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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: StJupsat.pas 4.04 *}
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{*********************************************************}
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{* SysTools: Astronomical Routines *}
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{* (for the four "Gallilean" moons of Jupiter *}
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{* Callisto, Europa, Ganymede, and Io) *}
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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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(* **************************************************************
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The formulae in this unit are based on DYNAMICAL time, which is based
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on the actual rotation of the Earth and is gradually slowing. Universal
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Time is based on a fixed rotation rate. To directly compare results in
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the astronomical literature (and Meeus' examples), you must use a Universal
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Time that is adjusted by the value Delta T. This value is approximately 1 min
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in the latter part of the 20th century and will be about 80 seconds in the
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year 2020. As an example, to compare the High Precision positions for
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1992 December 16 (Meeus' example), you must use a Universal Time of
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1992 December 16 at 00:00:59 which equals 00:00:00 Dynamical Time
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The Shadows parameter is used for high precision calculations only. If True,
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the positions are calculated as seen from the SUN, not the Earth. For eclipses
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of the satellites by Jupiter, in effect, the position is in reference to the
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SHADOW of Jupiter in space, not the planet itself. For shadow transits, where
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the shadow of the satellite is projected onto the surface of the planet, the
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position is that of the satellite's shadow in reference to Jupiter and not
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the satellite itself.
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The purpose of the Shadows parameter is to complete the prediction for
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satellite phenomenon. For example, using Shadow := False, the result may
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indicate that a satellite goes behind Jupiter at a given instant but not
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if the satellite is visible because it is in Jupiter's shadow. Setting
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Shadow := True for the same time will indicate if the planet is in or out
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of Jupiter's shadow.
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(Shadow := FALSE) and (abs(satellite X-coordinate) = 1)
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-------------------------------------------------------
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If the X-value is negative and heading towards 0, the satellite is entering
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the front of the planet.
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If the X-value is negative and increasing, the satellite is coming from
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behind the planet.
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If the X-value is positive and heading towards 0, the satellite is going
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behind the planet.
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If the X-value is positive and increasing, the satellite is leaving
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the front of the planet.
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(Shadow := TRUE) and (abs(satellite X-coordinate) = 1)
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-------------------------------------------------------
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If the X-value is negative and heading towards 0, the satellite's shadow is
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entering the planet's disc.
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If the X-value is negative and increasing, the satellite is leaving the
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planet's shadow.
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If the X-value is positive and heading towards 0, the satellite entering
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the planet's shadow.
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If the X-value is positive and increasing, the satellite's shadow is
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leaving the planet.
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The X and Y coordinates are based on the equatorial radius of Jupiter. Because
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the planet is considerably flattened by its rapid rotation, the polar diameter
