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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: StAstro.pas 4.04 *}
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{*********************************************************}
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{* SysTools: Astronomical Routines *}
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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 source files, Brian D. Warner, 1995. }
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{ }
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{ ************************************************************** }
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unit StAstro;
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interface
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uses
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Windows, SysUtils,
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StConst, StBase, StDate, StStrS, StDateSt, StMath;
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type
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TStTwilight = (ttCivil, ttNautical, ttAstronomical);
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TStRiseSetRec = record
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ORise : TStTime;
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OSet : TStTime;
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end;
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TStPosRec = record
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RA,
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DC : Double;
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end;
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TStPosRecArray = array[1..3] of TStPosRec;
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TStSunXYZRec = record
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SunX,
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SunY,
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SunZ,
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RV,
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SLong,
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SLat : Double;
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end;
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TStLunarRecord = record
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T : array[0..1] of TStDateTimeRec;
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end;
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TStPhaseRecord = packed record
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NMDate,
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FQDate,
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FMDate,
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LQDate : Double;
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end;
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TStPhaseArray = array[0..13] of TStPhaseRecord;
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TStDLSDateRec = record
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Starts : TStDate;
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Ends : TStDate;
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end;
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TStMoonPosRec = record
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RA,
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DC,
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Phase,
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Dia,
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Plx,
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Elong : Double;
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end;
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const
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radcor = 57.29577951308232; {number of degrees in a radian}
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StdDate = 2451545.0; {Ast. Julian Date for J2000 Epoch}
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OB2000 = 0.409092804; {J2000 obliquity of the ecliptic (radians)}
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{Sun procedures/functions}
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function AmountOfSunlight(LD : TStDate; Longitude, Latitude : Double) : TStTime;
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{-compute the hours, min, sec of sunlight on a given date}
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function FixedRiseSet(LD : TStDate; RA, DC, Longitude, Latitude : Double) : TStRiseSetRec;
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{-compute the rise and set time for a fixed object, e.g., a star}
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function SunPos(UT : TStDateTimeRec) : TStPosRec;
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{-compute the J2000 RA/Declination of the Sun}
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function SunPosPrim(UT : TStDateTimeRec) : TStSunXYZRec;
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{-compute the J2000 geocentric rectangular & ecliptic coordinates of the sun}
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function SunRiseSet(LD : TStDate; Longitude, Latitude : Double) : TStRiseSetRec;
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{-compute the Sun rise or set time}
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function Twilight(LD : TStDate; Longitude, Latitude : Double; TwiType : TStTwilight) : TStRiseSetRec;
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{-compute the beginning and end of twilight (civil, nautical, or astron.)}
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{Lunar procedures/functions}
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function LunarPhase(UT : TStDateTimeRec) : Double;
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{-compute the phase of the moon}
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function MoonPos(UT : TStDateTimeRec) : TStMoonPosRec;
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{-compute the J2000 RA/Declination of the moon}
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function MoonRiseSet(LD : TStDate; Longitude, Latitude : Double) : TStRiseSetRec;
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{-compute the Moon rise and set time}
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function FirstQuarter(D : TStDate) : TStLunarRecord;
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{-compute date/time of FirstQuarter(s)}
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function FullMoon(D : TStDate) : TStLunarRecord;
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{-compute the date/time of FullMoon(s)}
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function LastQuarter(D : TStDate) : TStLunarRecord;
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{-compute the date/time of LastQuarter(s)}
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function NewMoon(D : TStDate) : TStLunarRecord;
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{-compute the date/time of NewMoon(s)}
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function NextFirstQuarter(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the next closest FirstQuarter}
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function NextFullMoon(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the next closest FullMoon}
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function NextLastQuarter(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the next closest LastQuarter}
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function NextNewMoon(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the next closest NewMoon}
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function PrevFirstQuarter(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the prev closest FirstQuarter}
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function PrevFullMoon(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the prev closest FullMoon}
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function PrevLastQuarter(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the prev closest LastQuarter}
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function PrevNewMoon(D : TStDate) : TStDateTimeRec;
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{-compute the date/time of the prev closest NewMoon}
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{Calendar procedures/functions}
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function SiderealTime(UT : TStDateTimeRec) : Double;
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{-compute Sidereal Time at Greenwich}
