//Static methods
//////////////////////////////// Implementation ///////////////////////////////
public static CAASaturnRingDetails Calculate(double JD)
{
//What will be the return value
CAASaturnRingDetails details = new CAASaturnRingDetails();
double T = (JD - 2451545) / 36525;
double T2 = T * T;
//Step 1. Calculate the inclination of the plane of the ring and the longitude of the ascending node referred to the ecliptic and mean equinox of the date
double i = 28.075216 - 0.012998 * T + 0.000004 * T2;
double irad = CT.D2R(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = CT.D2R(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
double l0 = CAAEarth.EclipticLongitude(JD);
double b0 = CAAEarth.EclipticLatitude(JD);
l0 += CAAFK5.CorrectionInLongitude(l0, b0, JD);
double l0rad = CT.D2R(l0);
b0 += CAAFK5.CorrectionInLatitude(l0, JD);
double b0rad = CT.D2R(b0);
double R = CAAEarth.RadiusVector(JD);
//Step 3. Calculate the corresponding coordinates l,b,r for Saturn but for the instance t-lightraveltime
double DELTA = 9;
double PreviousEarthLightTravelTime = 0;
double EarthLightTravelTime = ELL.DistanceToLightTime(DELTA);
double JD1 = JD - EarthLightTravelTime;
bool bIterate = true;
double x = 0;
double y = 0;
double z = 0;
double l = 0;
double b = 0;
double r = 0;
while (bIterate)
{
//Calculate the position of Saturn
l = CAASaturn.EclipticLongitude(JD1);
b = CAASaturn.EclipticLatitude(JD1);
l += CAAFK5.CorrectionInLongitude(l, b, JD1);
b += CAAFK5.CorrectionInLatitude(l, JD1);
double lrad = CT.D2R(l);
double brad = CT.D2R(b);
r = CAASaturn.RadiusVector(JD1);
//Step 4
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
EarthLightTravelTime = ELL.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(EarthLightTravelTime - PreviousEarthLightTravelTime) > 2E-6); //2E-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - EarthLightTravelTime;
PreviousEarthLightTravelTime = EarthLightTravelTime;
}
}
//Step 5. Calculate Saturn's geocentric Longitude and Latitude
double lambda = Math.Atan2(y, x);
double beta = Math.Atan2(z, Math.Sqrt(x * x + y * y));
//Step 6. Calculate B, a and b
details.B = Math.Asin(Math.Sin(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad) - Math.Cos(irad) * Math.Sin(beta));
details.a = 375.35 / DELTA;
details.b = details.a * Math.Sin(Math.Abs(details.B));
details.B = CT.R2D(details.B);
//Step 7. Calculate the longitude of the ascending node of Saturn's orbit
double N = 113.6655 + 0.8771 * T;
double Nrad = CT.D2R(N);
double ldash = l - 0.01759 / r;
double ldashrad = CT.D2R(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = CT.D2R(bdash);
//Step 8. Calculate Bdash
details.Bdash = CT.R2D(Math.Asin(Math.Sin(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad) - Math.Cos(irad) * Math.Sin(bdashrad)));
//Step 9. Calculate DeltaU
double U1 = Math.Atan2(Math.Sin(irad) * Math.Sin(bdashrad) + Math.Cos(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad), Math.Cos(bdashrad) * Math.Cos(ldashrad - omegarad));
double U2 = Math.Atan2(Math.Sin(irad) * Math.Sin(beta) + Math.Cos(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad), Math.Cos(beta) * Math.Cos(lambda - omegarad));
details.DeltaU = CT.R2D(Math.Abs(U1 - U2));
//Step 10. Calculate the Nutations
double Obliquity = CAANutation.TrueObliquityOfEcliptic(JD);
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
//Step 11. Calculate the Ecliptical longitude and latitude of the northern pole of the ring plane
double lambda0 = omega - 90;
double beta0 = 90 - i;
//Step 12. Correct lambda and beta for the aberration of Saturn