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is less than 1. To avoid dealing with an elliptical disc for Jupiter, multiply
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the Y values only by 1.071374. This creates a "circular Jupiter" and so makes
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determining if the satellite is above or below Jupiter easier
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(abs(Y-coordinate) > 1).
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****************************************************************** *)
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unit StJupsat;
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interface
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type
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TStJupSatPos = packed record
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X : Double;
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Y : Double;
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end;
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TStJupSats = packed record
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Io : TStJupSatPos;
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Europa : TStJupSatPos;
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Ganymede : TStJupSatPos;
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Callisto : TStJupSatPos;
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end;
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function GetJupSats(JD : TDateTime; HighPrecision, Shadows : Boolean) : TStJupSats;
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implementation
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uses
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StDate, StAstro, StAstroP, StJup, StMath;
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type
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SunCoordsRec = packed record
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X, Y, Z : Double;
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L, B, R : Double;
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end;
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TranformRec = packed record
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A, B, C : array[1..6] of Double;
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end;
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function SunCoords(JD : Double) : SunCoordsRec;
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var
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L, B, R,
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T0, TM,
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RS,
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OB, A : Double;
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begin
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T0 := (JD - StdDate) / 365250;
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TM := T0/100;
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RS := radcor * 3600;
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OB := 0.4090928042223
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- 4680.93/RS * TM
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- 1.55/RS * sqr(TM)
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+ 1999.25/RS * sqr(TM) * TM
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- 51.38/RS * sqr(sqr(TM))
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- 249.67/RS * sqr(sqr(TM)) * TM
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- 39.05/RS * sqr(sqr(TM)) * sqr(TM)
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+ 7.12/RS * sqr(sqr(TM)) * sqr(TM) * TM
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+ 27.87/RS * sqr(sqr(sqr(TM)));
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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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| 179 |
+ 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 := 628331966747.0
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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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| 210 |
+ 109 * cos(2.966000 + 1577.344*T0)
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| 211 |
+ 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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| 218 |
+ 36 * cos(0.470000 + 775.52*T0)
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| 219 |
+ 29 * cos(2.650000 + 7.11*T0)
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| 220 |
+ 21 * cos(5.340000 + 0.98*T0)
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| 221 |
+ 19 * cos(1.850000 + 5486.78*T0)
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| 222 |
+ 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 := 52919
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+ 8720 * cos(1.0721 + 6283.0758*T0)
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+ 309 * cos(0.867 + 12566.152*T0)
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| 230 |
+ 27 * cos(0.050 + 3.52*T0)
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| 231 |
+ 16 * cos(5.190 + 26.30*T0)
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| 232 |
+ 16 * cos(3.68 + 155.42*T0)
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| 233 |
+ 10 * cos(0.76 + 18849.23*T0)
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| 234 |
+ 9 * cos(2.06 + 77713.77*T0)
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| 235 |
+ 7 * cos(0.83 + 775.52*T0)
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| 236 |
+ 5 * cos(4.66 + 1577.34*T0);
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L := L + (A * sqr(T0));