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function Solstice(Y, Epoch : Integer; Summer : Boolean) : TStDateTimeRec;
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{-compute the date/time of the summer or winter solstice}
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function Equinox(Y, Epoch : Integer; Vernal : Boolean) : TStDateTimeRec;
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{-compute the date/time of the vernal/autumnal equinox}
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function Easter(Y, Epoch : Integer) : TStDate;
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{-compute the date of Easter (astronmical calendar)}
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{Astronomical Julian Date Conversions}
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function DateTimeToAJD(D : TDateTime) : Double;
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{Conversion routines}
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function HoursMin(RA : Double) : String;
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{-convert RA to hh:mm:ss string}
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function DegsMin(DC : Double) : String;
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{-convert Declination to +/-dd:mm:ss string}
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function AJDToDateTime(D : Double) : TDateTime;
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implementation
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var
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AJDOffset : Double;
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function CheckDate(UT : TStDateTimeRec) : Boolean;
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begin
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with UT do begin
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if (D < MinDate) or (D > MaxDate) or
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(T < 0) or (T > MaxTime) then
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Result := False
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else
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Result := True;
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end;
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end;
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function CheckYear(Y, Epoch : Integer) : Integer;
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begin
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if Y < 100 then begin
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if Y >= (Epoch mod 100) then
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Result := ((Epoch div 100) * 100) + Y
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else
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Result := ((Epoch div 100) * 100) + 100 + Y;
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end else
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Result := Y;
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end;
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function SiderealTime(UT : TStDateTimeRec) : Double;
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{-compute Sidereal Time at Greenwich in degrees}
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var
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T,
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JD : Double;
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begin
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if not CheckDate(UT) then begin
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Result := -1;
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Exit;
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end;
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JD := AstJulianDate(UT.D) + UT.T/86400;
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T := (JD - 2451545.0) / 36525.0;
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Result := 280.46061837
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+ 360.98564736629 * (JD - 2451545.0)
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+ 0.000387933 * sqr(T)
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- (sqr(T) * T / 38710000);
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Result := Frac(Result/360.0) * 360.0;
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if Result < 0 then
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Result := 360 + Result;
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end;
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function SunPosPrim(UT : TStDateTimeRec) : TStSunXYZRec;
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{-compute J2000 XYZ coordinates of the Sun}
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var
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JD,
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T0,
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A,
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L,
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B,
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X,Y,Z : Double;
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begin
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if not CheckDate(UT) then begin
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with Result do begin
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SunX := -99;
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SunY := -99;
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SunZ := -99;
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RV := -99;
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SLong := -99;
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SLat := -99;
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end;
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Exit;
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end;
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JD := AstJulianDate(UT.D) + UT.T/86400;
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T0 := (JD - StdDate) / 365250;
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{solar longitude}
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L := 175347046
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+ 3341656 * cos(4.6692568 + 6283.07585*T0)
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+ 34894 * cos(4.6261000 + 12566.1517*T0)
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+ 3497 * cos(2.7441000 + 5753.3849*T0)
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+ 3418 * cos(2.8289000 + 3.5231*T0)
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+ 3136 * cos(3.6277000 + 77713.7715*T0)
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+ 2676 * cos(4.4181000 + 7860.4194*T0)
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+ 2343 * cos(6.1352000 + 3930.2097*T0)
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+ 1324 * cos(0.7425000 + 11506.7698*T0)
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+ 1273 * cos(2.0371000 + 529.6910*T0)
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+ 1199 * cos(1.1096000 + 1577.3435*T0)
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+ 990 * cos(5.2330000 + 5884.9270*T0)
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+ 902 * cos(2.0450000 + 26.1490*T0)
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+ 857 * cos(3.5080000 + 398.149*T0)
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+ 780 * cos(1.1790000 + 5223.694*T0)
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+ 753 * cos(2.5330000 + 5507.553*T0)
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+ 505 * cos(4.5830000 + 18849.228*T0)
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+ 492 * cos(4.2050000 + 775.523*T0)
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+ 357 * cos(2.9200000 + 0.067*T0)
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+ 317 * cos(5.8490000 + 11790.626*T0)
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+ 284 * cos(1.8990000 + 796.298*T0)
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+ 271 * cos(0.3150000 + 10977.079*T0)
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+ 243 * cos(0.3450000 + 5486.778*T0)
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+ 206 * cos(4.8060000 + 2544.314*T0)
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+ 205 * cos(1.8690000 + 5573.143*T0)
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+ 202 * cos(2.4580000 + 6069.777*T0)
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+ 156 * cos(0.8330000 + 213.299*T0)
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+ 132 * cos(3.4110000 + 2942.463*T0)
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+ 126 * cos(1.0830000 + 20.775*T0)
