MoonDist,
|
| 491 |
|
|
DistRatio,
|
| 492 |
|
|
Alpha,
|
| 493 |
|
|
Theta,
|
| 494 |
|
|
Sun1,
|
| 495 |
|
|
Sun2,
|
| 496 |
|
|
Moon1,
|
| 497 |
|
|
Moon2,
|
| 498 |
|
|
Dbl3,
|
| 499 |
|
|
F1, F2 : Double;
|
| 500 |
|
|
DTRec : TStDateTimeRec;
|
| 501 |
|
|
SunXYZ : TStSunXYZRec;
|
| 502 |
|
|
Sun : TStPosRec;
|
| 503 |
|
|
Moon : TStMoonPosRec;
|
| 504 |
|
|
begin
|
| 505 |
|
|
{compute BesselianElements every 10 minutes starting 2 hours prior to CentralJD}
|
| 506 |
|
|
{but forcing positions to be at multiple of ten minutes}
|
| 507 |
|
|
for I := 1 to 25 do begin
|
| 508 |
|
|
CurJD := CentralJD + ((I-13) * (10/1440));
|
| 509 |
|
|
DTRec.D := AstJulianDateToStDate(CurJD, True);
|
| 510 |
|
|
if ((Frac(CurJD) + 0.5) >= 1) then
|
| 511 |
|
|
Mins := Trunc(((Frac(CurJD) + 0.5)-1) * 1440)
|
| 512 |
|
|
else
|
| 513 |
|
|
Mins := Trunc((Frac(CurJD) + 0.5) * 1440);
|
| 514 |
|
|
{changed because, for example, both 25 and 35 rounded to 30}
|
| 515 |
|
|
Mins := ((Mins + 5) div 10) * 10;
|
| 516 |
|
|
if (Mins = 1440) then
|
| 517 |
|
|
Mins := 0;
|
| 518 |
|
|
DTRec.T := Mins * 60;
|
| 519 |
|
|
|
| 520 |
|
|
SidTime := SiderealTime(DTRec) / radcor;
|
| 521 |
|
|
SunXYZ := SunPosPrim(DTRec);
|
| 522 |
|
|
Sun := SunPos(DTRec);
|
| 523 |
|
|
Moon := MoonPos(DTRec);
|
| 524 |
|
|
|
| 525 |
|
|
Sun1 := Sun.RA/radcor;
|
| 526 |
|
|
Sun2 := Sun.DC/radcor;
|
| 527 |
|
|
Moon1 := Moon.RA/radcor;
|
| 528 |
|
|
Moon2 := Moon.DC/radcor;
|
| 529 |
|
|
|
| 530 |
|
|
FBesselianElements[I].JD := StDateToDateTime(DTRec.D)
|
| 531 |
|
|
+ StTimeToDateTime(DTRec.T);
|
| 532 |
|
|
|
| 533 |
|
|
SunDist := 1.0 / sin(8.794/SunXYZ.RV/3600.0/radcor);
|
| 534 |
|
|
MoonDist := 1.0 / sin(Moon.Plx/radcor);
|
| 535 |
|
|
DistRatio := MoonDist / SunDist;
|
| 536 |
|
|
|
| 537 |
|
|
Theta := DistRatio/cos(Sun2) * cos(Moon2) * (Moon1 - Sun1);
|
| 538 |
|
|
Theta := Theta/(1.0-DistRatio);
|
| 539 |
|
|
Alpha := Sun1 - Theta;
|
| 540 |
|
|
|
| 541 |
|
|
Theta := DistRatio/(1.0 - DistRatio) * (Moon2 - Sun2);
|
| 542 |
|
|
|
| 543 |
|
|
FBesselianElements[I].Delta := Sun2 - Theta;
|
| 544 |
|
|
FBesselianElements[I].Angle := SidTime - Alpha;
|
| 545 |
|
|
FBesselianElements[I].XAxis := MoonDist * cos(Moon2) * (sin(Moon1 - Alpha));
|
| 546 |
|
|
|
| 547 |
|
|
Dbl3 := FBesselianElements[I].Delta;
|
| 548 |
|
|
FBesselianElements[I].YAxis := MoonDist * (sin(Moon2) * cos(Dbl3)