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A := 289 * cos(5.844 + 6283.076*T0)
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+ 35
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+ 17 * cos(5.49 + 12566.15*T0)
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| 242 |
+ 3 * cos(5.20 + 155.42*T0)
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+ 1 * cos(4.72 + 3.52*T0);
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L := L + (A * sqr(T0) * T0);
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A := 114 * cos(3.142);
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L := L + (A * sqr(sqr(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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+ 80 * cos(3.88 + 5223.69*T0)
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| 254 |
+ 44 * cos(3.70 + 2352.87*T0)
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+ 32 * cos(4.00 + 1577.34*T0);
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A := 9 * cos(3.90 + 5507.550*T0)
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+ 6 * cos(1.73 + 5223.690*T0);
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B := B + (A * T0);
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B := B / 1.0E+8;
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{solar radius vector (astronomical units)}
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R := 100013989
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+ 1670700 * cos(3.0984635 + 6283.07585*T0)
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+ 13956 * cos(3.05525 + 12566.15170*T0)
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| 267 |
+ 3084 * cos(5.1985 + 77713.7715*T0)
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| 268 |
+ 1628 * cos(1.1739 + 5753.3849*T0)
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| 269 |
+ 1576 * cos(2.8649 + 7860.4194*T0)
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| 270 |
+ 925 * cos(5.453 + 11506.770*T0)
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| 271 |
+ 542 * cos(4.564 + 3930.210*T0)
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| 272 |
+ 472 * cos(3.661 + 5884.927*T0)
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| 273 |
+ 346 * cos(0.964 + 5507.553*T0)
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| 274 |
+ 329 * cos(5.900 + 5223.694*T0)
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| 275 |
+ 307 * cos(0.299 + 5573.143*T0)
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| 276 |
+ 243 * cos(4.273 + 11790.629*T0)
|
| 277 |
+ 212 * cos(5.847 + 1577.344*T0)
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| 278 |
+ 186 * cos(5.022 + 10977.079*T0)
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| 279 |
+ 175 * cos(3.012 + 18849.228*T0)
|
| 280 |
+ 110 * cos(5.055 + 5486.778*T0)
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| 281 |
+ 98 * cos(0.89 + 6069.78*T0)
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| 282 |
+ 86 * cos(5.69 + 15720.84*T0)
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| 283 |
+ 86 * cos(1.27 +161000.69*T0)
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| 284 |
+ 65 * cos(0.27 + 17260.15*T0)
|
| 285 |
+ 63 * cos(0.92 + 529.69*T0)
|
| 286 |
+ 57 * cos(2.01 + 83996.85*T0)
|
| 287 |
+ 56 * cos(5.24 + 71430.70*T0)
|
| 288 |
+ 49 * cos(3.25 + 2544.31*T0)
|
| 289 |
+ 47 * cos(2.58 + 775.52*T0)
|
| 290 |
+ 45 * cos(5.54 + 9437.76*T0)
|
| 291 |
+ 43 * cos(6.01 + 6275.96*T0)
|
| 292 |
+ 39 * cos(5.36 + 4694.00*T0)
|
| 293 |
+ 38 * cos(2.39 + 8827.39*T0)
|
| 294 |
+ 37 * cos(0.83 + 19651.05*T0)
|
| 295 |
+ 37 * cos(4.90 + 12139.55*T0)
|
| 296 |
+ 36 * cos(1.67 + 12036.46*T0)
|
| 297 |
+ 35 * cos(1.84 + 2942.46*T0)
|
| 298 |
+ 33 * cos(0.24 + 7084.90*T0)
|
| 299 |
+ 32 * cos(0.18 + 5088.63*T0)
|
| 300 |
+ 32 * cos(1.78 + 398.15*T0)
|
| 301 |
+ 28 * cos(1.21 + 6286.60*T0)
|
| 302 |
+ 28 * cos(1.90 + 6279.55*T0)
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| 303 |
+ 26 * cos(4.59 + 10447.39*T0);
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| 304 |
R := R / 1.0E+8;
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| 305 |
|
| 306 |
A := 103019 * cos(1.107490 + 6283.075850*T0)
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| 307 |
+ 1721 * cos(1.0644 + 12566.1517*T0)
|
| 308 |
+ 702 * cos(3.142)
|
| 309 |
+ 32 * cos(1.02 + 18849.23*T0)
|
| 310 |
+ 31 * cos(2.84 + 5507.55*T0)
|
| 311 |
+ 25 * cos(1.32 + 5223.69*T0)
|
| 312 |
+ 18 * cos(1.42 + 1577.34*T0)
|
| 313 |
+ 10 * cos(5.91 + 10977.08*T0)
|
| 314 |
+ 9 * cos(1.42 + 6275.96*T0)
|
| 315 |
+ 9 * cos(0.27 + 5486.78*T0);
|
| 316 |
R := R + (A * T0 / 1.0E+8);
|
| 317 |
|
| 318 |
A := 4359 * cos(5.7846 + 6283.0758*T0)
|
| 319 |
+ 124 * cos(5.579 + 12566.152*T0)
|
| 320 |
+ 12 * cos(3.14)
|
| 321 |
+ 9 * cos(3.63 + 77713.77*T0)
|
| 322 |
+ 6 * cos(1.87 + 5573.14*T0)
|
| 323 |
+ 3 * cos(5.47 + 18849.23*T0);
|
| 324 |
R := R + (A * sqr(T0) / 1.0E+8);
|
| 325 |
|
| 326 |
L := (L + PI);
|
| 327 |
L := Frac(L / 2.0 / PI) * 2.0 * Pi;
|
| 328 |
if L < 0 then
|
| 329 |
L := L + (2.0*PI);
|
| 330 |
B := -B;
|
| 331 |
|
| 332 |
Result.L := L;
|
| 333 |
Result.B := B;
|
| 334 |
Result.R := R;
|
| 335 |
Result.X := R * cos(B) * cos(L);
|
| 336 |
Result.Y := R * (cos(B) * sin(L) * cos(OB) - sin(B) * sin(OB));
|
| 337 |
Result.Z := R * (cos(B) * sin(L) * sin(OB) + sin(B) * cos(OB));
|
| 338 |
end;
|
| 339 |
|
| 340 |
|
| 341 |
{-------------------------------------------------------------------------}
|
| 342 |
|
| 343 |
function JupSatsLo(AJD : Double) : TStJupSats;
|
| 344 |
var
|
| 345 |
DateDif, {d}
|
| 346 |
ArgJup, {V}
|
| 347 |
AnomE, {M}
|
| 348 |
AnomJ, {N}
|
| 349 |
DeltaLong, {J}
|
| 350 |
ECenterE, {A}
|
| 351 |
ECenterJ, {B}
|
| 352 |
K,
|
| 353 |