lambda += CT.D2R(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += CT.D2R(0.005693 * Math.Sin(l0rad - lambda) * Math.Sin(beta));
//Step 13. Add nutation in longitude to lambda0 and lambda
//double NLrad = CAACoordinateTransformation::DegreesToRadians(NutationInLongitude/3600);
lambda = CT.R2D(lambda);
lambda += NutationInLongitude / 3600;
lambda = CT.M360(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = CT.M360(lambda0);
//Step 14. Convert to equatorial coordinates
beta = CT.R2D(beta);
COR GeocentricEclipticSaturn = CT.Ec2Eq(lambda, beta, Obliquity);
double alpha = CT.H2R(GeocentricEclipticSaturn.X);
double delta = CT.D2R(GeocentricEclipticSaturn.Y);
COR GeocentricEclipticNorthPole = CT.Ec2Eq(lambda0, beta0, Obliquity);
double alpha0 = CT.H2R(GeocentricEclipticNorthPole.X);
double delta0 = CT.D2R(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = CT.R2D(Math.Atan2(Math.Cos(delta0) * Math.Sin(alpha0 - alpha), Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(alpha0 - alpha)));
return(details);
}
//Static methods
public static CAASaturnMoonsDetails Calculate(double JD)
{
//Calculate the position of the Sun
double sunlong = CAASun.GeometricEclipticLongitude(JD);
double sunlongrad = CAACoordinateTransformation.DegreesToRadians(sunlong);
double beta = CAASun.GeometricEclipticLatitude(JD);
double betarad = CAACoordinateTransformation.DegreesToRadians(beta);
double R = CAAEarth.RadiusVector(JD);
//Calculate the the light travel time from Saturn to the Earth
double DELTA = 9;
double PreviousEarthLightTravelTime = 0;
double EarthLightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
double JD1 = JD - EarthLightTravelTime;
bool bIterate = true;
double x = 0;
double y = 0;
double z = 0;
double l = 0;
double lrad = 0;
double b = 0;
double brad = 0;
double r = 0;
while (bIterate)
{
//Calculate the position of Jupiter
l = CAASaturn.EclipticLongitude(JD1);
lrad = CAACoordinateTransformation.DegreesToRadians(l);
b = CAASaturn.EclipticLatitude(JD1);
brad = CAACoordinateTransformation.DegreesToRadians(b);
r = CAASaturn.RadiusVector(JD1);
x = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
y = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
z = r * Math.Sin(brad) + R * Math.Sin(betarad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
EarthLightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(EarthLightTravelTime - PreviousEarthLightTravelTime) > 2E-6); //2E-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - EarthLightTravelTime;
PreviousEarthLightTravelTime = EarthLightTravelTime;
}
}
//Calculate the details as seen from the earth
CAASaturnMoonsDetails details1 = CalculateHelper(JD, sunlongrad, betarad, R);
FillInPhenomenaDetails(ref details1.Satellite1);
FillInPhenomenaDetails(ref details1.Satellite2);
FillInPhenomenaDetails(ref details1.Satellite3);
FillInPhenomenaDetails(ref details1.Satellite4);
FillInPhenomenaDetails(ref details1.Satellite5);
FillInPhenomenaDetails(ref details1.Satellite6);
FillInPhenomenaDetails(ref details1.Satellite7);
FillInPhenomenaDetails(ref details1.Satellite8);
//Calculate the the light travel time from Saturn to the Sun
JD1 = JD - EarthLightTravelTime;
l = CAASaturn.EclipticLongitude(JD1);
lrad = CAACoordinateTransformation.DegreesToRadians(l);
b = CAASaturn.EclipticLatitude(JD1);
brad = CAACoordinateTransformation.DegreesToRadians(b);
r = CAASaturn.RadiusVector(JD1);
x = r * Math.Cos(brad) * Math.Cos(lrad);
y = r * Math.Cos(brad) * Math.Sin(lrad);
z = r * Math.Sin(brad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
double SunLightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
//Calculate the details as seen from the Sun