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+ 115 * cos(0.6450000 + 0.980*T0)
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+ 103 * cos(0.6360000 + 4694.003*T0)
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+ 102 * cos(0.9760000 + 15720.839*T0)
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+ 102 * cos(4.2670000 + 7.114*T0)
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+ 99 * cos(6.2100000 + 2146.170*T0)
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+ 98 * cos(0.6800000 + 155.420*T0)
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+ 86 * cos(5.9800000 +161000.690*T0)
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+ 85 * cos(1.3000000 + 6275.960*T0)
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+ 85 * cos(3.6700000 + 71430.700*T0)
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+ 80 * cos(1.8100000 + 17260.150*T0);
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A := 628307584999.0
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+ 206059 * cos(2.678235 + 6283.07585*T0)
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+ 4303 * cos(2.635100 + 12566.1517*T0)
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+ 425 * cos(1.590000 + 3.523*T0)
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+ 119 * cos(5.796000 + 26.298*T0)
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+ 109 * cos(2.966000 + 1577.344*T0)
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+ 93 * cos(2.590000 + 18849.23*T0)
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+ 72 * cos(1.140000 + 529.69*T0)
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+ 68 * cos(1.870000 + 398.15*T0)
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+ 67 * cos(4.410000 + 5507.55*T0)
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+ 59 * cos(2.890000 + 5223.69*T0)
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+ 56 * cos(2.170000 + 155.42*T0)
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+ 45 * cos(0.400000 + 796.30*T0)
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+ 36 * cos(0.470000 + 775.52*T0)
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+ 29 * cos(2.650000 + 7.11*T0)
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+ 21 * cos(5.340000 + 0.98*T0)
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+ 19 * cos(1.850000 + 5486.78*T0)
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+ 19 * cos(4.970000 + 213.30*T0)
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+ 17 * cos(2.990000 + 6275.96*T0)
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+ 16 * cos(0.030000 + 2544.31*T0);
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L := L + (A * T0);
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A := 8722 * cos(1.0725 + 6283.0758*T0)
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+ 991 * cos(3.1416)
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+ 295 * cos(0.437 + 12566.1520*T0)
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+ 27 * cos(0.050 + 3.52*T0)
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+ 16 * cos(5.190 + 26.30*T0)
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+ 16 * cos(3.69 + 155.42*T0)
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+ 9 * cos(0.30 + 18849.23*T0)
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+ 9 * cos(2.06 + 77713.77*T0);
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L := L + (A * sqr(T0));
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A := 289 * cos(5.842 + 6283.076*T0)
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+ 21 * cos(6.05 + 12566.15*T0)
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+ 3 * cos(5.20 + 155.42*T0)
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+ 3 * cos(3.14);
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L := L + (A * sqr(T0) * T0);
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L := L / 1.0E+8;
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{solar latitude}
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B := 280 * cos(3.199 + 84334.662*T0)
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+ 102 * cos(5.422 + 5507.553*T0)
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| 342 |
+ 80 * cos(3.88 + 5223.69*T0)
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| 343 |
+ 44 * cos(3.70 + 2352.87*T0)
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+ 32 * cos(4.00 + 1577.34*T0);
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| 345 |
B := B / 1.0E+8;
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| 346 |
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| 347 |
A := 227778 * cos(3.413766 + 6283.07585*T0)
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| 348 |
+ 3806 * cos(3.3706 + 12566.1517*T0)
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| 349 |
+ 3620
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| 350 |
+ 72 * cos(3.33 + 18849.23*T0)
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| 351 |
+ 8 * cos(3.89 + 5507.55*T0)
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| 352 |
+ 8 * cos(1.79 + 5223.69*T0)
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| 353 |
+ 6 * cos(5.20 + 2352.87*T0);
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| 354 |
B := B + (A * T0 / 1.0E+8);
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| 355 |
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| 356 |
A := 9721 * cos(5.1519 + 6283.07585*T0)
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| 357 |
+ 233 * cos(3.1416)
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| 358 |
+ 134 * cos(0.644 + 12566.152*T0)
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| 359 |
+ 7 * cos(1.07 + 18849.23*T0);
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| 360 |
B := B + (A * sqr(T0) / 1.0E+8);
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| 361 |
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| 362 |
A := 276 * cos(0.595 + 6283.076*T0)
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| 363 |
+ 17 * cos(3.14)
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| 364 |
+ 4 * cos(0.12 + 12566.15*T0);
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| 365 |
B := B + (A * sqr(T0) * T0 / 1.0E+8);
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| 366 |
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| 367 |
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| 368 |
{solar radius vector (astronomical units)}
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| 369 |
Result.RV := 100013989
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| 370 |
+ 1670700 * cos(3.0984635 + 6283.07585*T0)
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| 371 |
+ 13956 * cos(3.05525 + 12566.15170*T0)
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| 372 |
+ 3084 * cos(5.1985 + 77713.7715*T0)
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| 373 |
+ 1628 * cos(1.1739 + 5753.3849*T0)
|
| 374 |
+ 1576 * cos(2.8649 + 7860.4194*T0)
|
| 375 |
+ 925 * cos(5.453 + 11506.770*T0)
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| 376 |
+ 542 * cos(4.564 + 3930.210*T0)
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| 377 |
+ 472 * cos(3.661 + 5884.927*T0)
|
| 378 |
+ 346 * cos(0.964 + 5507.553*T0)
|
| 379 |
+ 329 * cos(5.900 + 5223.694*T0)
|
| 380 |
+ 307 * cos(0.299 + 5573.143*T0)
|
| 381 |
+ 243 * cos(4.273 + 11790.629*T0)
|
| 382 |
+ 212 * cos(5.847 + 1577.344*T0)
|
| 383 |
+ 186 * cos(5.022 + 10977.079*T0)
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| 384 |
+ 175 * cos(3.012 + 18849.228*T0)
|
| 385 |
+ 110 * cos(5.055 + 5486.778*T0)
|
| 386 |
+ 98 * cos(0.89 + 6069.78*T0)
|
| 387 |
+ 86 * cos(5.69 + 15720.84*T0)
|
| 388 |
+ 86 * cos(1.27 +161000.69*T0)
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| 389 |
+ 65 * cos(0.27 + 17260.15*T0)
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| 390 |
+ 63 * cos(0.92 + 529.69*T0)
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| 391 |
+ 57 * cos(2.01 + 83996.85*T0)
|
| 392 |
+ 56 * cos(5.24 + 71430.70*T0)
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| 393 |
+ 49 * cos(3.25 + 2544.31*T0)
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| 394 |
+ 47 * cos(2.58 + 775.52*T0)
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| 395 |
+ 45 * cos(5.54 + 9437.76*T0)
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| 396 |
+ 43 * cos(6.01 + 6275.96*T0)
|
| 397 |
+ 39 * cos(5.36 + 4694.00*T0)
|
| 398 |
+ 38 * cos(2.39 + 8827.39*T0)
|
| 399 |
+ 37 * cos(0.83 + 19651.05*T0)
|
| 400 |
+ 37 * cos(4.90 + 12139.55*T0)
|
| 401 |
+ 36 * cos(1.67 + 12036.46*T0)
|
| 402 |
+ 35 * cos(1.84 + 2942.46*T0)
|
| 403 |
+ 33 * cos(0.24 + 7084.90*T0)
|
| 404 |
+ 32 * cos(0.18 + 5088.63*T0)
|
| 405 |
+ 32 * cos(1.78 + 398.15*T0)
|
| 406 |
+ 28 * cos(1.21 + 6286.60*T0)
|
| 407 |
+ 28 * cos(1.90 + 6279.55*T0)
|
| 408 |