RVE, {R}
|
| 354 |
RVJ, {r}
|
| 355 |
EJDist, {Delta}
|
| 356 |
Phase, {Psi}
|
| 357 |
Lambda, {Lambda}
|
| 358 |
DS, DE, {DS, DE}
|
| 359 |
Mu1, Mu2,
|
| 360 |
Mu3, Mu4, {Mu1 - Mu4}
|
| 361 |
G, H, {G, H}
|
| 362 |
TmpDbl1,
|
| 363 |
TmpDbl2,
|
| 364 |
R1, R2,
|
| 365 |
R3, R4 {R1 - R4}
|
| 366 |
: Double;
|
| 367 |
|
| 368 |
begin
|
| 369 |
AJD := DateTimeToAJD(AJD);
|
| 370 |
DateDif := AJD - 2451545.0;
|
| 371 |
ArgJup := 172.74 + (0.00111588 * DateDif);
|
| 372 |
ArgJup := Frac(ArgJup/360.0) * 360.0;
|
| 373 |
if (ArgJup < 0) then
|
| 374 |
ArgJup := 360.0 + ArgJup;
|
| 375 |
ArgJup := ArgJup / radcor;
|
| 376 |
|
| 377 |
AnomE := 357.529 + (0.9856003 * DateDif);
|
| 378 |
AnomE := Frac(AnomE/360.0) * 360.0;
|
| 379 |
if (AnomE < 0) then
|
| 380 |
AnomE := 360.0 + AnomE;
|
| 381 |
AnomE := AnomE / radcor;
|
| 382 |
|
| 383 |
AnomJ := 20.020 + (0.0830853 * DateDif + (0.329 * sin(ArgJup)));
|
| 384 |
AnomJ := Frac(AnomJ/360.0) * 360.0;
|
| 385 |
if (AnomJ < 0) then
|
| 386 |
AnomJ := 360.0 + AnomJ;
|
| 387 |
AnomJ := AnomJ / radcor;
|
| 388 |
|
| 389 |
DeltaLong := 66.115 + (0.9025179 * DateDif - (0.329 * sin(ArgJup)));
|
| 390 |
DeltaLong := Frac(DeltaLong/360.0) * 360.0;
|
| 391 |
if (DeltaLong < 0) then
|
| 392 |
DeltaLong := 360.0 + DeltaLong;
|
| 393 |
DeltaLong := DeltaLong / radcor;
|
| 394 |
|
| 395 |
ECenterE := 1.915 * sin(AnomE) + 0.020 * sin(2*AnomE);
|
| 396 |
ECenterE := ECenterE / radcor;
|
| 397 |
|
| 398 |
ECenterJ := 5.555 * sin(AnomJ) + 0.168 * sin(2*AnomJ);
|
| 399 |
ECenterJ := ECenterJ / radcor;
|
| 400 |
|
| 401 |
K := (DeltaLong + ECenterE - ECenterJ);
|
| 402 |
|
| 403 |
RVE := 1.00014 - (0.01671 * cos(AnomE)) - (0.00014 * cos(2*AnomE));
|
| 404 |
RVJ := 5.20872 - (0.25208 * cos(AnomJ)) - (0.00611 * cos(2*AnomJ));
|
| 405 |
|
| 406 |
EJDist := sqrt(sqr(RVJ) + sqr(RVE) - (2 * RVJ * RVE * cos(K)));
|
| 407 |
|
| 408 |
Phase := RVE/EJDist * sin(K);
|
| 409 |
Phase := StInvSin(Phase);
|
| 410 |
|
| 411 |
if ((sin(K) < 0) and (Phase > 0)) or
|
| 412 |
((sin(K) > 0) and (Phase < 0)) then
|
| 413 |
Phase := -Phase;
|
| 414 |
|
| 415 |
Lambda := 34.35 + (0.083091 * DateDif) + (0.329 * sin(ArgJup));
|
| 416 |
Lambda := Lambda / radcor + ECenterJ;
|
| 417 |
|
| 418 |
DS := 3.12 * sin(Lambda + 42.8 / radcor);
|
| 419 |
DE := DS - 2.22 * sin(Phase) * cos(Lambda + 22/radcor)
|
| 420 |
- 1.30 * ((RVJ - EJDist) / EJDist) * sin(Lambda - 100.5/radcor);
|
| 421 |
DE := DE / radcor;
|
| 422 |
|
| 423 |
Mu1 := 163.8067 + 203.4058643 * (DateDif - (EJDist / 173));
|
| 424 |
Mu1 := Frac(Mu1/360.0) * 360.0;
|
| 425 |
if (Mu1 < 0) then
|
| 426 |
Mu1 := 360.0 + Mu1;
|
| 427 |
Mu1 := Mu1 / radcor + Phase - ECenterJ;
|
| 428 |
|
| 429 |
Mu2 := 358.4108 + 101.2916334 * (DateDif - (EJDist / 173));
|
| 430 |
Mu2 := Frac(Mu2/360.0) * 360.0;
|
| 431 |
if (Mu2 < 0) then
|
| 432 |
Mu2 := 360.0 + Mu2;
|
| 433 |
Mu2 := Mu2 / radcor + Phase - ECenterJ;
|
| 434 |
|
| 435 |
Mu3 := 5.7129 + 50.2345179 * (DateDif - (EJDist / 173));
|
| 436 |
Mu3 := Frac(Mu3/360.0) * 360.0;
|
| 437 |
if (Mu3 < 0) then
|
| 438 |
Mu3 := 360.0 + Mu3;
|
| 439 |
Mu3 := Mu3 / radcor + Phase - ECenterJ;
|
| 440 |
|
| 441 |
Mu4 := 224.8151 + 21.4879801 * (DateDif - (EJDist / 173));
|
| 442 |
Mu4 := Frac(Mu4/360.0) * 360.0;
|
| 443 |
if (Mu4 < 0) then
|
| 444 |
Mu4 := 360.0 + Mu4;
|
| 445 |
Mu4 := Mu4 / radcor + Phase - ECenterJ;
|
| 446 |
|
| 447 |
G := 331.18 + 50.310482 * (DateDif - (EJDist / 173));
|
| 448 |
G := Frac(G/360.0) * 360.0;
|
| 449 |
if (G < 0) then
|
| 450 |
G := 360.0 + G;
|
| 451 |
G := G / radcor;
|
| 452 |
H := 87.40 + 21.569231 * (DateDif - (EJDist / 173));
|
| 453 |
H := Frac(H/360.0) * 360.0;
|
| 454 |
if (H < 0) then
|
| 455 |
H := 360.0 + H;
|
| 456 |
H := H / radcor;
|
| 457 |
|
| 458 |
TmpDbl1 := 0.473 * sin(2 * (Mu1 - Mu2)) / radcor;
|
| 459 |
TmpDbl2 := 1.065 * sin(2 * (Mu2 - Mu3)) / radcor;
|
| 460 |
|
| 461 |
R1 := 5.9073 - 0.0244 * cos(2 * (Mu1 - Mu2));
|
| 462 |
R2 := 9.3991 - 0.0882 * cos(2 * (Mu2 - Mu3));
|
| 463 |
R3 := 14.9924 - 0.0216 * cos(G);
|
| 464 |
R4 := 26.3699 - 0.1935 * cos(H);
|
| 465 |
|
| 466 |
Mu1 := Mu1 + TmpDbl1;
|
| 467 |
Mu2 := Mu2 + TmpDbl2;
|
| 468 |
Mu3 := Mu3 + (0.165 * sin(G)) / radcor;
|
| 469 |
Mu4 := Mu4 + (0.841 * sin(H)) / radcor;
|
| 470 |
|
| 471 |
Result.Io.X := R1 * sin(Mu1);
|
| 472 |
Result.Io.Y := -R1 * cos(Mu1) * sin(DE);
|
| 473 |
|
| 474 |
Result.Europa.X := R2 * sin(Mu2);
|
| 475 |
Result.Europa.Y := -R2 * cos(Mu2) * sin(DE);
|
| 476 |
|
| 477 |
Result.Ganymede.X := R3 * sin(Mu3);
|
| 478 |
Result.Ganymede.Y := -R3 * cos(Mu3) * sin(DE);
|
| 479 |
|
| 480 |
Result.Callisto.X := R4 * sin(Mu4);
|
| 481 |
Result.Callisto.Y := -R4 * cos(Mu4) * sin(DE);
|
| 482 |
end;
|
| 483 |
|
| 484 |
{-------------------------------------------------------------------------}
|
| 485 |
|
| 486 |
function JupSatsHi(AJD : Double; Shadows : Boolean) : TStJupSats;
|
| 487 |
var
|
| 488 |
I : longint;
|
| 489 |
SunPos : SunCoordsRec;
|
| 490 |
STUT : TStDateTimeRec;
|
| 491 |
JupPos : TStEclipticalCord;
|
| 492 |
|
| 493 |
SatX : array[1..5] of Double;
|
| 494 |
SatY : array[1..5] of Double;
|
| 495 |
SatZ : array[1..5] of Double;
|
| 496 |
|
| 497 |
TD1,
|
| 498 |
TD2,
|
| 499 |
Angle, {Temporary Double values}
|
| 500 |
LTime, {Tau}
|
| 501 |
AJDT, {AJD adjusted for light time (Tau)}
|
| 502 |
JupX,
|
| 503 |
JupY,
|
| 504 |
JupZ, {Jupiter's geocentric rectangular coordinates}
|
| 505 |
EJDist, {Delta}
|
| 506 |
Jup1,
|
| 507 |
Jup2, {/\, Alpha}
|
| 508 |
DateDif, {t}
|
| 509 |
L1, L2,
|
| 510 |
L3, L4, {script L1-4}
|
| 511 |
Pi1, Pi2,
|
| 512 |
Pi3, Pi4, {Pi1-4}
|
| 513 |
W1, W2,
|
| 514 |
W3, W4, {Omega1-4}
|
| 515 |
Inequality, {upside down L}
|
| 516 |
PhiLambda,
|
| 517 |
NodeJup, {Psi}
|
| 518 |
AnomJup, {G}
|
| 519 |
AnomSat, {G'}