|
| 549 |
|
|
- cos(Moon2) * sin(Dbl3) * cos(Moon1 - Alpha));
|
| 550 |
|
|
|
| 551 |
|
|
Theta := DistRatio * SunXYZ.RV;
|
| 552 |
|
|
Theta := SunXYZ.RV - Theta;
|
| 553 |
|
|
F1 := StInvSin(0.004664012/Theta);
|
| 554 |
|
|
F2 := StInvSin(0.004640787/Theta);
|
| 555 |
|
|
|
| 556 |
|
|
Theta := MoonDist * (sin(Moon2) * sin(Dbl3) + cos(Moon2)
|
| 557 |
|
|
* cos(Dbl3) * cos(Moon1 - Alpha));
|
| 558 |
|
|
FBesselianElements[I].L1 := (Theta + 0.272453/sin(F1)) * StTan(F1);
|
| 559 |
|
|
FBesselianElements[I].L2 := (Theta - 0.272453/sin(F2)) * StTan(F2);
|
| 560 |
|
|
|
| 561 |
|
|
if (I = 13) then
|
| 562 |
|
|
F0 := StTan(F2);
|
| 563 |
|
|
|
| 564 |
|
|
if (I = 16) then begin
|
| 565 |
|
|
FUPrime := FBesselianElements[16].Angle - FBesselianElements[10].Angle;
|
| 566 |
|
|
FDPrime := FBesselianElements[16].Delta - FBesselianElements[10].Delta;
|
| 567 |
|
|
end;
|
| 568 |
|
|
end;
|
| 569 |
|
|
end;
|
| 570 |
|
|
|
| 571 |
|
|
procedure TStEclipses.GetShadowPath(I1, I2 : Integer; Path : TStList);
|
| 572 |
|
|
var
|
| 573 |
|
|
J,
|
| 574 |
|
|
I3, I4,
|
| 575 |
|
|
I5, I6 : integer;
|
| 576 |
|
|
|
| 577 |
|
|
Delta,
|
| 578 |
|
|
Dbl1,
|
| 579 |
|
|
Dbl2,
|
| 580 |
|
|
P1,
|
| 581 |
|
|
XAxis,
|
| 582 |
|
|
YAxis,
|
| 583 |
|
|
Eta,
|
| 584 |
|
|
R1, R2,
|
| 585 |
|
|
D1, D2,
|
| 586 |
|
|
D3, D4,
|
| 587 |
|
|
V3, V4,
|
| 588 |
|
|
V5, V6, V7,
|
| 589 |
|
|
XPrime,
|
| 590 |
|
|
YPrime : Double;
|
| 591 |
|
|
|
| 592 |
|
|
Position : PStLongLat;
|
| 593 |
|
|
begin
|
| 594 |
|
|
for J := I1 to I2 do begin
|
| 595 |
|
|
Eta := 0.00669454;
|
| 596 |
|
|
Delta := FBesselianElements[J].Delta;
|
| 597 |
|
|
XAxis := FBesselianElements[J].XAxis;
|
| 598 |
|
|
YAxis := FBesselianElements[J].YAxis;
|
| 599 |
|
|
|
| 600 |
|
|
R1 := sqrt(1.0 - Eta * sqr(cos(Delta)));
|
| 601 |
|
|
R2 := sqrt(1.0 - Eta * sqr(sin(Delta)));
|
| 602 |
|
|
|
| 603 |
|
|
D1 := sin(Delta) / R1;
|
| 604 |
|
|
D2 := sqrt(1.0 - Eta) * cos(Delta) / R1;
|
| 605 |
|
|
D3 := Eta * sin(Delta) * cos(Delta) / R1 / R2;
|
| 606 |
|
|
D4 := sqrt(1.0 - Eta) / R1 / R2;
|
| 607 |
|
|
|
| 608 |
|
|
V3 := YAxis / R1;
|
| 609 |
|
|
V4 := sqrt(1.0 - sqr(XAxis) - sqr(V3));
|
| 610 |
|
|
V5 := R2 * (V4 * D4 - V3 * D3);
|
| 611 |
|
|
V6 := FUPrime * (-YAxis * sin(Delta) + V5 * cos(Delta));
|
| 612 |
|
|
V7 := FUPrime * XAxis * sin(Delta) - FDPrime * V5;
|
| 613 |
|
|
|
| 614 |