+ 26 * cos(4.59 + 10447.39*T0);
|
| 409 |
Result.RV := Result.RV / 1.0E+8;
|
| 410 |
|
| 411 |
A := 103019 * cos(1.107490 + 6283.075850*T0)
|
| 412 |
+ 1721 * cos(1.0644 + 12566.1517*T0)
|
| 413 |
+ 702 * cos(3.142)
|
| 414 |
+ 32 * cos(1.02 + 18849.23*T0)
|
| 415 |
+ 31 * cos(2.84 + 5507.55*T0)
|
| 416 |
+ 25 * cos(1.32 + 5223.69*T0)
|
| 417 |
+ 18 * cos(1.42 + 1577.34*T0)
|
| 418 |
+ 10 * cos(5.91 + 10977.08*T0)
|
| 419 |
+ 9 * cos(1.42 + 6275.96*T0)
|
| 420 |
+ 9 * cos(0.27 + 5486.78*T0);
|
| 421 |
Result.RV := Result.RV + (A * T0 / 1.0E+8);
|
| 422 |
|
| 423 |
A := 4359 * cos(5.7846 + 6283.0758*T0)
|
| 424 |
+ 124 * cos(5.579 + 12566.152*T0)
|
| 425 |
+ 12 * cos(3.14)
|
| 426 |
+ 9 * cos(3.63 + 77713.77*T0)
|
| 427 |
+ 6 * cos(1.87 + 5573.14*T0)
|
| 428 |
+ 3 * cos(5.47 + 18849.23*T0);
|
| 429 |
Result.RV := Result.RV + (A * sqr(T0) / 1.0E+8);
|
| 430 |
|
| 431 |
L := (L + PI);
|
| 432 |
L := Frac(L / 2.0 / PI) * 2.0 * Pi;
|
| 433 |
if L < 0 then
|
| 434 |
L := L + (2.0*PI);
|
| 435 |
B := -B;
|
| 436 |
|
| 437 |
Result.SLong := L * radcor;
|
| 438 |
Result.SLat := B * radcor;
|
| 439 |
|
| 440 |
X := Result.RV * cos(B) * cos(L);
|
| 441 |
Y := Result.RV * cos(B) * sin(L);
|
| 442 |
Z := Result.RV * sin(B);
|
| 443 |
|
| 444 |
Result.SunX := X + 4.40360E-7 * Y - 1.90919E-7 * Z;
|
| 445 |
Result.SunY := -4.79966E-7 * X + 0.917482137087 * Y - 0.397776982902 * Z;
|
| 446 |
Result.SunZ := 0.397776982902 * Y + 0.917482137087 * Z;
|
| 447 |
end;
|
| 448 |
|
| 449 |
function MoonPosPrim(UT : TStDateTimeRec) : TStMoonPosRec;
|
| 450 |
{-computes J2000 coordinates of the moon}
|
| 451 |
var
|
| 452 |
JD,
|
| 453 |
TD,
|
| 454 |
JCent,
|
| 455 |
JC2, JC3, JC4,
|
| 456 |
LP, D,
|
| 457 |
M, MP,
|
| 458 |
F, I,
|
| 459 |
A1,A2,A3,
|
| 460 |
MoonLong,
|
| 461 |
MoonLat,
|
| 462 |
MoonDst,
|
| 463 |
S1,C1,
|
| 464 |
SunRA,
|
| 465 |
SunDC,
|
| 466 |
EE,EES : Double;
|
| 467 |
|
| 468 |
SP : TStSunXYZRec;
|
| 469 |
|
| 470 |
begin
|
| 471 |
JD := AstJulianDate(UT.D) + UT.T/86400;
|
| 472 |
JCent := (JD - 2451545) / 36525;
|
| 473 |
JC2 := sqr(JCent);
|
| 474 |
JC3 := JC2 * JCent;
|
| 475 |
JC4 := sqr(JC2);
|
| 476 |
|
| 477 |
SP := SunPosPrim(UT);
|
| 478 |
SunRA := StInvTan2(SP.SunX, SP.SunY) * radcor;
|
| 479 |
SunDC := StInvSin(SP.SunZ / SP.RV) * radcor;
|
| 480 |
|
| 481 |
|
| 482 |
{Lunar mean longitude}
|
| 483 |
LP := 218.3164591 + (481267.88134236 * JCent)
|
| 484 |
- (1.3268E-3 * JC2) + (JC3 / 538841) - (JC4 / 65194000);
|
| 485 |
LP := Frac(LP/360) * 360;
|
| 486 |
if LP < 0 then
|
| 487 |
LP := LP + 360;
|
| 488 |
LP := LP/radcor;
|
| 489 |
|
| 490 |
{Lunar mean elongation}
|
| 491 |
D := 297.8502042 + (445267.1115168 * JCent)
|
| 492 |
- (1.63E-3 * JC2) + (JC3 / 545868) - (JC4 / 113065000);
|
| 493 |
D := Frac(D/360) * 360;
|
| 494 |
if D < 0 then
|
| 495 |
D := D + 360;
|
| 496 |
D := D/radcor;
|
| 497 |
|
| 498 |
{Solar mean anomaly}
|
| 499 |
M := 357.5291092 + (35999.0502909 * JCent)
|
| 500 |
- (1.536E-4 * JC2) + (JC3 / 24490000);
|
| 501 |
M := Frac(M/360) * 360;
|
| 502 |
if M < 0 then
|
| 503 |
M := M + 360;
|
| 504 |
M := M/radcor;
|
| 505 |
|
| 506 |
{Lunar mean anomaly}
|
| 507 |
MP := 134.9634114 + (477198.8676313 * JCent)
|
| 508 |
+ (8.997E-3 * JC2) + (JC3 / 69699) - (JC4 / 14712000);
|
| 509 |
MP := Frac(MP/360) * 360;
|
| 510 |
if MP < 0 then
|
| 511 |
MP := MP + 360;
|
| 512 |
MP := MP/radcor;
|
| 513 |
|
| 514 |
{Lunar argument of latitude}
|
| 515 |
F := 93.2720993 + (483202.0175273 * JCent)
|
| 516 |
- (3.4029E-3 * JC2) - (JC3 / 3526000) + (JC4 / 863310000);
|
| 517 |
F := Frac(F/360) * 360;
|
| 518 |
if F < 0 then
|
| 519 |
F := F + 360;
|
| 520 |
F := F/radcor;
|
| 521 |
|
| 522 |
|
| 523 |
{Other required arguments}
|
| 524 |
A1 := 119.75 + (131.849 * JCent);
|
| 525 |
A1 := Frac(A1/360) * 360;
|
| 526 |
if A1 < 0 then
|
| 527 |
A1 := A1 + 360;
|
| 528 |
A1 := A1/radcor;
|
| 529 |
|
| 530 |
A2 := 53.09 + (479264.290 * JCent);
|
| 531 |
A2 := Frac(A2/360) * 360;
|
| 532 |
if A2 < 0 then
|
| 533 |
A2 := A2 + 360;
|
| 534 |
A2 := A2/radcor;
|
| 535 |
|
| 536 |
A3 := 313.45 + (481266.484 * JCent);
|
| 537 |
A3 := Frac(A3/360) * 360;
|
| 538 |
if A3 < 0 then
|
| 539 |
A3 := A3 + 360;
|
| 540 |
A3 := A3/radcor;
|
| 541 |
|
| 542 |
{Earth's orbital eccentricity}
|
| 543 |
EE := 1.0 - (2.516E-3 * JCent) - (7.4E-6 * JC2);
|
| 544 |
EES := sqr(EE);
|
| 545 |
|
| 546 |
MoonLong := 6288774 * sin(MP)
|
| 547 |
+ 1274027 * sin(2*D - MP)
|
| 548 |
+ 658314 * sin(2*D)
|
| 549 |
+ 213618 * sin(2*MP)
|
| 550 |
- 185116 * sin(M) * EE
|
| 551 |
- 114332 * sin(2*F)
|
| 552 |
+ 58793 * sin(2*(D-MP))
|
| 553 |
+ 57066 * sin(2*D-M-MP) * EE
|
| 554 |
+ 53322 * sin(2*D-MP)
|
| 555 |
+ 45758 * sin(2*D-M) * EE
|
| 556 |
- 40923 * sin(M-MP) * EE
|
| 557 |
- 34720 * sin(D)
|
| 558 |
- 30383 * sin(M+MP) * EE
|
| 559 |
+ 15327 * sin(2*(D-F))
|
| 560 |
- 12528 * sin(MP+2*F)
|
| 561 |
+ 10980 * sin(MP-2*F)
|
| 562 |
+ 10675 * sin(4*D-MP)
|
| 563 |
+ 10034 * sin(3*MP)
|
| 564 |
+ 8548 * sin(4*D-2*MP)
|
| 565 |
- 7888 * sin(2*D+M-MP) * EE
|
| 566 |
- 6766 * sin(2*D+M) * EE
|
| 567 |
- 5163 * sin(D-MP)
|
| 568 |
+ 4987 * sin(D+M) * EE
|
| 569 |
+ 4036 * sin(2*D-M+MP) * EE
|
| 570 |
+ 3994 * sin(2*(D+MP))
|
| 571 |
+ 3861 * sin(4*D)
|
| 572 |
+ 3665 * sin(2*D-3*MP)
|
| 573 |
- 2689 * sin(M-2*MP) * EE
|
| 574 |
- 2602 * sin(2*D-MP+2*F)
|
| 575 |
+ 2390 * sin(2*D-M-2*MP) * EE
|
| 576 |
- 2348 * sin(D-MP)
|
| 577 |
+ 2236 * sin(2*(D-M)) * EES
|
| 578 |
- 2120 * sin(M-2*MP) * EE
|
| 579 |
- 2069 * sin(2*M) * EE
|
| 580 |
+ 2048 * sin(2*D-2*M-MP) * EES
|
| 581 |
- 1773 * sin(2*D+MP-2*F)
|
| 582 |
- 1595 * sin(2*(D+F))
|
| 583 |
+ 1215 * sin(4*D-M-MP) * EE
|
| 584 |
- 1110 * sin(2*(MP+F))
|
| 585 |
- 892 * sin(3*D-MP)
|
| 586 |
- 810 * sin(2*D-M-MP) * EE
|
| 587 |
+ 759 * sin(4*D-M-2*MP) * EE
|
| 588 |
- 713 * sin(2*M-MP) * EE
|
| 589 |
- 700 * sin(2*D+2*M-MP) * EES
|
| 590 |
+ 691 * sin(2*D+M-2*MP) * EE
|
| 591 |
+ 596 * sin(2*D-M-2*F) * EE
|
| 592 |
+ 549 * sin(4*D+MP)
|
| 593 |
+ 537 * sin(4*MP)
|
| 594 |
+ 520 * sin(4*D-M) * EE;
|
| 595 |
|
| 596 |
MoonDst := - 20905355 * cos(MP)
|
| 597 |
- 3699111 * cos(2*D - MP)
|
| 598 |
- 2955968 * cos(2*D)
|
| 599 |
- 569925 * cos(2*MP)
|
| 600 |
+ 48888 * cos(M) * EE
|
| 601 |
- 3149 * cos(2*F)
|
| 602 |
+ 246158 * cos(2*(D-MP))
|
| 603 |
- 152138 * cos(2*D-M-MP) * EE
|
| 604 |
- 170733 * cos(2*D-MP)
|
| 605 |
- 204586 * cos(2*D-M) * EE
|
| 606 |
- 129620 * cos(M-MP) * EE
|
| 607 |
+ 108743 * cos(D)
|
| 608 |
+ 104755 * cos(M-MP) * EE
|
| 609 |
+ 10321 * cos(2*D-2*F)
|
| 610 |
+ 79661 * cos(MP-2*F)
|
| 611 |
- 34782 * cos(4*D-MP)
|
| 612 |
- 23210 * cos(3*MP)
|
| 613 |
- 21636 * cos(4*D-2*MP)
|
| 614 |
+ 24208 * cos(2*D+M-MP) * EE
|
| 615 |
+ 30824 * cos(2*D-M) * EE
|
| 616 |
- 8379 * cos(D-MP)
|
| 617 |
- 16675 * cos(D+M) * EE
|
| 618 |
- 12831 * cos(2*D-M+MP) * EE
|
| 619 |
- 10445 * cos(2*D+2*MP)
|
| 620 |
- 11650 * cos(4*D) * EE
|
| 621 |
+ 14403 * cos(2*D+3*MP)
|
| 622 |
- 7003 * cos(M-2*MP) * EE
|
| 623 |
+ 10056 * cos(2*D-M-2*MP) * EE
|
| 624 |
+ 6322 * cos(D+MP)
|
| 625 |
- 9884 * cos(2*D-2*M) * EES
|
| 626 |
+ 5751 * cos(M+2*MP) * EE
|
| 627 |
- 4950 * cos(2*D-2*M-MP) * EES
|
| 628 |
+ 4130 * cos(2*D+MP+2*F)
|
| 629 |
- 3958 * cos(4*D-M-MP) * EE
|
| 630 |
+ 3258 * cos(3*D-MP)
|
| 631 |
+ 2616 * cos(2*D+M+MP) * EE
|
| 632 |
- 1897 * cos(4*D-M-2*MP) * EE
|
| 633 |
- 2117 * cos(2*M-MP) * EES
|
| 634 |
+ 2354 * cos(2*D+2*M-MP) * EES
|
| 635 |
- 1423 * cos(4*D+MP)
|
| 636 |
- 1117 * cos(4*MP)
|
| 637 |
- 1571 * cos(4*D-M) * EE
|
| 638 |
- 1739 * cos(D-2*MP)
|
| 639 |
- 4421 * cos(2*MP-2*F)
|
| 640 |
+ 1165 * cos(2*M+MP)
|
| 641 |
+ 8752 * cos(2*D-MP-2*F);
|
| 642 |
|
| 643 |
MoonLat := 5128122 * sin(F)
|
| 644 |
+ 280602 * sin(MP+F)
|
| 645 |
+ 277693 * sin(MP-F)
|
| 646 |
+ 173237 * sin(2*D-F)
|
| 647 |
+ 55413 * sin(2*D-MP+F)
|
| 648 |
+ 46271 * sin(2*D-MP-F)
|
| 649 |
+ 32573 * sin(2*D+F)
|
| 650 |
+ 17198 * sin(2*MP+F)
|
| 651 |
+ 9266 * sin(2*D+MP-F)
|
| 652 |
+ 8822 * sin(2*MP-F)
|
| 653 |
+ 8216 * sin(2*D-M-F) * EE
|
| 654 |
+ 4324 * sin(2*D-2*MP-F)
|
| 655 |
+ 4200 * sin(2*D+MP+F)
|
| 656 |
- 3359 * sin(2*D+M-F) * EE
|
| 657 |
+ 2463 * sin(2*D-M-MP+F) * EE
|
| 658 |
+ 2211 * sin(2*D-M+F) * EE
|
| 659 |
+ 2065 * sin(2*D-M-MP-F) * EE
|
| 660 |
- 1870 * sin(M-MP-F) * EE
|
| 661 |
+ 1828 * sin(4*D-MP-F)
|
| 662 |
- 1794 * sin(M+F) * EE
|
| 663 |
- 1749 * sin(3*F)
|
| 664 |
- 1565 * sin(M-MP+F) * EE
|
| 665 |
- 1491 * sin(D+F)
|
| 666 |
- 1475 * sin(M+MP+F) * EE
|
| 667 |
- 1410 * sin(M+MP-F) * EE
|
| 668 |
- 1344 * sin(M-F) * EE
|
| 669 |
- 1335 * sin(D-F)
|
| 670 |
+ 1107 * sin(3*MP+F)
|
| 671 |
+ 1021 * sin(4*D-F)
|
| 672 |
+ 833 * sin(4*D-MP+F)
|
| 673 |
+ 777 * sin(MP-3*F)
|
| 674 |
+ 671 * sin(4*D-2*MP+F)
|
| 675 |
+ 607 * sin(2*D-3*F)
|
| 676 |
+ 596 * sin(2*D+2*MP-F)
|
| 677 |
+ 491 * sin(2*D-M+MP-F) * EE
|
| 678 |
- 451 * sin(2*D-2*MP+F)
|
| 679 |