|
| 520 |
LongPerJ,
|
| 521 |
S1, S2,
|
| 522 |
S3, S4, {Sum1-4}
|
| 523 |
TL1, TL2,
|
| 524 |
TL3, TL4, {Capital L1-4}
|
| 525 |
B1, B2,
|
| 526 |
B3, B4, {tangent of latitude}
|
| 527 |
R1, R2,
|
| 528 |
R3, R4, {radius vector}
|
| 529 |
T0, {Julian Centuries}
|
| 530 |
Precession, {P}
|
| 531 |
Inclination {I}
|
| 532 |
|
| 533 |
: Double;
|
| 534 |
Transforms : array[1..5] of TranformRec;
|
| 535 |
|
| 536 |
begin
|
| 537 |
FillChar(Result, SizeOf(TStJupSats), #0);
|
| 538 |
AJD := DateTimeToAJD(AJD);
|
| 539 |
SunPos := SunCoords(AJD);
|
| 540 |
|
| 541 |
if not Shadows then begin
|
| 542 |
TD1 := 5;
|
| 543 |
AJDT := AJD - 0.0057755183 * TD1; {first guess}
|
| 544 |
repeat
|
| 545 |
JupPos := ComputeJupiter(AJDT);
|
| 546 |
|
| 547 |
JupX := JupPos.R0 * cos(JupPos.B0) * cos(JupPos.L0)
|
| 548 |
+ SunPos.R * cos(SunPos.L);
|
| 549 |
JupY := JupPos.R0 * cos(JupPos.B0) * sin(JupPos.L0)
|
| 550 |
+ SunPos.R * sin(SunPos.L);
|
| 551 |
JupZ := JupPos.R0 * sin(JupPos.B0);
|
| 552 |
|
| 553 |
EJDist := sqrt(sqr(JupX) + sqr(JupY) + sqr(JupZ));
|
| 554 |
TD2 := abs(EJDist - TD1);
|
| 555 |
if abs(TD2) > 0.0005 then begin
|
| 556 |
AJDT := AJD - 0.0057755183 * ((EJDist + TD1) / 2);
|
| 557 |
TD1 := EJDist;
|
| 558 |
end;
|
| 559 |
until (TD2 <= 0.0005);
|
| 560 |
end else begin
|
| 561 |
JupPos := ComputeJupiter(AJD);
|
| 562 |
|
| 563 |
JupX := JupPos.R0 * cos(JupPos.B0) * cos(JupPos.L0);
|
| 564 |
JupY := JupPos.R0 * cos(JupPos.B0) * sin(JupPos.L0);
|
| 565 |
JupZ := JupPos.R0 * sin(JupPos.B0);
|
| 566 |
EJDist := sqrt(sqr(JupX+SunPos.X) +
|
| 567 |
sqr(JupY+SunPos.Y) + sqr(JupZ+SunPos.Z));
|
| 568 |
end;
|
| 569 |
|
| 570 |
Jup1 := StInvTan2(JupX, JupY);
|
| 571 |
Jup2 := ArcTan(JupZ / sqrt(sqr(JupX) + sqr(JupY)));
|
| 572 |
|
| 573 |
DateDif := AJD - 2443000.5 - (0.0057755183 * EJDist);
|
| 574 |
|
| 575 |
L1 := 106.07947 + 203.488955432 * DateDif;
|
| 576 |
L1 := Frac(L1/360.0) * 360.0;
|
| 577 |
if (L1 < 0) then
|
| 578 |
L1 := 360.0 + L1;
|
| 579 |
L1 := L1 / radcor;
|
| 580 |
|
| 581 |
L2 := 175.72938 + 101.374724550 * DateDif;
|
| 582 |
L2 := Frac(L2/360.0) * 360.0;
|
| 583 |
if (L2 < 0) then
|
| 584 |
L2 := 360.0 + L2;
|
| 585 |
L2 := L2 / radcor;
|
| 586 |
|
| 587 |
L3 := 120.55434 + 50.317609110 * DateDif;
|
| 588 |
L3 := Frac(L3/360.0) * 360.0;
|
| 589 |
if (L3 < 0) then
|
| 590 |
L3 := 360.0 + L3;
|
| 591 |
L3 := L3 / radcor;
|
| 592 |
|
| 593 |
L4 := 84.44868 + 21.571071314 * DateDif;
|
| 594 |
L4 := Frac(L4/360.0) * 360.0;
|
| 595 |
if (L4 < 0) then
|
| 596 |
L4 := 360.0 + L4;
|
| 597 |
L4 := L4 / radcor;
|
| 598 |
|
| 599 |
Pi1 := 58.3329 + 0.16103936 * DateDif;
|
| 600 |
Pi1 := Frac(Pi1/360.0) * 360.0;
|
| 601 |
if (Pi1 < 0) then
|
| 602 |
Pi1 := 360.0 + Pi1;
|
| 603 |
Pi1 := Pi1 / radcor;
|
| 604 |
|
| 605 |
Pi2 := 132.8959 + 0.04647985 * DateDif;
|
| 606 |
Pi2 := Frac(Pi2/360.0) * 360.0;
|
| 607 |
if (Pi2 < 0) then
|
| 608 |
Pi2 := 360.0 + Pi2;
|
| 609 |
Pi2 := Pi2 / radcor;
|
| 610 |
|
| 611 |
Pi3 := 187.2887 + 0.00712740 * DateDif;
|
| 612 |
Pi3 := Frac(Pi3/360.0) * 360.0;
|
| 613 |
if (Pi3 < 0) then
|
| 614 |
Pi3 := 360.0 + Pi3;
|
| 615 |
Pi3 := Pi3 / radcor;
|
| 616 |
|
| 617 |
Pi4 := 335.3418 + 0.00183998 * DateDif;
|
| 618 |
Pi4 := Frac(Pi4/360.0) * 360.0;
|
| 619 |
if (Pi4 < 0) then
|
| 620 |
Pi4 := 360.0 + Pi4;
|
| 621 |
Pi4 := Pi4 / radcor;
|
| 622 |
|
| 623 |
W1 := 311.0793 - 0.13279430 * DateDif;
|
| 624 |
W1 := Frac(W1/360.0) * 360.0;
|
| 625 |
if (W1 < 0) then
|
| 626 |
W1 := 360.0 + W1;
|
| 627 |
W1 := W1 / radcor;
|
| 628 |
|
| 629 |
W2 := 100.5099 - 0.03263047 * DateDif;
|
| 630 |
W2 := Frac(W2/360.0) * 360.0;
|
| 631 |
if (W2 < 0) then
|
| 632 |
W2 := 360.0 + W2;
|
| 633 |
W2 := W2 / radcor;
|
| 634 |
|
| 635 |
W3 := 119.1688 - 0.00717704 * DateDif;
|
| 636 |
W3 := Frac(W3/360.0) * 360.0;
|
| 637 |
if (W3 < 0) then
|
| 638 |
W3 := 360.0 + W3;
|
| 639 |
W3 := W3 / radcor;
|
| 640 |
|
| 641 |
W4 := 322.5729 - 0.00175934 * DateDif;
|
| 642 |
W4 := Frac(W4/360.0) * 360.0;
|
| 643 |
if (W4 < 0) then
|
| 644 |
W4 := 360.0 + W4;
|
| 645 |
W4 := W4 / radcor;
|
| 646 |
|
| 647 |
Inequality := 0.33033 * sin((163.679 + 0.0010512*DateDif) / radcor)
|
| 648 |
+ 0.03439 * sin((34.486 - 0.0161731*DateDif) / radcor);
|
| 649 |
Inequality := Inequality / radcor;
|
| 650 |
|
| 651 |
PhiLambda := 191.8132 + 0.17390023 * DateDif;
|
| 652 |
PhiLambda := Frac(PhiLambda / 360.0) * 360.0;
|
| 653 |
if (PhiLambda < 0) then
|
| 654 |
PhiLambda := 360.0 + PhiLambda;
|
| 655 |
PhiLambda := PhiLambda / radcor;
|
| 656 |
|
| 657 |
NodeJup := 316.5182 - 0.00000208 * DateDif;
|
| 658 |
NodeJup := Frac(NodeJup / 360.0) * 360.0;
|
| 659 |
if (NodeJup < 0) then
|
| 660 |
NodeJup := 360.0 + NodeJup;
|
| 661 |
NodeJup := NodeJup / radcor;
|
| 662 |
|
| 663 |
AnomJup := 30.23756 + 0.0830925701 * DateDif;
|
| 664 |
AnomJup := Frac(AnomJup / 360.0) * 360.0;
|
| 665 |
if (AnomJup < 0) then
|
| 666 |
AnomJup := 360.0 + AnomJup;
|
| 667 |
AnomJup := AnomJup / radcor + Inequality;
|
| 668 |
|
| 669 |
AnomSat := 31.97853 + 0.0334597339 * DateDif;
|
| 670 |
AnomSat := Frac(AnomSat / 360.0) * 360.0;
|
| 671 |
if (AnomSat < 0) then
|
| 672 |
AnomSat := 360.0 + AnomSat;
|
| 673 |
AnomSat := AnomSat / radcor;
|
| 674 |
|
| 675 |
LongPerJ := 13.469942 / radcor;
|
| 676 |
|
| 677 |
S1 := 0.47259 * sin(2*(L1-L2))
|
| 678 |
- 0.03480 * sin(Pi3-Pi4)
|
| 679 |
- 0.01756 * sin(Pi1 + Pi3 - 2*LongPerJ - 2*AnomJup)
|
| 680 |
+ 0.01080 * sin(L2 - 2*L3 + Pi3)
|
| 681 |
+ 0.00757 * sin(PhiLambda)
|
| 682 |
+ 0.00663 * sin(L2 - 2*L3 + Pi4)
|
| 683 |
+ 0.00453 * sin(L1 - Pi3)
|
| 684 |
+ 0.00453 * sin(L2 - 2*L3 + Pi2)
|
| 685 |
- 0.00354 * sin(L1-L2)
|
| 686 |
- 0.00317 * sin(2*NodeJup - 2*LongPerJ)
|
| 687 |
- 0.00269 * sin(L2 - 2*L3 + Pi1)
|
| 688 |
+ 0.00263 * sin(L1 - Pi4)
|