|
|
if ((I2-I1) div 2) >= 4 then begin
|
| 615 |
|
|
I3 := (I2-I1) div 2;
|
| 616 |
|
|
I4 := I1 + I3;
|
| 617 |
|
|
I5 := I4 - 3;
|
| 618 |
|
|
I6 := I4 + 3;
|
| 619 |
|
|
XPrime := FBesselianElements[I6].XAxis
|
| 620 |
|
|
- FBesselianElements[I5].XAxis;
|
| 621 |
|
|
YPrime := FBesselianElements[I6].YAxis
|
| 622 |
|
|
- FBesselianElements[I5].YAxis;
|
| 623 |
|
|
end else begin
|
| 624 |
|
|
XPrime := (FBesselianElements[J+1].XAxis -
|
| 625 |
|
|
FBesselianElements[J-1].XAxis) * 3;
|
| 626 |
|
|
YPrime := (FBesselianElements[J+1].YAxis -
|
| 627 |
|
|
FBesselianElements[J-1].YAxis) * 3;
|
| 628 |
|
|
end;
|
| 629 |
|
|
|
| 630 |
|
|
New(Position);
|
| 631 |
|
|
Dbl1 := sqrt(sqr(XPrime - V6) + sqr(YPrime - V7));
|
| 632 |
|
|
Position^.JD := FBesselianElements[J].JD;
|
| 633 |
|
|
|
| 634 |
|
|
Dbl2 := (FBesselianElements[J].L2 - V5 * F0) / Dbl1;
|
| 635 |
|
|
Dbl2 := abs(Dbl2 * 120);
|
| 636 |
|
|
Position^.Duration := int(Dbl2) + frac(Dbl2) * 0.6;
|
| 637 |
|
|
|
| 638 |
|
|
Dbl1 := -V3 * D1 + V4 * D2;
|
| 639 |
|
|
P1 := StInvTan2(Dbl1, XAxis);
|
| 640 |
|
|
|
| 641 |
|
|
Dbl2 := (FBesselianElements[J].Angle - P1) * radcor;
|
| 642 |
|
|
Dbl2 := frac(Dbl2 / 360.0) * 360;
|
| 643 |
|
|
if (Dbl2 < 0) then
|
| 644 |
|
|
Dbl2 := Dbl2 + 360.0;
|
| 645 |
|
|
if (Dbl2 > 180.0) and (Dbl2 < 360.0) then
|
| 646 |
|
|
Dbl2 := Dbl2 - 360.0;
|
| 647 |
|
|
Position^.Longitude := Dbl2;
|
| 648 |
|
|
|
| 649 |
|
|
Dbl1 := StInvSin(V3 * D2 + V4 * D1);
|
| 650 |
|
|
Dbl2 := ArcTan(1.003364 * StTan(Dbl1)) * radcor;
|
| 651 |
|
|
Position^.Latitude := Dbl2;
|
| 652 |
|
|
|
| 653 |
|
|
Path.Append(Position);
|
| 654 |
|
|
end;
|
| 655 |
|
|
end;
|
| 656 |
|
|
|
| 657 |
|
|
procedure TStEclipses.NonPartialSolarEclipse(CentralJD, Mu, Gamma : Double);
|
| 658 |
|
|
var
|
| 659 |
|
|
SolEc : PStEclipseRecord;
|
| 660 |
|
|
I1, I2 : Integer;
|
| 661 |
|
|
begin
|
| 662 |
|
|
New(SolEc);
|
| 663 |
|
|
if (Mu < 0) then
|
| 664 |
|
|
SolEc^.EType := etSolarTotal
|
| 665 |
|
|
else if (Mu > 0.0047) then
|
| 666 |
|
|
SolEc^.EType := etSolarAnnular
|
| 667 |
|
|
else begin
|
| 668 |
|
|
if (Mu < (0.00464 * sqrt(1 - sqr(Gamma)))) then
|
| 669 |
|
|
SolEc^.EType := etSolarAnnularTotal
|
| 670 |
|
|
else
|
| 671 |
|
|
SolEc^.EType := etSolarTotal;
|
| 672 |
|
|
end;
|
| 673 |
|
|
|
| 674 |
|
|
SolEc^.Magnitude := -1;
|
| 675 |
|
|
if (Gamma > 0) then
|