+ 439 * sin(3*MP-F)
|
| 680 |
+ 422 * sin(2*D+2*MP+F)
|
| 681 |
+ 421 * sin(2*D-3*MP-F)
|
| 682 |
- 366 * sin(2*D+M-MP+F) * EE
|
| 683 |
- 351 * sin(2*D+M+F) * EE
|
| 684 |
+ 331 * sin(4*D+F)
|
| 685 |
+ 315 * sin(2*D-M+MP+F) * EE
|
| 686 |
+ 302 * sin(2*D-2*M-F) * EES
|
| 687 |
- 283 * sin(MP + 3*F)
|
| 688 |
- 229 * sin(2*D+M+MP-F) * EE
|
| 689 |
+ 223 * sin(D+M-F) * EE
|
| 690 |
+ 223 * sin(D+M+F) * EE;
|
| 691 |
|
| 692 |
MoonLong := MoonLong
|
| 693 |
+ 3958 * sin(A1)
|
| 694 |
+ 1962 * sin(LP-F)
|
| 695 |
+ 318 * sin(A2);
|
| 696 |
|
| 697 |
MoonLat := MoonLat
|
| 698 |
- 2235 * sin(LP)
|
| 699 |
+ 382 * sin(A3)
|
| 700 |
+ 175 * sin(A1-F)
|
| 701 |
+ 175 * sin(A1+F)
|
| 702 |
+ 127 * sin(LP-MP)
|
| 703 |
- 115 * sin(LP+MP);
|
| 704 |
|
| 705 |
MoonLong := LP + MoonLong/1000000/radcor;
|
| 706 |
MoonLat := MoonLat/1000000/radcor;
|
| 707 |
MoonDst := 385000.56 + MoonDst/1000;
|
| 708 |
|
| 709 |
Result.Plx := StInvSin(6378.14/MoonDst) * radcor;
|
| 710 |
Result.Dia := 358473400 / MoonDst * 2 / 3600;
|
| 711 |
|
| 712 |
S1 := sin(MoonLong) * cos(OB2000) - StTan(MoonLat) * sin(OB2000);
|
| 713 |
C1 := cos(MoonLong);
|
| 714 |
Result.RA := StInvTan2(C1, S1) * radcor;
|
| 715 |
|
| 716 |
TD := sin(MoonLat) * cos(OB2000)
|
| 717 |
+ cos(MoonLat) * sin(OB2000) * sin(MoonLong);
|
| 718 |
TD := StInvSin(TD);
|
| 719 |
Result.DC := TD * radcor;
|
| 720 |
|
| 721 |
I := sin(SunDC/radcor) * sin(TD)
|
| 722 |
+ cos(SunDC/radcor) * cos(TD) * cos((SunRA-Result.RA)/radcor);
|
| 723 |
Result.Phase := (1 - I) / 2;
|
| 724 |
|
| 725 |
I := StInvCos(I) * radcor;
|
| 726 |
Result.Elong := (Result.RA - SunRA);
|
| 727 |
if Result.Elong < 0 then
|
| 728 |
Result.Elong := 360 + Result.Elong;
|
| 729 |
if Result.Elong >= 180 then begin
|
| 730 |
Result.Phase := -Result.Phase; {waning moon}
|
| 731 |
Result.Elong := -I
|
| 732 |
end else
|
| 733 |
Result.Elong := I;
|
| 734 |
end;
|
| 735 |
|
| 736 |
function AmountOfSunlight(LD : TStDate; Longitude, Latitude : Double): TStTime;
|
| 737 |
{-compute the hours, min, sec of sunlight on a given date}
|
| 738 |
var
|
| 739 |
RS : TStRiseSetRec;
|
| 740 |
begin
|
| 741 |
RS := SunRiseSet(LD, Longitude, Latitude);
|
| 742 |
with RS do begin
|
| 743 |
if ORise = -3 then begin
|
| 744 |
{sun is always above the horizon}
|
| 745 |
Result := SecondsInDay;
|
| 746 |
Exit;
|
| 747 |
end;
|
| 748 |
|
| 749 |
if ORise = -2 then begin
|
| 750 |
{sun is always below horizon}
|
| 751 |
Result := 0;
|
| 752 |
Exit;
|
| 753 |
end;
|
| 754 |
|
| 755 |
if (ORise > -1) then begin
|
| 756 |
if (OSet > -1) then
|
| 757 |
Result := OSet - ORise
|
| 758 |
else
|
| 759 |
Result := SecondsInDay - ORise;
|
| 760 |
end else begin
|
| 761 |
if (OSet > -1) then
|
| 762 |
Result := OSet
|
| 763 |
else
|
| 764 |
Result := 0;
|
| 765 |
end;
|
| 766 |
end;
|
| 767 |
if (Result < 0) then
|
| 768 |
Result := Result + SecondsInDay
|
| 769 |
else if (Result >= SecondsInDay) then
|
| 770 |
Result := Result - SecondsInDay;
|
| 771 |
end;
|
| 772 |
|
| 773 |
function SunPos(UT : TStDateTimeRec) : TStPosRec;
|
| 774 |
{-compute the RA/Declination of the Sun}
|
| 775 |
var
|
| 776 |
SP : TStSunXYZRec;
|
| 777 |
begin
|
| 778 |
if not CheckDate(UT) then begin
|
| 779 |
Result.RA := -1;
|
| 780 |
Result.DC := -99;
|
| 781 |
Exit;
|
| 782 |
end;
|
| 783 |
|
| 784 |
SP := SunPosPrim(UT);
|
| 785 |
Result.RA := StInvTan2(SP.SunX, SP.SunY) * radcor;
|
| 786 |
Result.DC := StInvSin(SP.SunZ / SP.RV) * radcor;
|
| 787 |
end;
|
| 788 |
|
| 789 |
function RiseSetPrim(LD : TStDate;
|
| 790 |
Longitude, Latitude, H0 : Double;
|
| 791 |
PR : TStPosRecArray;
|
| 792 |
ApproxOnly : Boolean) : TStRiseSetRec;
|
| 793 |
{-primitive routine for finding rise/set times}
|
| 794 |
var
|
| 795 |
ST,
|
| 796 |
NST,
|
| 797 |
HA,
|
| 798 |
LatR,
|
| 799 |
N1,
|
| 800 |
N2,
|
| 801 |
N3,
|
| 802 |
TTran,
|
| 803 |
TRise,
|
| 804 |
TSet,
|
| 805 |
TV1,
|
| 806 |
TV2,
|
| 807 |
A1,
|
| 808 |
A2,
|
| 809 |
DeltaR,
|
| 810 |
DeltaS,
|
| 811 |
RA,
|
| 812 |
DC,
|
| 813 |
Alt : Double;
|
| 814 |
|
| 815 |
ICount : SmallInt;
|
| 816 |
|
| 817 |
UT : TStDateTimeRec;
|
| 818 |
begin
|
| 819 |
H0 := H0/radcor;
|
| 820 |
|
| 821 |
UT.D := LD;
|
| 822 |
UT.T := 0;
|
| 823 |
ST := SiderealTime(UT);
|
| 824 |
|
| 825 |
LatR := Latitude/radcor;
|
| 826 |
|
| 827 |
{check if object never rises/sets}
|
| 828 |
N1 := sin(H0) - sin(LatR) * sin(PR[2].DC/radcor);
|
| 829 |
N2 := cos(LatR) * cos(PR[2].DC/radcor);
|
| 830 |
|
| 831 |
HA := N1 / N2;
|
| 832 |
if (abs(HA) >= 1) then begin
|
| 833 |
{ if ((Latitude - 90) >= 90) then begin}
|
| 834 |
if (HA > 0) then begin
|
| 835 |
{object never rises}
|
| 836 |
Result.ORise := -2;
|
| 837 |
Result.OSet := -2;
|
| 838 |
end else begin
|
| 839 |
{object never sets, i.e., it is circumpolar}
|
| 840 |
Result.ORise := -3;
|
| 841 |
Result.OSet := -3;
|
| 842 |
end;
|
| 843 |
Exit;
|
| 844 |
end;
|
| 845 |
|
| 846 |
HA := StInvCos(HA) * radcor;
|
| 847 |
if HA > 180 then
|
| 848 |
HA := HA - 180;
|
| 849 |
if HA < 0 then
|
| 850 |
HA := HA + 180;
|
| 851 |
|
| 852 |
{compute approximate hour angle at transit}
|
| 853 |
TTran := (PR[2].RA - Longitude - ST) / 360;
|
| 854 |
if abs(TTran) >= 1 then
|
| 855 |
TTran:= Frac(TTran);
|
| 856 |
if TTran < 0 then
|
| 857 |
TTran := TTran + 1;
|
| 858 |
|
| 859 |
TRise := TTran - HA/360;
|
| 860 |
TSet := TTran + HA/360;
|
| 861 |
if abs(TRise) >= 1 then
|
| 862 |
TRise:= Frac(TRise);
|
| 863 |
if TRise < 0 then
|
| 864 |
TRise := TRise + 1;
|
| 865 |
|
| 866 |
if abs(TSet) >= 1 then
|
| 867 |
TSet := Frac(TSet);
|
| 868 |
if TSet < 0 then
|
| 869 |
TSet := TSet + 1;
|
| 870 |
|
| 871 |
if not ApproxOnly then begin
|
| 872 |
{refine rise time by interpolation/iteration}
|
| 873 |
ICount := 0;
|
| 874 |
TV1 := 0;
|
| 875 |
A1 := 0;
|
| 876 |
repeat
|
| 877 |
NST := ST + 360.985647 * TRise;
|
| 878 |
NST := Frac(NST / 360.0) * 360;
|
| 879 |
N1 := PR[2].RA - PR[1].RA;
|
| 880 |
N2 := PR[3].RA - PR[2].RA;
|
| 881 |
N3 := N2 - N1;
|
| 882 |
RA := PR[2].RA + TRise/2 * (N1 + N2 + TRise*N3);
|
| 883 |
|
| 884 |
N1 := PR[2].DC - PR[1].DC;
|
| 885 |
N2 := PR[3].DC - PR[2].DC;
|
| 886 |
N3 := N2 - N1;
|
| 887 |
DC := PR[2].DC + TRise/2 * (N1 + N2 + TRise*N3);
|
| 888 |
DC := DC/radcor;
|
| 889 |
|
| 890 |
HA := (NST + Longitude - RA) / radcor;
|
| 891 |
Alt := StInvSin(sin(LatR) * sin(DC) + cos(LatR) * cos(DC) * cos(HA));
|
| 892 |
DeltaR := ((Alt - H0) * radcor) / (360 * cos(DC) * cos(LatR) * sin(HA));
|
| 893 |
TRise := TRise + DeltaR;
|
| 894 |
Inc(ICount);
|
| 895 |
if (ICount > 3) and (abs(DeltaR) >= 0.0005) then begin
|
| 896 |
if (ICount = 4) then begin
|
| 897 |
TV1 := TRise;
|
| 898 |
A1 := (Alt-H0) * radcor;
|
| 899 |
end else if (ICount = 5) then begin
|
| 900 |
TV2 := TRise;
|
| 901 |
A2 := (Alt-H0) * radcor;
|
| 902 |
|
| 903 |
TRise := TV1 + (A1 / A2) * (TV1 - TV2);
|
| 904 |
break;
|
| 905 |
end;
|
| 906 |
end;
|
| 907 |
until (abs(DeltaR) < 0.0005); {0.0005d = 0.72 min}
|
| 908 |
|
| 909 |
{refine set time by interpolation/iteration}
|
| 910 |
ICount := 0;
|
| 911 |
TV1 := 0;
|
| 912 |
A1 := 0;
|
| 913 |
repeat
|
| 914 |
NST := ST + 360.985647 * TSet;
|
| 915 |
NST := Frac(NST / 360.0) * 360;
|
| 916 |
N1 := PR[2].RA - PR[1].RA;
|
| 917 |
N2 := PR[3].RA - PR[2].RA;
|
| 918 |
N3 := N2 - N1;
|
| 919 |
RA := PR[2].RA + TSet/2 * (N1 + N2 + TSet*N3);
|
| 920 |
|
| 921 |
N1 := PR[2].DC - PR[1].DC;
|
| 922 |
N2 := PR[3].DC - PR[2].DC;
|
| 923 |
N3 := N2 - N1;
|
| 924 |
DC := PR[2].DC + TSet/2 * (N1 + N2 + TSet*N3);
|
| 925 |
DC := DC/radcor;
|
| 926 |
|
| 927 |
HA := (NST + Longitude - RA) / radcor;
|
| 928 |
Alt := StInvSin(sin(LatR) * sin(DC) + cos(LatR) * cos(DC) * cos(HA));
|
| 929 |
DeltaS := ((Alt - H0) * radcor) / (360 * cos(DC) * cos(LatR) * sin(HA));
|
| 930 |
TSet := TSet + DeltaS;
|
| 931 |
Inc(ICount);
|
| 932 |
if (ICount > 3) and (abs(DeltaS) >= 0.0005) then begin
|
| 933 |
if (ICount = 4) then begin
|
| 934 |
TV1 := TSet;
|
| 935 |
A1 := (Alt-H0) * radcor;
|
| 936 |
end else if (ICount = 5) then begin
|
| 937 |
TV2 := TSet;
|
| 938 |
A2 := (Alt-H0) * radcor;
|
| 939 |
|
| 940 |
TSet := TV1 + (A1 / A2) * (TV1 - TV2);
|
| 941 |
break;
|
| 942 |
end;
|
| 943 |
end;
|
| 944 |
until (abs(DeltaS) < 0.0005); {0.0005d = 0.72 min}
|
| 945 |
end;
|
| 946 |
|
| 947 |
if (TRise >= 0) and (TRise < 1) then
|
| 948 |
Result.ORise := Trunc(TRise * SecondsInDay)
|
| 949 |
else begin
|
| 950 |
if TRise < 0 then
|
| 951 |
Result.ORise := Trunc((TRise + 1) * SecondsInDay)
|
| 952 |
else
|
| 953 |
Result.ORise := Trunc(Frac(TRise) * SecondsInDay);
|
| 954 |
end;
|
| 955 |
if Result.ORise < 0 then
|
| 956 |
Inc(Result.ORise, SecondsInDay);
|
| 957 |
if Result.ORise >= SecondsInDay then
|
| 958 |
Dec(Result.ORise, SecondsInDay);
|
| 959 |
|
| 960 |
|
| 961 |
if (TSet >= 0) and (TSet < 1) then
|
| 962 |
Result.OSet := Trunc(TSet * SecondsInDay)
|
| 963 |
else begin
|
| 964 |