| 689 |
+ 0.00186 * sin(L1 - Pi1)
|
| 690 |
- 0.00186 * sin(AnomJup)
|
| 691 |
+ 0.00167 * sin(Pi2 - Pi3)
|
| 692 |
+ 0.00158 * sin(4*(L1-L2))
|
| 693 |
- 0.00155 * sin(L1 - L3)
|
| 694 |
- 0.00142 * sin(NodeJup + W3 - 2*LongPerJ - 2*AnomJup)
|
| 695 |
- 0.00115 * sin(2*(L1 - 2*L2 + W2))
|
| 696 |
+ 0.00089 * sin(Pi2 - Pi4)
|
| 697 |
+ 0.00084 * sin(W2 - W3)
|
| 698 |
+ 0.00084 * sin(L1 + Pi3 - 2*LongPerJ - 2*AnomJup)
|
| 699 |
+ 0.00053 * sin(NodeJup - W2);
|
| 700 |
|
| 701 |
S2 := 1.06476 * sin(2*(L2-L3))
|
| 702 |
+ 0.04253 * sin(L1 - 2*L2 + Pi3)
|
| 703 |
+ 0.03579 * sin(L2 - Pi3)
|
| 704 |
+ 0.02383 * sin(L1 - 2*L2 + Pi4)
|
| 705 |
+ 0.01977 * sin(L2 - Pi4)
|
| 706 |
- 0.01843 * sin(PhiLambda)
|
| 707 |
+ 0.01299 * sin(Pi3 - Pi4)
|
| 708 |
- 0.01142 * sin(L2 - L3)
|
| 709 |
+ 0.01078 * sin(L2 - Pi2)
|
| 710 |
- 0.01058 * sin(AnomJup)
|
| 711 |
+ 0.00870 * sin(L2 - 2*L3 + Pi2)
|
| 712 |
- 0.00775 * sin(2*(NodeJup - LongPerJ))
|
| 713 |
+ 0.00524 * sin(2*(L1-L2))
|
| 714 |
- 0.00460 * sin(L1-L3)
|
| 715 |
+ 0.00450 * sin(L2 - 2*L3 + Pi1)
|
| 716 |
+ 0.00327 * sin(NodeJup - 2*AnomJup + W3 - 2*LongPerJ)
|
| 717 |
- 0.00296 * sin(Pi1 + Pi3 - 2*LongPerJ - 2*AnomJup)
|
| 718 |
- 0.00151 * sin(2*AnomJup)
|
| 719 |
+ 0.00146 * sin(NodeJup - W3)
|
| 720 |
+ 0.00125 * sin(NodeJup - W4)
|
| 721 |
- 0.00117 * sin(L1 -2*L3 + Pi3)
|
| 722 |
- 0.00095 * sin(2*(L2-W2))
|
| 723 |
+ 0.00086 * sin(2*(L1-2*L2 +W2))
|
| 724 |
- 0.00086 * sin(5*AnomSat - 2*AnomJup + 52.225/radcor)
|
| 725 |
- 0.00078 * sin(L2-L4)
|
| 726 |
- 0.00064 * sin(L1 - 2*L3 + Pi4)
|
| 727 |
- 0.00063 * sin(3*L3 - 7*L4 + 4*Pi4)
|
| 728 |
+ 0.00061 * sin(Pi1 - Pi4)
|
| 729 |
+ 0.00058 * sin(2*(NodeJup - LongPerJ - AnomJup))
|
| 730 |
+ 0.00058 * sin(W3 - W4)
|
| 731 |
+ 0.00056 * sin(2*(L2-L4))
|
| 732 |
+ 0.00055 * sin(2*(L1-L3))
|
| 733 |
+ 0.00052 * sin(3*L3 - 7*L4 + Pi3 + 3*Pi4)
|
| 734 |
- 0.00043 * sin(L1 - Pi3)
|
| 735 |
+ 0.00042 * sin(Pi3 - Pi2)
|
| 736 |
+ 0.00041 * sin(5*(L2-L3))
|
| 737 |
+ 0.00041 * sin(Pi4 - LongPerJ)
|
| 738 |
+ 0.00038 * sin(L2 - Pi1)
|
| 739 |
+ 0.00032 * sin(W2 - W3)
|
| 740 |
+ 0.00032 * sin(2*(L3 - AnomJup - LongPerJ))
|
| 741 |
+ 0.00029 * sin(Pi1 - Pi3);
|
| 742 |
|
| 743 |
S3 := 0.16477 * sin(L3 - Pi3)
|
| 744 |
+ 0.09062 * sin(L3 - Pi4)
|
| 745 |
- 0.06907 * sin(L2 - L3)
|
| 746 |
+ 0.03786 * sin(Pi3 - Pi4)
|
| 747 |
+ 0.01844 * sin(2*(L3-L4))
|
| 748 |
- 0.01340 * sin(AnomJup)
|
| 749 |
+ 0.00703 * sin(L2 - 2*L3 + Pi3)
|
| 750 |
- 0.00670 * sin(2*(NodeJup - LongPerJ))
|
| 751 |
- 0.00540 * sin(L3-L4)
|
| 752 |
+ 0.00481 * sin(Pi1 + Pi3 -2*LongPerJ - 2*AnomJup)
|
| 753 |
- 0.00409 * sin(L2 - 2*L3 + Pi2)
|
| 754 |
+ 0.00379 * sin(L2 - 2*L3 + Pi4)
|
| 755 |
+ 0.00235 * sin(NodeJup - W3)
|
| 756 |
+ 0.00198 * sin(NodeJup - W4)
|
| 757 |
+ 0.00180 * sin(PhiLambda)
|
| 758 |
+ 0.00129 * sin(3*(L3-L4))
|
| 759 |
+ 0.00124 * sin(L1-L3)
|
| 760 |
- 0.00119 * sin(5*AnomSat - 2*AnomJup + 52.225/radcor)
|
| 761 |
+ 0.00109 * sin(L1-L2)
|
| 762 |
- 0.00099 * sin(3*L3 - 7*L4 + 4*Pi4)
|
| 763 |
+ 0.00091 * sin(W3 - W4)
|
| 764 |
+ 0.00081 * sin(3*L3 - 7*L4 + Pi3 + 3*Pi4)
|
| 765 |
- 0.00076 * sin(2*L2 - 3*L3 + Pi3)
|
| 766 |
+ 0.00069 * sin(Pi4 - LongPerJ)
|
| 767 |
- 0.00058 * sin(2*L3 - 3*L4 + Pi4)
|
| 768 |
+ 0.00057 * sin(L3 + Pi3 - 2*LongPerJ - 2*AnomJup)
|
| 769 |
- 0.00057 * sin(L3 - 2*L4 + Pi4)
|
| 770 |
- 0.00052 * sin(Pi2 - Pi3)
|
| 771 |
- 0.00052 * sin(L2 - 2*L3 + Pi1)
|
| 772 |
+ 0.00048 * sin(L3 - 2*L4 + Pi3)
|
| 773 |
- 0.00045 * sin(2*L2 - 3*L3 + Pi4)
|
| 774 |
- 0.00041 * sin(Pi2 - Pi4)
|
| 775 |
- 0.00038 * sin(2*AnomJup)
|
| 776 |
- 0.00033 * sin(Pi3 - Pi4 + W3 - W4)
|
| 777 |
- 0.00032 * sin(3*L3 - 7*L4 + 2*Pi3 + 2*Pi4)
|
| 778 |
+ 0.00030 * sin(4*(L3-L4))
|
| 779 |
- 0.00029 * sin(W3 + NodeJup - 2*LongPerJ - 2*AnomJup)
|
| 780 |
+ 0.00029 * sin(L3 + Pi4 - 2*LongPerJ - 2*AnomJup)
|
| 781 |
+ 0.00026 * sin(L3 - LongPerJ - AnomJup)
|
| 782 |
+ 0.00024 * sin(L2 - 3*L3 + 2*L4)
|
| 783 |
+ 0.00021 * sin(2*(L3 - LongPerJ - AnomJup))
|
| 784 |
- 0.00021 * sin(L3 - Pi2)
|
| 785 |
+ 0.00017 * sin(2*(L3 - Pi3));
|
| 786 |
|
| 787 |
S4 := 0.84109 * sin(L4 - Pi4)
|
| 788 |
+ 0.03429 * sin(Pi4 - Pi3)
|
| 789 |
- 0.03305 * sin(2*(NodeJup - LongPerJ))
|
| 790 |
- 0.03211 * sin(AnomJup)
|
| 791 |
- 0.01860 * sin(L4 - Pi3)
|
| 792 |
+ 0.01182 * sin(NodeJup - W4)
|
| 793 |
+ 0.00622 * sin(L4 + Pi4 - 2*AnomJup - 2*LongPerJ)
|
| 794 |
+ 0.00385 * sin(2*(L4 - Pi4))
|
| 795 |
- 0.00284 * sin(5*AnomSat - 2*AnomJup + 52.225/radcor)
|
| 796 |
- 0.00233 * sin(2*(NodeJup - Pi4))
|
| 797 |
- 0.00223 * sin(L3 - L4)
|
| 798 |
- 0.00208 * sin(L4 - LongPerJ)
|
| 799 |
+ 0.00177 * sin(NodeJup + W4 - 2*Pi4)
|
| 800 |
+ 0.00134 * sin(Pi4 - LongPerJ)
|
| 801 |
+ 0.00125 * sin(2*(L4 - AnomJup - LongPerJ))
|
| 802 |
- 0.00117 * sin(2*AnomJup)
|
| 803 |
- 0.00112 * sin(2*(L3 - L4))
|
| 804 |
+ 0.00106 * sin(3*L3 - 7*L4 + 4*Pi4)
|
| 805 |
+ 0.00102 * sin(L4 - AnomJup - LongPerJ)
|
| 806 |
+ 0.00096 * sin(2*L4 - NodeJup - W4)
|
| 807 |
+ 0.00087 * sin(2*(NodeJup - W4))
|
| 808 |
- 0.00087 * sin(3*L3 - 7*L4 + Pi3 + 3*Pi4)
|
| 809 |
+ 0.00085 * sin(L3 - 2*L4 + Pi4)
|
| 810 |
- 0.00081 * sin(2*(L4 - NodeJup))
|
| 811 |
+ 0.00071 * sin(L4 + Pi4 -2*LongPerJ - 3*AnomJup)
|
| 812 |
+ 0.00060 * sin(L1 - L4)
|
| 813 |
- 0.00056 * sin(NodeJup - W3)
|
| 814 |
- 0.00055 * sin(L3 - 2*L4 + Pi3)
|
| 815 |
+ 0.00051 * sin(L2 - L4)
|
| 816 |
+ 0.00042 * sin(2*(NodeJup - AnomJup - LongPerJ))
|
| 817 |
+ 0.00039 * sin(2*(Pi4 - W4))
|
| 818 |
+ 0.00036 * sin(NodeJup + LongPerJ - Pi4 - W4)
|
| 819 |
+ 0.00035 * sin(2*AnomSat - AnomJup + 188.37/radcor)
|
| 820 |
- 0.00035 * sin(L4 - Pi4 + 2*LongPerJ - 2*NodeJup)
|
| 821 |
- 0.00032 * sin(L4 + Pi4 - 2*LongPerJ - AnomJup)
|
| 822 |
+ 0.00030 * sin(3*L3 - 7*L4 + 2*Pi3 + 2*Pi4)
