GLScene/AdvDemos/Earth/USolarSystem.pas

//
// The graphics rendering engine GLScene http://glscene.org
//
unit USolarSystem;

(*
  Solar system planetary elements and positions utility unit.
  Based on document by Paul Schlyter (Stockholm, Sweden)
  http://www.stjarnhimlen.se/comp/ppcomp.html
  Coordinates system takes Z as "up", ie. normal to the ecliptic plane,
  "axis" around which the planets turn.
*)
interface

uses
  System.SysUtils,
  System.Math,
  GLS.VectorGeometry;

type

  TOrbitalElements = record
    N: Double; // longitude of the ascending node
    i: Double; // inclination to the ecliptic (plane of the Earth's orbit)
    w: Double; // argument of perihelion
    a: Double; // semi-major axis, or mean distance from Sun
    e: Double; // eccentricity (0=circle, 0-1=ellipse, 1=parabola)
    M: Double; // mean anomaly (0 at perihelion; increases uniformly with time)
  end;

  TOrbitalElementsData = record
    NConst, NVar: Double; // longitude of the ascending node
    iConst, iVar: Double;
    // inclination to the ecliptic (plane of the Earth's orbit)
    wConst, wVar: Double; // argument of perihelion
    aConst, aVar: Double; // semi-major axis, or mean distance from Sun
    eConst, eVar: Double; // eccentricity (0=circle, 0-1=ellipse, 1=parabola)
    MConst, MVar: Double;
    // mean anomaly (0 at perihelion; increases uniformly with time)
  end;

const

  // geocentric sun elements (?)
  cSunOrbitalElements: TOrbitalElementsData = (NConst: 0.0; NVar: 0.0;
    iConst: 0.0; iVar: 0.0; wConst: 282.9404; wVar: 4.70935E-5;
    aConst: 1.000000; aVar: 0.0; // (AU)
    eConst: 0.016709; eVar: - 1.151E-9; MConst: 356.0470; MVar: 0.9856002585);

  // geocentric moon elements
  cMoonOrbitalElements: TOrbitalElementsData = (NConst: 125.1228;
    NVar: - 0.0529538083; iConst: 5.1454; iVar: 0.0; wConst: 318.0634;
    wVar: 0.1643573223; aConst: 60.2666; aVar: 0.0; // (Earth radii)
    eConst: 0.054900; eVar: 0.0; MConst: 115.3654; MVar: 13.0649929509);

  // heliocentric mercury elements
  cMercuryOrbitalElements: TOrbitalElementsData = (NConst: 48.3313;
    NVar: 3.24587E-5; iConst: 7.0047; iVar: 5.00E-8; wConst: 29.1241;
    wVar: 1.01444E-5; aConst: 0.387098; aVar: 0.0; // (AU)
    eConst: 0.205635; eVar: 5.59E-10; MConst: 168.6562; MVar: 4.0923344368);

  // heliocentric venus elements
  cVenusOrbitalElements: TOrbitalElementsData = (NConst: 76.6799;
    NVar: 2.46590E-5; iConst: 3.3946; iVar: 2.75E-8; wConst: 54.8910;
    wVar: 1.38374E-5; aConst: 0.723330; aVar: 0.0; // (AU)
    eConst: 0.006773; eVar: - 1.302E-9; MConst: 48.0052; MVar: 1.6021302244);

  // heliocentric mars elements
  cMarsOrbitalElements: TOrbitalElementsData = (NConst: 49.5574;
    NVar: 2.11081E-5; iConst: 1.8497; iVar: - 1.78E-8; wConst: 286.5016;
    wVar: 2.92961E-5; aConst: 1.523688; aVar: 0.0; // (AU)
    eConst: 0.093405; eVar: 2.516E-9; MConst: 18.6021; MVar: 0.5240207766);

  // heliocentric jupiter elements
  cJupiterOrbitalElements: TOrbitalElementsData = (NConst: 100.4542;
    NVar: 2.76854E-5; iConst: 1.3030; iVar: - 1.557E-7; wConst: 273.8777;
    wVar: 1.64505E-5; aConst: 5.20256; aVar: 0.0; // (AU)
    eConst: 0.048498; eVar: 4.469E-9; MConst: 19.8950; MVar: 0.0830853001);

  // heliocentric saturn elements
  cSaturnOrbitalElements: TOrbitalElementsData = (NConst: 113.6634;
    NVar: 2.38980E-5; iConst: 2.4886; iVar: - 1.081E-7; wConst: 339.3939;
    wVar: 2.97661E-5; aConst: 9.55475; aVar: 0.0; // (AU)
    eConst: 0.055546; eVar: - 9.499E-9; MConst: 316.9670; MVar: 0.0334442282);