if TSet < 0 then
|
| 965 |
Result.OSet := Trunc((TSet + 1) * SecondsInDay)
|
| 966 |
else
|
| 967 |
Result.OSet := Trunc(Frac(TSet) * SecondsInDay);
|
| 968 |
end;
|
| 969 |
if Result.OSet < 0 then
|
| 970 |
Inc(Result.OSet, SecondsInDay);
|
| 971 |
if Result.OSet >= SecondsInDay then
|
| 972 |
Dec(Result.OSet, SecondsInDay);
|
| 973 |
end;
|
| 974 |
|
| 975 |
function SunRiseSet(LD : TStDate; Longitude, Latitude : Double) : TStRiseSetRec;
|
| 976 |
{-compute the Sun rise or set time}
|
| 977 |
{the value for H0 accounts for approximate refraction of 0.5667 deg. and}
|
| 978 |
{that rise or set is based on the upper limb instead of the center of the solar disc}
|
| 979 |
var
|
| 980 |
I : Integer;
|
| 981 |
H0 : Double;
|
| 982 |
UT : TStDateTimeRec;
|
| 983 |
RP : TStPosRecArray;
|
| 984 |
begin
|
| 985 |
Dec(LD);
|
| 986 |
H0 := -0.8333;
|
| 987 |
UT.T := 0;
|
| 988 |
UT.D := LD-1;
|
| 989 |
|
| 990 |
if CheckDate(UT) then begin
|
| 991 |
UT.D := UT.D + 2;
|
| 992 |
if (not CheckDate(UT)) then begin
|
| 993 |
Result.ORise := -4;
|
| 994 |
Result.OSet := -4;
|
| 995 |
Exit;
|
| 996 |
end else
|
| 997 |
UT.D := UT.D-2;
|
| 998 |
end else begin
|
| 999 |
Result.ORise := -4;
|
| 1000 |
Result.OSet := -4;
|
| 1001 |
Exit;
|
| 1002 |
end;
|
| 1003 |
|
| 1004 |
for I := 1 to 3 do begin
|
| 1005 |
RP[I] := SunPos(UT);
|
| 1006 |
if I >= 2 then begin
|
| 1007 |
if RP[I].RA < RP[I-1].RA then
|
| 1008 |
RP[I].RA := RP[I].RA + 360;
|
| 1009 |
end;
|
| 1010 |
Inc(UT.D);
|
| 1011 |
end;
|
| 1012 |
Result := RiseSetPrim(LD, Longitude, Latitude, H0, RP, False);
|
| 1013 |
end;
|
| 1014 |
|
| 1015 |
function Twilight(LD : TStDate; Longitude, Latitude : Double;
|
| 1016 |
TwiType : TStTwilight) : TStRiseSetRec;
|
| 1017 |
{-compute the beginning or end of twilight}
|
| 1018 |
{twilight computations are based on the zenith distance of the center }
|
| 1019 |
{of the solar disc.}
|
| 1020 |
{Civil = 6 deg. below the horizon}
|
| 1021 |
{Nautical = 12 deg. below the horizon}
|
| 1022 |
{Astronomical = 18 deg. below the horizon}
|
| 1023 |
var
|
| 1024 |
I : Integer;
|
| 1025 |
H0 : Double;
|
| 1026 |
UT : TStDateTimeRec;
|
| 1027 |
RP : TStPosRecArray;
|
| 1028 |
begin
|
| 1029 |
UT.D := LD-1;
|
| 1030 |
UT.T := 0;
|
| 1031 |
|
| 1032 |
if CheckDate(UT) then begin
|
| 1033 |
UT.D := UT.D + 2;
|
| 1034 |
if (not CheckDate(UT)) then begin
|
| 1035 |
Result.ORise := -4;
|
| 1036 |
Result.OSet := -4;
|
| 1037 |
Exit;
|
| 1038 |
end else
|
| 1039 |
UT.D := UT.D-2;
|
| 1040 |
end else begin
|
| 1041 |
Result.ORise := -4;
|
| 1042 |
Result.OSet := -4;
|
| 1043 |
Exit;
|
| 1044 |
end;
|
| 1045 |
|
| 1046 |
case TwiType of
|
| 1047 |
ttCivil : H0 := -6.0;
|
| 1048 |
ttNautical : H0 := -12.0;
|
| 1049 |
ttAstronomical : H0 := -18.0;
|
| 1050 |
else
|
| 1051 |
H0 := -18.0;
|
| 1052 |
end;
|
| 1053 |
|
| 1054 |
for I := 1 to 3 do begin
|
| 1055 |
UT.D := LD + I-1;
|
| 1056 |
RP[I] := SunPos(UT);
|
| 1057 |
if (I > 1) then begin
|
| 1058 |
if RP[I].RA < RP[I-1].RA then
|
| 1059 |
RP[I].RA := RP[I].RA + 360.0;
|
| 1060 |
end;
|
| 1061 |
end;
|
| 1062 |
Result := RiseSetPrim(LD, Longitude, Latitude, H0, RP, False);
|
| 1063 |
end;
|
| 1064 |
|
| 1065 |
function FixedRiseSet(LD : TStDate;
|
| 1066 |
RA, DC, Longitude, Latitude : Double) : TStRiseSetRec;
|
| 1067 |
{-compute the rise/set time for a fixed object, e.g., star}
|
| 1068 |
{the value for H0 accounts for approximate refraction of 0.5667 deg.}
|
| 1069 |
{this routine does not refine the intial estimate and so may be off by five}
|
| 1070 |
{minutes or so}
|
| 1071 |
var
|
| 1072 |
H0 : Double;
|
| 1073 |
UT : TStDateTimeRec;
|
| 1074 |
RP : TStPosRecArray;
|
| 1075 |
begin
|
| 1076 |
H0 := -0.5667;
|
| 1077 |
UT.T := 0;
|
| 1078 |
UT.D := LD;
|
| 1079 |
|
| 1080 |
if not CheckDate(UT) then begin
|
| 1081 |
Result.ORise := -4;
|
| 1082 |
Result.OSet := -4;
|
| 1083 |
Exit;
|
| 1084 |
end;
|
| 1085 |
|
| 1086 |
RP[2].RA := RA;
|
| 1087 |
RP[2].DC := DC;
|
| 1088 |
Result := RiseSetPrim(LD, Longitude, Latitude, H0, RP, True);
|
| 1089 |
end;
|
| 1090 |
|
| 1091 |
function MoonPos(UT : TStDateTimeRec) : TStMoonPosRec;
|
| 1092 |
{-compute the J2000 RA/Declination of the moon}
|
| 1093 |
begin
|
| 1094 |
if not CheckDate(UT) then begin
|
| 1095 |
Result.RA := -1;
|
| 1096 |
Result.DC := -1;
|
| 1097 |
Exit;
|
| 1098 |
end;
|
| 1099 |
Result := MoonPosPrim(UT);
|
| 1100 |
end;
|
| 1101 |
|
| 1102 |
function MoonRiseSet(LD : TStDate; Longitude, Latitude : Double) : TStRiseSetRec;
|
| 1103 |
{compute the Moon rise and set time}
|
| 1104 |
{the value for H0 accounts for approximate refraction of 0.5667 deg., }
|
| 1105 |
{that rise or set is based on the upper limb instead of the center of the}
|
| 1106 |
{lunar disc, and the lunar parallax. In accordance with American Ephemeris }
|
| 1107 |
{practice, the phase of the moon is not taken into account, i.e., the time}
|
| 1108 |
{is based on the upper limb whether it is lit or not}
|
| 1109 |
var
|
| 1110 |
I : Integer;
|
| 1111 |
H0 : Double;
|
| 1112 |
UT : TStDateTimeRec;
|
| 1113 |
RP : TStPosRecArray;
|
| 1114 |
MPR : TStMoonPosRec;
|
| 1115 |
begin
|
| 1116 |
H0 := 0.125; { default value }
|
| 1117 |
|
| 1118 |
Dec(LD);
|
| 1119 |
UT.T := 0;
|
| 1120 |
UT.D := LD;
|
| 1121 |
|
| 1122 |
if CheckDate(UT) then begin
|
| 1123 |
UT.D := UT.D + 2;
|
| 1124 |
if (not CheckDate(UT)) then begin
|
| 1125 |
Result.ORise := -4;
|
| 1126 |
Result.OSet := -4;
|
| 1127 |
Exit;
|
| 1128 |
end else
|
| 1129 |
UT.D := UT.D-2;
|
| 1130 |
end else begin
|
| 1131 |
Result.ORise := -4;
|
| 1132 |
Result.OSet := -4;
|
| 1133 |
Exit;
|
| 1134 |
end;
|
| 1135 |
|
| 1136 |
for I := 1 to 3 do begin
|
| 1137 |
MPR := MoonPos(UT);
|
| 1138 |
RP[I].RA := MPR.RA;
|
| 1139 |
RP[I].DC := MPR.DC;
|
| 1140 |
if I >= 2 then begin
|
| 1141 |
if I = 2 then
|
| 1142 |
H0 := 0.7275*MPR.Plx - 0.5667;
|
| 1143 |
if RP[I].RA < RP[I-1].RA then
|
| 1144 |
RP[I].RA := RP[I].RA + 360;
|
| 1145 |
end;
|
| 1146 |
Inc(UT.D);
|
| 1147 |
end;
|
| 1148 |
Result := RiseSetPrim(LD, Longitude, Latitude, H0, RP, False);
|
| 1149 |
end;
|
| 1150 |
|
| 1151 |
function LunarPhase(UT : TStDateTimeRec) : Double;
|
| 1152 |
{-compute the phase of the moon}
|
| 1153 |
{The value is positive if between New and Full Moon}
|
| 1154 |
{ negative if between Full and New Moon}
|
| 1155 |
var
|
| 1156 |
MPR : TStMoonPosRec;
|
| 1157 |
begin
|
| 1158 |
MPR := MoonPosPrim(UT);
|
| 1159 |
Result := MPR.Phase;
|
| 1160 |
end;
|
| 1161 |
|
| 1162 |
procedure GetPhases(K : Double; var PR : TStPhaseRecord);
|
| 1163 |
{primitive routine to find the date/time of phases in a lunar cycle}
|
| 1164 |
var
|
| 1165 |
JD,
|
| 1166 |
NK,
|
| 1167 |
TD,
|
| 1168 |
J1,
|
| 1169 |
J2,
|
| 1170 |
J3 : Double;
|
| 1171 |
|
| 1172 |
step : Integer;
|
| 1173 |
|
| 1174 |
E,
|
| 1175 |
FP,
|
| 1176 |
S1,
|
| 1177 |
M1,
|
| 1178 |
M2,
|
| 1179 |
M3 : Double;
|
| 1180 |
|
| 1181 |
function AddCor : Double;
|
| 1182 |
begin
|
| 1183 |
AddCor := 0.000325 * sin((299.77 + 0.107408*K - 0.009173*J2)/radcor)
|
| 1184 |
+ 0.000165 * sin((251.88 + 0.016321*K)/radcor)
|
| 1185 |
+ 0.000164 * sin((251.83 + 26.651886*K)/radcor)
|
| 1186 |
+ 0.000126 * sin((349.42 + 36.412478*K)/radcor)
|
| 1187 |
+ 0.000110 * sin((84.660 + 18.206239*K)/radcor)
|
| 1188 |
+ 0.000062 * sin((141.74 + 53.303771*K)/radcor)
|
| 1189 |
+ 0.000060 * sin((207.14 + 2.453732*K)/radcor)
|
| 1190 |
+ 0.000056 * sin((154.84 + 7.306860*K)/radcor)
|
| 1191 |
+ 0.000047 * sin((34.520 + 27.261239*K)/radcor)
|
| 1192 |
+ 0.000042 * sin((207.19 + 0.121824*K)/radcor)
|
| 1193 |
+ 0.000040 * sin((291.34 + 1.844379*K)/radcor)
|
| 1194 |
+ 0.000037 * sin((161.72 + 24.198154*K)/radcor)
|
| 1195 |
+ 0.000035 * sin((239.56 + 25.513099*K)/radcor)
|
| 1196 |
+ 0.000023 * sin((331.55 + 3.592518*K)/radcor);
|
| 1197 |
end;
|
| 1198 |
|
| 1199 |
begin
|
| 1200 |
NK := K;
|
| 1201 |
FillChar(PR, SizeOf(TStPhaseRecord), #0);
|
| 1202 |
for step := 0 to 3 do begin
|
| 1203 |
K := NK + (step*0.25);
|
| 1204 |
FP := Frac(K);
|
| 1205 |
if FP < 0 then
|
| 1206 |
FP := FP + 1;
|
| 1207 |
|
| 1208 |
{compute Julian Centuries}
|
| 1209 |
J1 := K / 1236.85;
|
| 1210 |
J2 := Sqr(J1);
|
| 1211 |
J3 := J2 * J1;
|
| 1212 |
|
| 1213 |
|
| 1214 |
{solar mean anomaly}
|
| 1215 |
S1 := 2.5534
|
| 1216 |
+ 29.1053569 * K
|
| 1217 |
- 0.0000218 * J2
|
| 1218 |
- 0.00000011 * J3;
|
| 1219 |
S1 := Frac(S1 / 360.0) * 360;
|
| 1220 |
if S1 < 0 then
|
| 1221 |
S1 := S1 + 360.0;
|
| 1222 |
|
| 1223 |
{lunar mean anomaly}
|
| 1224 |
M1 := 201.5643
|
| 1225 |
+ 385.81693528 * K
|
| 1226 |
+ 0.0107438 * J2
|
| 1227 |
+ 0.00001239 * J3
|
| 1228 |
- 0.000000058 * J2 * J2;
|
| 1229 |
M1 := Frac(M1 / 360.0) * 360;
|
| 1230 |
if M1 < 0 then
|
| 1231 |
M1 := M1 + 360.0;
|
| 1232 |
|
| 1233 |
{lunar argument of latitude}
|
| 1234 |
M2 := 160.7108
|
| 1235 |
+ 390.67050274 * K
|
| 1236 |
- 0.0016341 * J2
|
| 1237 |