|
| 823 |
+ 0.00030 * sin(2*AnomSat - 2*AnomJup + 149.15/radcor)
|
| 824 |
+ 0.00028 * sin(L4 - Pi4 + 2*NodeJup - 2*LongPerJ)
|
| 825 |
- 0.00028 * sin(2*(L4 - W4))
|
| 826 |
- 0.00027 * sin(Pi3 - Pi4 + W3 - W4)
|
| 827 |
- 0.00026 * sin(5*AnomSat - 3*AnomJup + 188.37/radcor)
|
| 828 |
+ 0.00025 * sin(W4 - W3)
|
| 829 |
- 0.00025 * sin(L2 - 3*L3 + 2*L4)
|
| 830 |
- 0.00023 * sin(3*(L3 - L4))
|
| 831 |
+ 0.00021 * sin(2*L4 - 2*LongPerJ - 3*AnomJup)
|
| 832 |
- 0.00021 * sin(2*L3 - 3*L4 + Pi4)
|
| 833 |
+ 0.00019 * sin(L4 - Pi4 - AnomJup)
|
| 834 |
- 0.00019 * sin(2*L4 - Pi3 - Pi4)
|
| 835 |
- 0.00018 * sin(L4 - Pi4 + AnomJup)
|
| 836 |
- 0.00016 * sin(L4 + Pi3 -2*LongPerJ - 2*AnomJup);
|
| 837 |
|
| 838 |
S1 := S1/radcor;
|
| 839 |
S2 := S2/radcor;
|
| 840 |
S3 := S3/radcor;
|
| 841 |
S4 := S4/radcor;
|
| 842 |
|
| 843 |
TL1 := L1 + S1;
|
| 844 |
TL2 := L2 + S2;
|
| 845 |
TL3 := L3 + S3;
|
| 846 |
TL4 := L4 + S4;
|
| 847 |
|
| 848 |
B1 := 0.0006502 * sin(TL1 - W1)
|
| 849 |
+ 0.0001835 * sin(TL1 - W2)
|
| 850 |
+ 0.0000329 * sin(TL1 - W3)
|
| 851 |
- 0.0000311 * sin(TL1 - NodeJup)
|
| 852 |
+ 0.0000093 * sin(TL1 - W4)
|
| 853 |
+ 0.0000075 * sin(3*TL1 - 4*L2 - 1.9927/radcor * S1 + W2)
|
| 854 |
+ 0.0000046 * sin(TL1 + NodeJup - 2*LongPerJ - 2*AnomJup);
|
| 855 |
B1 := ArcTan(B1);
|
| 856 |
|
| 857 |
B2 := 0.0081275 * sin(TL2 - W2)
|
| 858 |
+ 0.0004512 * sin(TL2 - W3)
|
| 859 |
- 0.0003286 * sin(TL2 - NodeJup)
|
| 860 |
+ 0.0001164 * sin(TL2 - W4)
|
| 861 |
+ 0.0000273 * sin(L1 - 2*L3 + 1.0146/radcor * S2 + W2)
|
| 862 |
+ 0.0000143 * sin(TL2 + NodeJup - 2*LongPerJ - 2*AnomJup)
|
| 863 |
- 0.0000143 * sin(TL2 - W1)
|
| 864 |
+ 0.0000035 * sin(TL2 - NodeJup + AnomJup)
|
| 865 |
- 0.0000028 * sin(L1 - 2*L3 + 1.0146/radcor * S2 + W3);
|
| 866 |
B2 := ArcTan(B2);
|
| 867 |
|
| 868 |
B3 := 0.0032364 * sin(TL3 - W3)
|
| 869 |
- 0.0016911 * sin(TL3 - NodeJup)
|
| 870 |
+ 0.0006849 * sin(TL3 - W4)
|
| 871 |
- 0.0002806 * sin(TL3 - W2)
|
| 872 |
+ 0.0000321 * sin(TL3 + NodeJup - 2*LongPerJ - 2*AnomJup)
|
| 873 |
+ 0.0000051 * sin(TL3 - NodeJup + AnomJup)
|
| 874 |
- 0.0000045 * sin(TL3 - NodeJup - AnomJup)
|
| 875 |
- 0.0000045 * sin(TL3 + NodeJup - 2*LongPerJ)
|
| 876 |
+ 0.0000037 * sin(TL3 + NodeJup - 2*LongPerJ - 3*AnomJup)
|
| 877 |
+ 0.0000030 * sin(2*L2 - 3*TL3 + 4.03/radcor * S3 + W2)
|
| 878 |
- 0.0000021 * sin(2*L2 - 3*TL3 + 4.03/radcor * S3 + W3);
|
| 879 |
B3 := ArcTan(B3);
|
| 880 |
|
| 881 |
B4 := -0.0076579 * sin(TL4 - NodeJup)
|
| 882 |
+ 0.0044148 * sin(TL4 - W4)
|
| 883 |
- 0.0005106 * sin(TL4 - W3)
|
| 884 |
+ 0.0000773 * sin(TL4 + NodeJup - 2*LongPerJ - 2*AnomJup)
|
| 885 |
+ 0.0000104 * sin(TL4 - NodeJup + AnomJup)
|
| 886 |
- 0.0000102 * sin(TL4 - NodeJup - AnomJup)
|
| 887 |
+ 0.0000088 * sin(TL4 + NodeJup - 2*LongPerJ - 3*AnomJup)
|
| 888 |
- 0.0000038 * sin(TL4 + NodeJup - 2*LongPerJ - AnomJup);
|
| 889 |
B4 := ArcTan(B4);
|
| 890 |
|
| 891 |
R1 := -0.0041339 * cos(2*(L1-L2))
|
| 892 |
- 0.0000395 * cos(L1 - Pi3)
|
| 893 |
- 0.0000214 * cos(L1 - Pi4)
|
| 894 |
+ 0.0000170 * cos(L1 - L2)
|
| 895 |
- 0.0000162 * cos(L1 - Pi1)
|
| 896 |
- 0.0000130 * cos(4*(L1-L2))
|
| 897 |
+ 0.0000106 * cos(L1 - L3)
|
| 898 |
- 0.0000063 * cos(L1 + Pi3 - 2*LongPerJ - 2*AnomJup);
|
| 899 |
|
| 900 |
R2 := 0.0093847 * cos(L1-L2)
|
| 901 |
- 0.0003114 * cos(L2 - Pi3)
|
| 902 |
- 0.0001738 * cos(L2 - Pi4)
|
| 903 |
- 0.0000941 * cos(L2 - Pi2)
|
| 904 |
+ 0.0000553 * cos(L2 - L3)
|
| 905 |
+ 0.0000523 * cos(L1 - L3)
|
| 906 |
- 0.0000290 * cos(2*(L1-L2))
|
| 907 |
+ 0.0000166 * cos(2*(L2-W2))
|
| 908 |
+ 0.0000107 * cos(L1 - 2*L3 + Pi3)
|
| 909 |
- 0.0000102 * cos(L2 - Pi1)
|
| 910 |
- 0.0000091 * cos(2*(L1-L3));
|
| 911 |
|
| 912 |
R3 := -0.0014377 * cos(L3 - Pi3)
|
| 913 |
- 0.0007904 * cos(L3 - Pi4)
|
| 914 |
+ 0.0006342 * cos(L2 - L3)
|
| 915 |
- 0.0001758 * cos(2*(L3-L4))
|
| 916 |
+ 0.0000294 * cos(L3 - L4)
|
| 917 |
- 0.0000156 * cos(3*(L3-L4))
|
| 918 |
+ 0.0000155 * cos(L1 - L3)
|
| 919 |
- 0.0000153 * cos(L1 - L2)
|
| 920 |
+ 0.0000070 * cos(2*L2 - 3*L3 + Pi3)
|
| 921 |
- 0.0000051 * cos(L3 + Pi3 - 2*LongPerJ - 2*AnomJup);
|
| 922 |
|
| 923 |
R4 := -0.0073391 * cos(L4 - Pi4)
|
| 924 |
+ 0.0001620 * cos(L4 - Pi3)
|
| 925 |
+ 0.0000974 * cos(L3 - L4)
|
| 926 |
- 0.0000541 * cos(L4 + Pi4 - 2*LongPerJ - 2*AnomJup)
|
| 927 |
- 0.0000269 * cos(2*(L4-Pi4))
|
| 928 |
+ 0.0000182 * cos(L4- LongPerJ)
|
| 929 |
+ 0.0000177 * cos(2*(L3-L4))
|
| 930 |
- 0.0000167 * cos(2*L4 - NodeJup - W4)
|
| 931 |
+ 0.0000167 * cos(NodeJup - W4)
|
| 932 |
- 0.0000155 * cos(2*(L4-LongPerj-AnomJup))
|
| 933 |
+ 0.0000142 * cos(2*(L4-NodeJup))
|
| 934 |
+ 0.0000104 * cos(L1 - L4)
|
| 935 |
+ 0.0000092 * cos(L2 - L4)
|
| 936 |
- 0.0000089 * cos(L4 - LongPerJ - AnomJup)
|
| 937 |
- 0.0000062 * cos(L4 + Pi4 - 2*LongPerJ - 3*AnomJup)
|
| 938 |
+ 0.0000048 * cos(2*(L4-W4));
|
| 939 |
|
| 940 |
R1 := 5.90730 * (1 + R1);
|
| 941 |
R2 := 9.39912 * (1 + R2);
|
| 942 |
R3 := 14.99240 * (1 + R3);
|
| 943 |
R4 := 26.36990 * (1 + R4);
|
| 944 |
|
| 945 |
T0 := (AJD - 2433282.423) / 36525;
|
| 946 |
Precession := (1.3966626*T0 + 0.0003088*sqr(T0)) / radcor;
|
| 947 |
|
| 948 |
TL1 := TL1 + Precession;
|
| 949 |
TL2 := TL2 + Precession;
|
| 950 |
TL3 := TL3 + Precession;
|
| 951 |
TL4 := TL4 + Precession;
|
| 952 |
NodeJup := NodeJup + Precession;
|
| 953 |
|
| 954 |
T0 := (AJD - AstJulianDatePrim(1900, 1, 1, 0)) / 36525;
|
| 955 |
Inclination := (3.120262 + 0.0006*T0) / radcor;
|
| 956 |
|
| 957 |
SatX[1] := R1 * cos(TL1 - NodeJup) * cos(B1);
|
| 958 |
SatY[1] := R1 * sin(TL1 - NodeJup) * cos(B1);
|
| 959 |
SatZ[1] := R1 * sin(B1);
|
| 960 |
|
| 961 |
SatX[2] := R2 * cos(TL2 - NodeJup) * cos(B2);
|
| 962 |
SatY[2] := R2 * sin(TL2 - NodeJup) * cos(B2);
|
| 963 |
SatZ[2] := R2 * sin(B2);