CAASaturnMoonsDetails details2 = CalculateHelper(JD + SunLightTravelTime - EarthLightTravelTime, sunlongrad, betarad, 0);
FillInPhenomenaDetails(ref details2.Satellite1);
FillInPhenomenaDetails(ref details2.Satellite2);
FillInPhenomenaDetails(ref details2.Satellite3);
FillInPhenomenaDetails(ref details2.Satellite4);
FillInPhenomenaDetails(ref details2.Satellite5);
FillInPhenomenaDetails(ref details2.Satellite6);
FillInPhenomenaDetails(ref details2.Satellite7);
FillInPhenomenaDetails(ref details2.Satellite8);
//Finally transfer the required values from details2 to details1
details1.Satellite1.bInEclipse = details2.Satellite1.bInOccultation;
details1.Satellite2.bInEclipse = details2.Satellite2.bInOccultation;
details1.Satellite3.bInEclipse = details2.Satellite3.bInOccultation;
details1.Satellite4.bInEclipse = details2.Satellite4.bInOccultation;
details1.Satellite5.bInEclipse = details2.Satellite5.bInOccultation;
details1.Satellite6.bInEclipse = details2.Satellite6.bInOccultation;
details1.Satellite7.bInEclipse = details2.Satellite7.bInOccultation;
details1.Satellite8.bInEclipse = details2.Satellite8.bInOccultation;
details1.Satellite1.bInShadowTransit = details2.Satellite1.bInTransit;
details1.Satellite2.bInShadowTransit = details2.Satellite2.bInTransit;
details1.Satellite3.bInShadowTransit = details2.Satellite3.bInTransit;
details1.Satellite4.bInShadowTransit = details2.Satellite4.bInTransit;
details1.Satellite5.bInShadowTransit = details2.Satellite5.bInTransit;
details1.Satellite6.bInShadowTransit = details2.Satellite6.bInTransit;
details1.Satellite7.bInShadowTransit = details2.Satellite7.bInTransit;
details1.Satellite8.bInShadowTransit = details2.Satellite8.bInTransit;
return(details1);
}
public static EPD Calculate(double JD, EO @object)
{
//What will the the return value
EPD details = new EPD();
double JD0 = JD;
double L0 = 0;
double B0 = 0;
double R0 = 0;
double cosB0 = 0;
if (@object != EO.SUN)
{
L0 = CAAEarth.EclipticLongitude(JD0);
B0 = CAAEarth.EclipticLatitude(JD0);
R0 = CAAEarth.RadiusVector(JD0);
L0 = CT.D2R(L0);
B0 = CT.D2R(B0);
cosB0 = Math.Cos(B0);
}
//Calculate the initial values
double L = 0;
double B = 0;
double R = 0;
double Lrad;
double Brad;
double cosB;
double cosL;
double x;
double y;
double z;
bool bRecalc = true;
bool bFirstRecalc = true;
double LPrevious = 0;
double BPrevious = 0;
double RPrevious = 0;
while (bRecalc)
{
switch (@object)
{
case EO.SUN:
{
L = CAASun.GeometricEclipticLongitude(JD0);
B = CAASun.GeometricEclipticLatitude(JD0);
R = CAAEarth.RadiusVector(JD0);
break;
}
case EO.MERCURY:
{
L = CAAMercury.EclipticLongitude(JD0);
B = CAAMercury.EclipticLatitude(JD0);
R = CAAMercury.RadiusVector(JD0);
break;
}
case EO.VENUS:
{
L = CAAVenus.EclipticLongitude(JD0);
B = CAAVenus.EclipticLatitude(JD0);
R = CAAVenus.RadiusVector(JD0);
break;
}
case EO.MARS:
{
L = CAAMars.EclipticLongitude(JD0);
B = CAAMars.EclipticLatitude(JD0);
R = CAAMars.RadiusVector(JD0);
break;
}
case EO.JUPITER:
{
L = CAAJupiter.EclipticLongitude(JD0);
B = CAAJupiter.EclipticLatitude(JD0);
R = CAAJupiter.RadiusVector(JD0);
break;
}
case EO.SATURN:
{
L = CAASaturn.EclipticLongitude(JD0);
B = CAASaturn.EclipticLatitude(JD0);
R = CAASaturn.RadiusVector(JD0);
break;
}
case EO.URANUS:
{
L = CAAUranus.EclipticLongitude(JD0);
B = CAAUranus.EclipticLatitude(JD0);
R = CAAUranus.RadiusVector(JD0);
break;
}
case EO.NEPTUNE:
{
L = CAANeptune.EclipticLongitude(JD0);
B = CAANeptune.EclipticLatitude(JD0);
R = CAANeptune.RadiusVector(JD0);
break;
}
case EO.PLUTO:
{
L = CAAPluto.EclipticLongitude(JD0);
B = CAAPluto.EclipticLatitude(JD0);