| 676 |
|
|
SolEc^.Hemisphere := htNorthern
|
| 677 |
|
|
else
|
| 678 |
|
|
SolEc^.Hemisphere := htSouthern;
|
| 679 |
|
|
FillChar(SolEc^.LContacts, SizeOf(TStContactTimes), #0);
|
| 680 |
|
|
SolEc^.LContacts.MidEclipse := AJDtoDateTime(CentralJD);
|
| 681 |
|
|
|
| 682 |
|
|
GetBesselianElements(CentralJD);
|
| 683 |
|
|
|
| 684 |
|
|
{find limits - then go one step inside at each end}
|
| 685 |
|
|
I1 := 1;
|
| 686 |
|
|
while (sqr(FBesselianElements[I1].XAxis) +
|
| 687 |
|
|
sqr(FBesselianElements[I1].YAxis) >= 1.0) and (I1 < 25) do
|
| 688 |
|
|
Inc(I1);
|
| 689 |
|
|
Inc(I1);
|
| 690 |
|
|
|
| 691 |
|
|
I2 := I1;
|
| 692 |
|
|
repeat
|
| 693 |
|
|
if (I2 < 25) then begin
|
| 694 |
|
|
if (sqr(FBesselianElements[I2+1].XAxis) +
|
| 695 |
|
|
sqr(FBesselianElements[I2+1].YAxis) < 1) then
|
| 696 |
|
|
Inc(I2)
|
| 697 |
|
|
else
|
| 698 |
|
|
break;
|
| 699 |
|
|
end;
|
| 700 |
|
|
until (sqr(FBesselianElements[I2].XAxis) +
|
| 701 |
|
|
sqr(FBesselianElements[I2].YAxis) >= 1) or (I2 >= 25);
|
| 702 |
|
|
Dec(I2);
|
| 703 |
|
|
|
| 704 |
|
|
{this test accounts for non-central eclipses, i.e., those that are total}
|
| 705 |
|
|
{and/or annular but the axis of the moon's shadow does not touch the earth}
|
| 706 |
|
|
if (I1 <> I2) and (I1 < 26) and (I2 < 26) then begin
|
| 707 |
|
|
SolEc^.Path := TStList.Create(TStListNode);
|
| 708 |
|
|
SolEc^.Path.DisposeData := DisposePathData;
|
| 709 |
|
|
GetShadowPath(I1, I2, SolEc^.Path);
|
| 710 |
|
|
end else
|
| 711 |
|
|
SolEc^.Path := nil;
|
| 712 |
|
|
Self.Append(SolEc);
|
| 713 |
|
|
end;
|
| 714 |
|
|
|
| 715 |
|
|
procedure TStEclipses.PartialSolarEclipse(CentralJD, Mu, Gamma : Double);
|
| 716 |
|
|
var
|
| 717 |
|
|
SolEc : PStEclipseRecord;
|
| 718 |
|
|
begin
|
| 719 |
|
|
New(SolEc);
|
| 720 |
|
|
SolEc^.EType := etSolarPartial;
|
| 721 |
|
|
SolEc^.Magnitude := (1.5433 + Mu - abs(Gamma)) / (0.5461 + 2*Mu);
|
| 722 |
|
|
if (Gamma > 0) then
|
| 723 |
|
|
SolEc^.Hemisphere := htNorthern
|
| 724 |
|
|
else
|
| 725 |
|
|
SolEc^.Hemisphere := htSouthern;
|
| 726 |
|
|
FillChar(SolEc^.LContacts, SizeOf(TStContactTimes), #0);
|
| 727 |
|
|
SolEc^.LContacts.MidEclipse := AJDToDateTime(CentralJD);
|
| 728 |
|
|
SolEc^.Path := nil;
|
| 729 |
|
|
Self.Append(SolEc);
|
| 730 |
|
|
end;
|
| 731 |
|
|
|
| 732 |
|
|
|
| 733 |
|
|
end.
|
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