- 0.00000227 * J3
|
| 1238 |
+ 0.000000011 * J2 * J2;
|
| 1239 |
M2 := Frac(M2 / 360.0) * 360;
|
| 1240 |
if M2 < 0 then
|
| 1241 |
M2 := M2 + 360.0;
|
| 1242 |
|
| 1243 |
{lunar ascending node}
|
| 1244 |
M3 := 124.7746
|
| 1245 |
- 1.56375580 * K
|
| 1246 |
+ 0.0020691 * J2
|
| 1247 |
+ 0.00000215 * J3;
|
| 1248 |
M3 := Frac(M3 / 360.0) * 360;
|
| 1249 |
if M3 < 0 then
|
| 1250 |
M3 := M3 + 360.0;
|
| 1251 |
|
| 1252 |
{convert to radians}
|
| 1253 |
S1 := S1/radcor;
|
| 1254 |
M1 := M1/radcor;
|
| 1255 |
M2 := M2/radcor;
|
| 1256 |
M3 := M3/radcor;
|
| 1257 |
|
| 1258 |
{mean Julian Date for phase}
|
| 1259 |
JD := 2451550.09765
|
| 1260 |
+ 29.530588853 * K
|
| 1261 |
+ 0.0001337 * J2
|
| 1262 |
- 0.000000150 * J3
|
| 1263 |
+ 0.00000000073 * J2 * J2;
|
| 1264 |
|
| 1265 |
{earth's orbital eccentricity}
|
| 1266 |
E := 1.0 - 0.002516 * J1 - 0.0000074 * J2;
|
| 1267 |
|
| 1268 |
{New Moon date time}
|
| 1269 |
if FP < 0.01 then begin
|
| 1270 |
TD := - 0.40720 * sin(M1)
|
| 1271 |
+ 0.17241 * E * sin(S1)
|
| 1272 |
+ 0.01608 * sin(2*M1)
|
| 1273 |
+ 0.01039 * sin(2*M2)
|
| 1274 |
+ 0.00739 * E * sin(M1-S1)
|
| 1275 |
- 0.00514 * E * sin(M1 + S1)
|
| 1276 |
+ 0.00208 * E * E * sin(2 * S1)
|
| 1277 |
- 0.00111 * sin(M1 - 2*M2)
|
| 1278 |
- 0.00057 * sin(M1 + 2*M2)
|
| 1279 |
+ 0.00056 * E * sin(2*M1 + S1)
|
| 1280 |
- 0.00042 * sin(3 * M1)
|
| 1281 |
+ 0.00042 * E * sin(S1 + 2*M2)
|
| 1282 |
+ 0.00038 * E * sin(S1 - 2*M2)
|
| 1283 |
- 0.00024 * E * sin(2*(M1-S1))
|
| 1284 |
- 0.00017 * sin(M3)
|
| 1285 |
- 0.00007 * sin(M1 + 2*S1);
|
| 1286 |
JD := JD + TD + AddCor;
|
| 1287 |
PR.NMDate := JD;
|
| 1288 |
end;
|
| 1289 |
|
| 1290 |
{Full Moon date/time}
|
| 1291 |
if Abs(FP - 0.5) < 0.01 then begin
|
| 1292 |
TD := - 0.40614 * sin(M1)
|
| 1293 |
+ 0.17302 * E * sin(S1)
|
| 1294 |
+ 0.01614 * sin(2*M1)
|
| 1295 |
+ 0.01043 * sin(2*M2)
|
| 1296 |
+ 0.00734 * E * sin(M1-S1)
|
| 1297 |
- 0.00515 * E * sin(M1 + S1)
|
| 1298 |
+ 0.00209 * E * E * sin(2 * S1)
|
| 1299 |
- 0.00111 * sin(M1 - 2*M2)
|
| 1300 |
- 0.00057 * sin(M1 + 2*M2)
|
| 1301 |
+ 0.00056 * E * sin(2*M1 + S1)
|
| 1302 |
- 0.00042 * sin(3 * M1)
|
| 1303 |
+ 0.00042 * E * sin(S1 + 2*M2)
|
| 1304 |
+ 0.00038 * E * sin(S1 - 2*M2)
|
| 1305 |
- 0.00024 * E * sin(2*(M1-S1))
|
| 1306 |
- 0.00017 * sin(M3)
|
| 1307 |
- 0.00007 * sin(M1 + 2*S1);
|
| 1308 |
JD := JD + TD + AddCor;
|
| 1309 |
PR.FMDate := JD;
|
| 1310 |
end;
|
| 1311 |
|
| 1312 |
{Quarters date/time}
|
| 1313 |
if (abs(FP - 0.25) < 0.01) or (abs(FP - 0.75) < 0.01) then begin
|
| 1314 |
TD := - 0.62801 * sin(M1)
|
| 1315 |
+ 0.17172 * sin(S1) * E
|
| 1316 |
- 0.01183 * sin(M1+S1) * E
|
| 1317 |
+ 0.00862 * sin(2*M1)
|
| 1318 |
+ 0.00804 * sin(2*M2)
|
| 1319 |
+ 0.00454 * sin(M1-S1) * E
|
| 1320 |
+ 0.00204 * sin(2*S1) * E * E
|
| 1321 |
- 0.00180 * sin(M1 - 2*M2)
|
| 1322 |
- 0.00070 * sin(M1 + 2*M2)
|
| 1323 |
- 0.00040 * sin(3*M1)
|
| 1324 |
- 0.00034 * sin(2*M1-S1) * E
|
| 1325 |
+ 0.00032 * sin(S1 + 2*M2) * E
|
| 1326 |
+ 0.00032 * sin(S1 - 2*M2) * E
|
| 1327 |
- 0.00028 * sin(M1 + 2*S1) * E * E
|
| 1328 |
+ 0.00027 * sin(2*M1 + S1) * E
|
| 1329 |
- 0.00017 * sin(M3)
|
| 1330 |
- 0.00005 * sin(M1 - S1 - 2*M2);
|
| 1331 |
JD := JD + TD + AddCor;
|
| 1332 |
|
| 1333 |
{adjustment to computed Julian Date}
|
| 1334 |
TD := 0.00306
|
| 1335 |
- 0.00038 * E * cos(S1)
|
| 1336 |
+ 0.00026 * cos(M1)
|
| 1337 |
- 0.00002 * cos(M1-S1)
|
| 1338 |
+ 0.00002 * cos(M1+S1)
|
| 1339 |
+ 0.00002 * cos(2*M2);
|
| 1340 |
|
| 1341 |
if Abs(FP - 0.25) < 0.01 then
|
| 1342 |
PR.FQDate := JD + TD
|
| 1343 |
else
|
| 1344 |
PR.LQDate := JD - TD;
|
| 1345 |
end;
|
| 1346 |
end;
|
| 1347 |
end;
|
| 1348 |
|
| 1349 |
procedure PhasePrim(LD : TStDate; var PhaseArray : TStPhaseArray);
|
| 1350 |
{-primitive phase calculation}
|
| 1351 |
var
|
| 1352 |
I,
|
| 1353 |
D,
|
| 1354 |
M,
|
| 1355 |
Y : Integer;
|
| 1356 |
K, TD,
|
| 1357 |
LYear : Double;
|
| 1358 |
|
| 1359 |
begin
|
| 1360 |
StDateToDMY(LD, D, M, Y);
|
| 1361 |
LYear := Y - 0.05;
|
| 1362 |
K := (LYear - 2000) * 12.3685;
|
| 1363 |
K := Int(K);
|
| 1364 |
TD := K / 12.3685 + 2000;
|
| 1365 |
if TD > Y then
|
| 1366 |
K := K-1;
|
| 1367 |
|
| 1368 |
{compute phases for each lunar cycle throughout the year}
|
| 1369 |
for I := 0 to 13 do begin
|
| 1370 |
GetPhases(K, PhaseArray[I]);
|
| 1371 |
K := K + 1;
|
| 1372 |
end;
|
| 1373 |
end;
|
| 1374 |
|
| 1375 |
function GenSearchPhase(SD : TStDate; PV : Byte) : TStLunarRecord;
|
| 1376 |
{searches for the specified phase in the given month/year expressed by SD}
|
| 1377 |
var
|
| 1378 |
I,
|
| 1379 |
C,
|
| 1380 |
LD,
|
| 1381 |
LM,
|
| 1382 |
LY,
|
| 1383 |
TD,
|
| 1384 |
TM,
|
| 1385 |
TY : Integer;
|
| 1386 |
ADate : TStDate;
|
| 1387 |
JD : Double;
|
| 1388 |
PhaseArray : TStPhaseArray;
|
| 1389 |
begin
|
| 1390 |
C := 0;
|
| 1391 |
FillChar(Result, SizeOf(Result), $FF);
|
| 1392 |
|
| 1393 |
StDateToDMY(SD, LD, LM, LY);
|
| 1394 |
PhasePrim(SD, PhaseArray);
|
| 1395 |
for I := LM-1 to LM+1 do begin
|
| 1396 |
if (PV = 0) then
|
| 1397 |
JD := PhaseArray[I].NMDate
|
| 1398 |
else if (PV = 1) then
|
| 1399 |
JD := PhaseArray[I].FQDate
|
| 1400 |
else if (PV = 2) then
|
| 1401 |
JD := PhaseArray[I].FMDate
|
| 1402 |
else
|
| 1403 |
JD := PhaseArray[I].LQDate;
|
| 1404 |
ADate := AstJulianDateToStDate(JD, True);
|
| 1405 |
|
| 1406 |
StDateToDMY(ADate, TD, TM, TY);
|
| 1407 |
if TM < LM then
|
| 1408 |
continue
|
| 1409 |
else if TM = LM then begin
|
| 1410 |
Result.T[C].D := ADate;
|
| 1411 |
Result.T[C].T := Trunc((Frac(JD) + 0.5) * 86400);
|
| 1412 |
if Result.T[C].T >= SecondsInDay then
|
| 1413 |
Dec(Result.T[C].T, SecondsInDay);
|
| 1414 |
Inc(C);
|
| 1415 |
end;
|
| 1416 |
end;
|
| 1417 |
end;
|
| 1418 |
|
| 1419 |
function FirstQuarter(D : TStDate) : TStLunarRecord;
|
| 1420 |
{-compute date/time of FirstQuarter(s)}
|
| 1421 |
begin
|
| 1422 |
Result := GenSearchPhase(D, 1);
|
| 1423 |
end;
|
| 1424 |
|
| 1425 |
function FullMoon(D : TStDate) : TStLunarRecord;
|
| 1426 |
{-compute the date/time of FullMoon(s)}
|
| 1427 |
begin
|
| 1428 |
Result := GenSearchPhase(D, 2);
|
| 1429 |
end;
|
| 1430 |
|
| 1431 |
function LastQuarter(D: TStDate) : TStLunarRecord;
|
| 1432 |
{-compute the date/time of LastQuarter(s)}
|
| 1433 |
begin
|
| 1434 |
Result := GenSearchPhase(D, 3);
|
| 1435 |
end;
|
| 1436 |
|
| 1437 |
function NewMoon(D : TStDate) : TStLunarRecord;
|
| 1438 |
{-compute the date/time of NewMoon(s)}
|
| 1439 |
begin
|
| 1440 |
Result := GenSearchPhase(D, 0);
|
| 1441 |
end;
|
| 1442 |
|
| 1443 |
function NextPrevPhase(D : TStDate; Ph : Byte;
|
| 1444 |
FindNext : Boolean) : TStDateTimeRec;
|
| 1445 |
var
|
| 1446 |
LD,
|
| 1447 |
LM,
|
| 1448 |
LY : Integer;
|
| 1449 |
K,
|
| 1450 |
JD,
|
| 1451 |
TJD : Double;
|
| 1452 |
PR : TStPhaseRecord;
|
| 1453 |
OK : Boolean;
|
| 1454 |
begin
|
| 1455 |
if (D < MinDate) or (D > MaxDate) then begin
|
| 1456 |
Result.D := BadDate;
|
| 1457 |
Result.T := BadTime;
|
| 1458 |
Exit;
|
| 1459 |
end;
|
| 1460 |
|
| 1461 |
StDateToDMY(D, LD, LM, LY);
|
| 1462 |
K := ((LY + LM/12 + LD/365.25) - 2000) * 12.3685 - 0.5;
|
| 1463 |
if FindNext then
|
| 1464 |
K := Round(K)-1
|
| 1465 |
else
|
| 1466 |
K := Round(K)-2;
|
| 1467 |
|
| 1468 |
OK := False;
|
| 1469 |
TJD := AstJulianDate(D);
|
| 1470 |
repeat
|
| 1471 |
GetPhases(K, PR);
|
| 1472 |
|
| 1473 |
if (Ph = 0) then
|
| 1474 |
JD := PR.NMDate
|
| 1475 |
else if (Ph = 1) then
|
| 1476 |
JD := PR.FQDate
|
| 1477 |
else if (Ph = 2) then
|
| 1478 |
JD := PR.FMDate
|
| 1479 |
else
|
| 1480 |
JD := PR.LQDate;
|
| 1481 |
|
| 1482 |
if (FindNext) then begin
|
| 1483 |
if (JD > TJD) then
|
| 1484 |
OK := True
|
| 1485 |
else
|
| 1486 |
K := K + 1;
|
| 1487 |
end else begin
|
| 1488 |
if (JD < TJD) then
|
| 1489 |
OK := True
|
| 1490 |
else
|
| 1491 |
K := K - 1;
|
| 1492 |
end;
|
| 1493 |
until OK;
|
| 1494 |
|
| 1495 |
Result.D := AstJulianDateToStDate(JD, True);
|
| 1496 |
if (Result.D <> BadDate) then begin
|
| 1497 |
Result.T := Trunc((Frac(JD) + 0.5) * 86400);
|
| 1498 |
if Result.T >= SecondsInDay then
|
| 1499 |
Dec(Result.T, SecondsInDay);
|
| 1500 |
end else
|
| 1501 |
Result.T := BadTime;
|
| 1502 |
end;
|
| 1503 |
|
| 1504 |
function NextFirstQuarter(D : TStDate) : TStDateTimeRec;
|
| 1505 |
{-compute the date/time of the next closest FirstQuarter}
|
| 1506 |
begin
|
| 1507 |
Result := NextPrevPhase(D, 1, True);
|
| 1508 |
end;
|
| 1509 |
|
| 1510 |
function NextFullMoon(D : TStDate) : TStDateTimeRec;
|
| 1511 |
{-compute the date/time of the next closest FullMoon}
|
| 1512 |
begin
|
| 1513 |
Result := NextPrevPhase(D, 2, True);
|
| 1514 |
end;
|
| 1515 |
|
| 1516 |
function NextLastQuarter(D : TStDate) : TStDateTimeRec;
|
| 1517 |
{-compute the date/time of the next closest LastQuarter}
|
| 1518 |
begin
|
| 1519 |
Result := NextPrevPhase(D, 3, True);
|
| 1520 |
end;
|
| 1521 |
|
| 1522 |