  // heliocentric uranus elements
  cUranusOrbitalElements: TOrbitalElementsData = (NConst: 74.0005;
    NVar: 1.3978E-5; iConst: 0.7733; iVar: 1.9E-8; wConst: 96.6612;
    wVar: 3.0565E-5; aConst: 19.18171; aVar: - 1.55E-8; // (AU)
    eConst: 0.047318; eVar: 7.45E-9; MConst: 142.5905; MVar: 0.011725806);

  // heliocentric neptune elements
  cNeptuneOrbitalElements: TOrbitalElementsData = (NConst: 131.7806;
    NVar: 3.0173E-5; iConst: 1.7700; iVar: - 2.55E-7; wConst: 272.8461;
    wVar: - 6.027E-6; aConst: 30.05826; aVar: 3.313E-8; // (AU)
    eConst: 0.008606; eVar: 2.15E-9; MConst: 260.2471; MVar: 0.005995147);

  cAUToKilometers = 149.6E6; // astronomical units to kilometers
  cEarthRadius = 6400; // earth radius in kilometers

// Converts a TDateTime (GMT+0) into the julian day used for computations.
function GMTDateTimeToJulianDay(const dt: TDateTime): Double;
// Compute orbital elements for given julian day.
function ComputeOrbitalElements(const oeData: TOrbitalElementsData;
  const d: Double): TOrbitalElements;

// Compute the planet position for given julian day (in AU).
function ComputePlanetPosition(const orbitalElements: TOrbitalElements)
  : TAffineVector; overload;
function ComputePlanetPosition(const orbitalElementsData: TOrbitalElementsData;
  const d: Double): TAffineVector; overload;

// ------------------------------------------------------------------------------
implementation
// ------------------------------------------------------------------------------

function GMTDateTimeToJulianDay(const dt: TDateTime): Double;
begin
  Result := dt - EncodeDate(2000, 1, 1);
end;

function ComputeOrbitalElements(const oeData: TOrbitalElementsData;
  const d: Double): TOrbitalElements;
begin
  with Result, oeData do
  begin
    N := NConst + NVar * d;
    i := iConst + iVar * d;
    w := wConst + wVar * d;
    a := aConst + aVar * d;
    e := eConst + eVar * d;
    M := MConst + MVar * d;
  end;
end;

function ComputePlanetPosition(const orbitalElements: TOrbitalElements)
  : TAffineVector;
var
  eccentricAnomaly, eA0: Double;
  sm, cm, se, ce, si, ci, cn, sn, cvw, svw: Double;
  xv, yv, v, r: Double;
  nn: Integer; // numerical instability bailout
begin
  with orbitalElements do
  begin
    // E = M + e*(180/pi) * sin(M) * ( 1.0 + e * cos(M) )
    SinCos(M * cPIdiv180, sm, cm);
    eccentricAnomaly := M + e * c180divPI * sm * (1.0 + e * cm);

    nn := 0;
    repeat
      eA0 := eccentricAnomaly;
      // E1 = E0 - ( E0 - e*(180/pi) * sin(E0) - M ) / ( 1 - e * cos(E0) )
      SinCos(eA0 * cPIdiv180, se, ce);
      eccentricAnomaly := eA0 - (eA0 - e * c180divPI * se - M) / (1 - e * ce);
      Inc(nn);
    until (nn > 10) or (Abs(eccentricAnomaly - eA0) < 1E-4);

    SinCos(eccentricAnomaly * cPIdiv180, se, ce);
    xv := a * (ce - e);
    yv := a * (Sqrt(1.0 - e * e) * se);

    v := ArcTan2(yv, xv) * c180divPI;
    r := Sqrt(xv * xv + yv * yv);

    SinCos(i * cPIdiv180, si, ci);
    SinCos(N * cPIdiv180, sn, cn);
    SinCos((v + w) * cPIdiv180, svw, cvw);
  end;

  // xh = r * ( cos(N) * cos(v+w) - sin(N) * sin(v+w) * cos(i) )
  Result.X := r * (cn * cvw - sn * svw * ci);
  // yh = r * ( sin(N) * cos(v+w) + cos(N) * sin(v+w) * cos(i) )
  Result.Y := r * (sn * cvw + cn * svw * ci);
  // zh = r * ( sin(v+w) * sin(i) )
  Result.Z := r * (svw * si);
end;

function ComputePlanetPosition(const orbitalElementsData: TOrbitalElementsData;
  const d: Double): TAffineVector;
var
  oe: TOrbitalElements;
begin
  oe := ComputeOrbitalElements(orbitalElementsData, d);
  Result := ComputePlanetPosition(oe);
end;

end.