|
| 964 |
|
| 965 |
SatX[3] := R3 * cos(TL3 - NodeJup) * cos(B3);
|
| 966 |
SatY[3] := R3 * sin(TL3 - NodeJup) * cos(B3);
|
| 967 |
SatZ[3] := R3 * sin(B3);
|
| 968 |
|
| 969 |
SatX[4] := R4 * cos(TL4 - NodeJup) * cos(B4);
|
| 970 |
SatY[4] := R4 * sin(TL4 - NodeJup) * cos(B4);
|
| 971 |
SatZ[4] := R4 * sin(B4);
|
| 972 |
|
| 973 |
SatX[5] := 0;
|
| 974 |
SatY[5] := 0;
|
| 975 |
SatZ[5] := 1;
|
| 976 |
|
| 977 |
T0 := (AJD - 2451545.0) / 36525.0;
|
| 978 |
TD1 := 100.464441
|
| 979 |
+ 1.0209550 * T0
|
| 980 |
+ 0.00040117 * sqr(T0)
|
| 981 |
+ 0.000000569 * sqr(T0) * T0;
|
| 982 |
TD1 := TD1 / radcor;
|
| 983 |
|
| 984 |
TD2 := 1.303270
|
| 985 |
- 0.0054966 * T0
|
| 986 |
+ 0.00000465 * sqr(T0)
|
| 987 |
- 0.000000004 * sqr(T0) * T0;
|
| 988 |
TD2 := TD2 / radcor;
|
| 989 |
|
| 990 |
for I := 1 to 5 do begin
|
| 991 |
Transforms[I].A[1] := SatX[I];
|
| 992 |
Transforms[I].B[1] := SatY[I] * cos(Inclination)
|
| 993 |
- SatZ[I] * sin(Inclination);
|
| 994 |
Transforms[I].C[1] := SatY[I] * sin(Inclination)
|
| 995 |
+ SatZ[I] * cos(Inclination);
|
| 996 |
|
| 997 |
Transforms[I].A[2] := Transforms[I].A[1] * cos(NodeJup - TD1)
|
| 998 |
- Transforms[I].B[1] * sin(NodeJup - TD1);
|
| 999 |
Transforms[I].B[2] := Transforms[I].A[1] * sin(NodeJup - TD1)
|
| 1000 |
+ Transforms[I].B[1] * cos(NodeJup - TD1);
|
| 1001 |
Transforms[I].C[2] := Transforms[I].C[1];
|
| 1002 |
|
| 1003 |
Transforms[I].A[3] := Transforms[I].A[2];
|
| 1004 |
Transforms[I].B[3] := Transforms[I].B[2] * cos(TD2)
|
| 1005 |
- Transforms[I].C[2] * sin(TD2);
|
| 1006 |
Transforms[I].C[3] := Transforms[I].B[2] * sin(TD2)
|
| 1007 |
+ Transforms[I].C[2] * cos(TD2);
|
| 1008 |
|
| 1009 |
Transforms[I].A[4] := Transforms[I].A[3] * cos(TD1)
|
| 1010 |
- Transforms[I].B[3] * sin(TD1);
|
| 1011 |
Transforms[I].B[4] := Transforms[I].A[3] * sin(TD1)
|
| 1012 |
+ Transforms[I].B[3] * cos(TD1);
|
| 1013 |
Transforms[I].C[4] := Transforms[I].C[3];
|
| 1014 |
|
| 1015 |
Transforms[I].A[5] := Transforms[I].A[4] * sin(Jup1)
|
| 1016 |
- Transforms[I].B[4] * cos(Jup1);
|
| 1017 |
Transforms[I].B[5] := Transforms[I].A[4] * cos(Jup1)
|
| 1018 |
+ Transforms[I].B[4] * sin(Jup1);
|
| 1019 |
Transforms[I].C[5] := Transforms[I].C[4];
|
| 1020 |
|
| 1021 |
Transforms[I].A[6] := Transforms[I].A[5];
|
| 1022 |
Transforms[I].B[6] := Transforms[I].C[5] * sin(Jup2)
|
| 1023 |
+ Transforms[I].B[5] * cos(Jup2);
|
| 1024 |
Transforms[I].C[6] := Transforms[I].C[5] * cos(Jup2)
|
| 1025 |
- Transforms[I].B[5] * sin(Jup2);
|
| 1026 |
end;
|
| 1027 |
|
| 1028 |
Angle := StInvTan2(Transforms[5].C[6], Transforms[5].A[6]);
|
| 1029 |
|
| 1030 |
{Io calculations}
|
| 1031 |
Result.Io.X := Transforms[1].A[6] * cos(Angle)
|
| 1032 |
- Transforms[1].C[6] * sin(Angle);
|
| 1033 |
Result.Io.Y := Transforms[1].A[6] * sin(Angle)
|
| 1034 |
+ Transforms[1].C[6] * cos(Angle);
|
| 1035 |
TD1 := Transforms[1].B[6];
|
| 1036 |
|
| 1037 |
{correct for light time}
|
| 1038 |
TD2 := abs(TD1) / 17295 * sqrt(1 - sqr(Result.Io.X/R1));
|
| 1039 |
Result.Io.X := Result.Io.X + TD2;
|
| 1040 |
|
| 1041 |
{correct for perspective}
|
| 1042 |
TD2 := EJDist / (EJDist + TD1/2095);
|
| 1043 |
Result.Io.X := Result.Io.X * TD2;
|
| 1044 |
Result.Io.Y := Result.Io.Y * TD2;
|
| 1045 |
|
| 1046 |
{Europa calculations}
|
| 1047 |
Result.Europa.X := Transforms[2].A[6] * cos(Angle)
|
| 1048 |
- Transforms[2].C[6] * sin(Angle);
|
| 1049 |
Result.Europa.Y := Transforms[2].A[6] * sin(Angle)
|
| 1050 |
+ Transforms[2].C[6] * cos(Angle);
|
| 1051 |
TD1 := Transforms[2].B[6];
|
| 1052 |
|
| 1053 |
{correct for light time}
|
| 1054 |
TD2 := abs(TD1) / 21819 * sqrt(1 - sqr(Result.Europa.X/R2));
|
| 1055 |
Result.Europa.X := Result.Europa.X + TD2;
|
| 1056 |
|
| 1057 |
{correct for perspective}
|
| 1058 |
TD2 := EJDist / (EJDist + TD1/2095);
|
| 1059 |
Result.Europa.X := Result.Europa.X * TD2;
|
| 1060 |
Result.Europa.Y := Result.Europa.Y * TD2;
|
| 1061 |
|
| 1062 |
{Ganymede calculations}
|
| 1063 |
Result.Ganymede.X := Transforms[3].A[6] * cos(Angle)
|
| 1064 |
- Transforms[3].C[6] * sin(Angle);
|
| 1065 |
Result.Ganymede.Y := Transforms[3].A[6] * sin(Angle)
|
| 1066 |
+ Transforms[3].C[6] * cos(Angle);
|
| 1067 |
TD1 := Transforms[3].B[6];
|
| 1068 |
|
| 1069 |
{correct for light time}
|
| 1070 |
TD2 := abs(TD1) / 27558 * sqrt(1 - sqr(Result.Ganymede.X/R3));
|
| 1071 |
Result.Ganymede.X := Result.Ganymede.X + TD2;
|
| 1072 |
|
| 1073 |
{correct for perspective}
|
| 1074 |
TD2 := EJDist / (EJDist + TD1/2095);
|
| 1075 |
Result.Ganymede.X := Result.Ganymede.X * TD2;
|
| 1076 |
Result.Ganymede.Y := Result.Ganymede.Y * TD2;
|
| 1077 |
|
| 1078 |
{Callisto calculations}
|
| 1079 |
Result.Callisto.X := Transforms[4].A[6] * cos(Angle)
|
| 1080 |
- Transforms[4].C[6] * sin(Angle);
|
| 1081 |
Result.Callisto.Y := Transforms[4].A[6] * sin(Angle)
|
| 1082 |
+ Transforms[4].C[6] * cos(Angle);
|
| 1083 |
TD1 := Transforms[4].B[6];
|
| 1084 |
|
| 1085 |
{correct for light time}
|
| 1086 |
TD2 := abs(TD1) / 36548 * sqrt(1 - sqr(Result.Callisto.X/R4));
|
| 1087 |
Result.Callisto.X := Result.Callisto.X + TD2;
|
| 1088 |
|
| 1089 |
{correct for perspective}
|
| 1090 |
TD2 := EJDist / (EJDist + TD1/2095);
|
| 1091 |
Result.Callisto.X := Result.Callisto.X * TD2;
|
| 1092 |
Result.Callisto.Y := Result.Callisto.Y * TD2;
|
| 1093 |
end;
|
| 1094 |
|
| 1095 |
{-------------------------------------------------------------------------}
|
| 1096 |
|
| 1097 |
function GetJupSats(JD : TDateTime; HighPrecision, Shadows : Boolean) : TStJupSats;
|
| 1098 |
begin
|
| 1099 |
if not HighPrecision then
|
| 1100 |
Result := JupSatsLo(JD)
|
| 1101 |
else
|
| 1102 |
Result := JupSatsHi(JD, Shadows);
|
| 1103 |
end;
|
| 1104 |
|
| 1105 |
end.
|
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