function NextNewMoon(D : TStDate) : TStDateTimeRec;
|
| 1523 |
{-compute the date/time of the next closest NewMoon}
|
| 1524 |
begin
|
| 1525 |
Result := NextPrevPhase(D, 0, True);
|
| 1526 |
end;
|
| 1527 |
|
| 1528 |
function PrevFirstQuarter(D : TStDate) : TStDateTimeRec;
|
| 1529 |
{-compute the date/time of the prev closest FirstQuarter}
|
| 1530 |
begin
|
| 1531 |
Result := NextPrevPhase(D, 1, False);
|
| 1532 |
end;
|
| 1533 |
|
| 1534 |
function PrevFullMoon(D : TStDate) : TStDateTimeRec;
|
| 1535 |
{-compute the date/time of the prev closest FullMoon}
|
| 1536 |
begin
|
| 1537 |
Result := NextPrevPhase(D, 2, False);
|
| 1538 |
end;
|
| 1539 |
|
| 1540 |
function PrevLastQuarter(D : TStDate) : TStDateTimeRec;
|
| 1541 |
{-compute the date/time of the prev closest LastQuarter}
|
| 1542 |
begin
|
| 1543 |
Result := NextPrevPhase(D, 3, False);
|
| 1544 |
end;
|
| 1545 |
|
| 1546 |
function PrevNewMoon(D : TStDate) : TStDateTimeRec;
|
| 1547 |
{-compute the date/time of the prev closest NewMoon}
|
| 1548 |
begin
|
| 1549 |
Result := NextPrevPhase(D, 0, False);
|
| 1550 |
end;
|
| 1551 |
|
| 1552 |
{Calendar procedures/functions}
|
| 1553 |
|
| 1554 |
function SolEqPrim(Y : Integer; K : Byte) : TStDateTimeRec;
|
| 1555 |
{primitive routine for finding equinoxes and solstices}
|
| 1556 |
var
|
| 1557 |
JD, TD, LY,
|
| 1558 |
JCent, MA,
|
| 1559 |
SLong : Double;
|
| 1560 |
|
| 1561 |
begin
|
| 1562 |
JD := 0;
|
| 1563 |
Result.D := BadDate;
|
| 1564 |
Result.T := BadTime;
|
| 1565 |
|
| 1566 |
{the following algorithm is valid only in the range of [1000..3000 AD]}
|
| 1567 |
{but is limited to returning dates in [MinYear..MaxYear]}
|
| 1568 |
if (Y < MinYear) or (Y > MaxYear) then
|
| 1569 |
Exit;
|
| 1570 |
|
| 1571 |
{compute approximate date/time for specified event}
|
| 1572 |
LY := (Y - 2000) / 1000;
|
| 1573 |
case K of
|
| 1574 |
0 : JD := 2451623.80984
|
| 1575 |
+ 365242.37404 * LY
|
| 1576 |
+ 0.05169 * sqr(LY)
|
| 1577 |
- 0.00411 * LY * sqr(LY)
|
| 1578 |
- 0.00057 * sqr(sqr(LY));
|
| 1579 |
|
| 1580 |
1 : JD := 2451716.56767
|
| 1581 |
+ 365241.62603 * LY
|
| 1582 |
+ 0.00325 * sqr(LY)
|
| 1583 |
+ 0.00888 * LY * sqr(LY)
|
| 1584 |
- 0.00030 * sqr(sqr(LY));
|
| 1585 |
|
| 1586 |
2 : JD := 2451810.21715
|
| 1587 |
+ 365242.01767 * LY
|
| 1588 |
- 0.11575 * sqr(LY)
|
| 1589 |
+ 0.00337 * sqr(LY) * LY
|
| 1590 |
+ 0.00078 * sqr(sqr(LY));
|
| 1591 |
|
| 1592 |
3 : JD := 2451900.05952
|
| 1593 |
+ 365242.74049 * LY
|
| 1594 |
- 0.06223 * sqr(LY)
|
| 1595 |
- 0.00823 * LY * sqr(LY)
|
| 1596 |
+ 0.00032 * sqr(sqr(LY));
|
| 1597 |
end;
|
| 1598 |
|
| 1599 |
{refine date/time by computing corrections due to solar longitude,}
|
| 1600 |
{nutation and abberation. Iterate using the corrected time until}
|
| 1601 |
{correction is less than one minute}
|
| 1602 |
repeat
|
| 1603 |
Result.D := AstJulianDateToStDate(JD, True);
|
| 1604 |
Result.T := Trunc((Frac(JD) + 0.5) * 86400);
|
| 1605 |
if Result.T >= SecondsInDay then
|
| 1606 |
Dec(Result.T, SecondsInDay);
|
| 1607 |
JCent := (JD - 2451545.0)/36525.0;
|
| 1608 |
|
| 1609 |
{approximate solar longitude - no FK5 correction}
|
| 1610 |
SLong := 280.46645
|
| 1611 |
+ 36000.76983 * JCent
|
| 1612 |
+ 0.0003032 * sqr(JCent);
|
| 1613 |
SLong := Frac((SLong)/360.0) * 360.0;
|
| 1614 |
if SLong < 0 then
|
| 1615 |
SLong := SLong + 360;
|
| 1616 |
|
| 1617 |
{Equation of the center correction}
|
| 1618 |
MA := 357.52910
|
| 1619 |
+ 35999.05030 * JCent;
|
| 1620 |
MA := MA/radcor;
|
| 1621 |
SLong := SLong
|
| 1622 |
+ (1.914600 - 0.004817 * JCent - 0.000014 * sqr(JCent)) * sin(MA)
|
| 1623 |
+ (0.019993 - 0.000101 * JCent) * sin(2*MA);
|
| 1624 |
|
| 1625 |
{approximate nutation}
|
| 1626 |
TD := 125.04452
|
| 1627 |
- 1934.136261 * JCent
|
| 1628 |
+ 0.0020708 * sqr(JCent);
|
| 1629 |
TD := TD/radcor;
|
| 1630 |
TD := (-17.20 * sin(TD) - 1.32 * sin(2*SLong/radcor))/3600;
|
| 1631 |
|
| 1632 |
{approximate abberation - solar distance is assumed to be 1 A.U.}
|
| 1633 |
SLong := SLong - (20.4989/3600) + TD;
|
| 1634 |
|
| 1635 |
{correction to compute Julian Date for event}
|
| 1636 |
TD := 58 * sin((K*90 - SLong)/radcor);
|
| 1637 |
if abs(TD) >= 0.0005 then
|
| 1638 |
JD := JD + TD;
|
| 1639 |
until abs(TD) < 0.0005;
|
| 1640 |
end;
|
| 1641 |
|
| 1642 |
function Solstice(Y, Epoch : Integer; Summer : Boolean) : TStDateTimeRec;
|
| 1643 |
{-compute the date/time of the summer or winter solstice}
|
| 1644 |
{if Summer = True, compute astronomical summer solstice (summer in N. Hem.)}
|
| 1645 |
{ = False, compute astronomical winter solstice (winter in N. Hem.)}
|
| 1646 |
begin
|
| 1647 |
Y := CheckYear(Y, Epoch);
|
| 1648 |
if Summer then
|
| 1649 |
Result := SolEqPrim(Y, 1)
|
| 1650 |
else
|
| 1651 |
Result := SolEqPrim(Y, 3);
|
| 1652 |
end;
|
| 1653 |
|
| 1654 |
function Equinox(Y, Epoch : Integer; Vernal : Boolean) : TStDateTimeRec;
|
| 1655 |
{-compute the date/time of the vernal/autumnal equinox}
|
| 1656 |
{if Vernal = True, compute astronomical vernal equinox (spring in N. Hem.)}
|
| 1657 |
{ = False, compute astronomical autumnal equinox (fall in N. Hem.)}
|
| 1658 |
begin
|
| 1659 |
Y := CheckYear(Y, Epoch);
|
| 1660 |
if Vernal then
|
| 1661 |
Result := SolEqPrim(Y, 0)
|
| 1662 |
else
|
| 1663 |
Result := SolEqPrim(Y, 2);
|
| 1664 |
end;
|
| 1665 |
|
| 1666 |
function Easter(Y : Integer; Epoch : Integer) : TStDate;
|
| 1667 |
{-compute the date of Easter}
|
| 1668 |
var
|
| 1669 |
A, B,
|
| 1670 |
C, D,
|
| 1671 |
E, F,
|
| 1672 |
G, H,
|
| 1673 |
I, K,
|
| 1674 |
L, M,
|
| 1675 |
N, P : LongInt;
|
| 1676 |
begin
|
| 1677 |
Y := CheckYear(Y, Epoch);
|
| 1678 |
|
| 1679 |
if (Y < MinYear) or (Y > MaxYear) then begin
|
| 1680 |
Result := BadDate;
|
| 1681 |
Exit;
|
| 1682 |
end;
|
| 1683 |
|
| 1684 |
A := Y mod 19;
|
| 1685 |
B := Y div 100;
|
| 1686 |
C := Y mod 100;
|
| 1687 |
D := B div 4;
|
| 1688 |
E := B mod 4;
|
| 1689 |
F := (B+8) div 25;
|
| 1690 |
G := (B-F+1) div 3;
|
| 1691 |
H := (19*A + B - D - G + 15) mod 30;
|
| 1692 |
I := C div 4;
|
| 1693 |
K := C mod 4;
|
| 1694 |
L := (32 + 2*E + 2*I - H - K) mod 7;
|
| 1695 |
M := (A + 11*H + 22*L) div 451;
|
| 1696 |
N := (H + L - 7*M + 114) div 31;
|
| 1697 |
P := (H + L - 7*M + 114) mod 31 + 1;
|
| 1698 |
|
| 1699 |
Result := DMYToStDate(P, N, Y, Epoch);
|
| 1700 |
end;
|
| 1701 |
|
| 1702 |
{Conversion routines}
|
| 1703 |
function HoursMin(RA : Double) : String;
|
| 1704 |
{-convert RA to formatted hh:mm:ss string}
|
| 1705 |
var
|
| 1706 |
HR, MR : Double;
|
| 1707 |
HS, MS : string[12];
|
| 1708 |
|
| 1709 |
begin
|
| 1710 |
if abs(RA) >= 360.0 then
|
| 1711 |
RA := Frac(RA / 360.0) * 360;
|
| 1712 |
if RA < 0 then
|
| 1713 |
RA := RA + 360.0;
|
| 1714 |
|
| 1715 |
HR := Int(RA / 15.0);
|
| 1716 |
MR := Frac(RA / 15.0) * 60;
|
| 1717 |
|
| 1718 |
Str(MR:5:2, MS);
|
| 1719 |
if MS = '60.00' then begin
|
| 1720 |
MS := '00.00';
|
| 1721 |
HR := HR + 1;
|
| 1722 |
if HR = 24 then
|
| 1723 |
HS := '0'
|
| 1724 |
else
|
| 1725 |
Str(HR:2:0, HS);
|
| 1726 |
end else begin
|
| 1727 |
if MS[1] = ' ' then
|
| 1728 |
MS[1] := '0';
|
| 1729 |
Str(Hr:2:0, HS);
|
| 1730 |
end;
|
| 1731 |
Result := HS + ' ' + MS;
|
| 1732 |
end;
|
| 1733 |
|
| 1734 |
function DegsMin(DC : Double) : String;
|
| 1735 |
{-convert Declination to formatted +/-dd:mm:ss string}
|
| 1736 |
var
|
| 1737 |
DR, MR : Double;
|
| 1738 |
DS, MS : string[12];
|
| 1739 |
begin
|
| 1740 |
if abs(DC) > 90 then
|
| 1741 |
DC := Frac(DC / 90.0) * 90.0;
|
| 1742 |
|
| 1743 |
DR := Int(DC);
|
| 1744 |
MR := Frac(abs(DC)) * 60;
|
| 1745 |
|
| 1746 |
Str(MR:4:1, MS);
|
| 1747 |
if MS = '60.0' then begin
|
| 1748 |
MS := '00.0';
|
| 1749 |
if DC >= 0 then
|
| 1750 |
DR := DR + 1
|
| 1751 |
else
|
| 1752 |
DR := DR - 1;
|
| 1753 |
end;
|
| 1754 |
|
| 1755 |
if abs(DC) < 10 then begin
|
| 1756 |
Str(DR:2:0, DS);
|
| 1757 |
DS := TrimLeadS(DS);
|
| 1758 |
if DC < 0 then begin
|
| 1759 |
if DC > -1 then
|
| 1760 |
DS := '- 0'
|
| 1761 |
else
|
| 1762 |
DS := '- ' + DS[2];
|
| 1763 |
end else
|
| 1764 |
DS := '+ ' + DS;
|
| 1765 |
end else begin
|
| 1766 |
Str(DR:3:0, DS);
|
| 1767 |
DS := TrimLeadS(DS);
|
| 1768 |
if DC < 0 then begin
|
| 1769 |
Delete(DS,1,1);
|
| 1770 |
DS := '-' + DS;
|
| 1771 |
end else
|
| 1772 |
DS := '+' + DS;
|
| 1773 |
end;
|
| 1774 |
if MS[1] = ' ' then
|
| 1775 |
MS[1] := '0';
|
| 1776 |
Result := DS + ' ' + MS;
|
| 1777 |
end;
|
| 1778 |
|
| 1779 |
function DateTimeToAJD(D : TDateTime) : Double;
|
| 1780 |
begin
|
| 1781 |
Result := D + AJDOffset;
|
| 1782 |
end;
|
| 1783 |
|
| 1784 |
function AJDToDateTime(D : Double) : TDateTime;
|
| 1785 |
begin
|
| 1786 |
Result := D - AJDOffset;
|
| 1787 |
end;
|
| 1788 |
|
| 1789 |
|
| 1790 |
initialization
|
| 1791 |
AJDOffSet := AstJulianDatePrim(1600, 1, 1, 0) - EncodeDate(1600, 1, 1);
|
| 1792 |
end.
|
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