R = CAAPluto.RadiusVector(JD0);
break;
}
default:
{
Debug.Assert(false);
break;
}
}
if (!bFirstRecalc)
{
bRecalc = ((Math.Abs(L - LPrevious) > 0.00001) || (Math.Abs(B - BPrevious) > 0.00001) || (Math.Abs(R - RPrevious) > 0.000001));
LPrevious = L;
BPrevious = B;
RPrevious = R;
}
else
{
bFirstRecalc = false;
}
//Calculate the new value
if (bRecalc)
{
double distance = 0;
if (@object != EO.SUN)
{
Lrad = CT.D2R(L);
Brad = CT.D2R(B);
cosB = Math.Cos(Brad);
cosL = Math.Cos(Lrad);
x = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
y = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
z = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
distance = Math.Sqrt(x * x + y * y + z * z);
}
else
{
distance = R; //Distance to the sun from the earth is in fact the radius vector
}
//Prepare for the next loop around
JD0 = JD - ELL.DistanceToLightTime(distance);
}
}
Lrad = CT.D2R(L);
Brad = CT.D2R(B);
cosB = Math.Cos(Brad);
cosL = Math.Cos(Lrad);
x = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
y = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
z = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
double x2 = x * x;
double y2 = y * y;
details.ApparentGeocentricLatitude = CT.R2D(Math.Atan2(z, Math.Sqrt(x2 + y2)));
details.ApparentGeocentricDistance = Math.Sqrt(x2 + y2 + z * z);
details.ApparentGeocentricLongitude = CT.M360(CT.R2D(Math.Atan2(y, x)));
details.ApparentLightTime = ELL.DistanceToLightTime(details.ApparentGeocentricDistance);
//Adjust for Aberration
COR Aberration = ABR.EclipticAberration(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD);
details.ApparentGeocentricLongitude += Aberration.X;
details.ApparentGeocentricLatitude += Aberration.Y;
//convert to the FK5 system
double DeltaLong = CAAFK5.CorrectionInLongitude(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD);
details.ApparentGeocentricLatitude += CAAFK5.CorrectionInLatitude(details.ApparentGeocentricLongitude, JD);
details.ApparentGeocentricLongitude += DeltaLong;
//Correct for nutation
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
double Epsilon = CAANutation.TrueObliquityOfEcliptic(JD);
details.ApparentGeocentricLongitude += CT.DMS2D(0, 0, NutationInLongitude);
//Convert to RA and Dec
COR ApparentEqu = CT.Ec2Eq(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, Epsilon);
details.ApparentGeocentricRA = ApparentEqu.X;
details.ApparentGeocentricDeclination = ApparentEqu.Y;
return(details);
}
protected static CAASaturnMoonsDetails CalculateHelper(double JD, double sunlongrad, double betarad, double R)
{
//What will be the return value
CAASaturnMoonsDetails details = new CAASaturnMoonsDetails();
//Calculate the position of Saturn decreased by the light travel time from Saturn to the specified position
double DELTA = 9;
double PreviousLightTravelTime = 0;
double LightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
double x = 0;
double y = 0;
double z = 0;
double l = 0;
double lrad = 0;
double b = 0;
double brad = 0;
double r = 0;
double JD1 = JD - LightTravelTime;
bool bIterate = true;
while (bIterate)
{
//Calculate the position of Saturn
l = CAASaturn.EclipticLongitude(JD1);
lrad = CAACoordinateTransformation.DegreesToRadians(l);
b = CAASaturn.EclipticLatitude(JD1);
brad = CAACoordinateTransformation.DegreesToRadians(b);
r = CAASaturn.RadiusVector(JD1);
x = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
y = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
z = r * Math.Sin(brad) + R * Math.Sin(betarad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
LightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(LightTravelTime - PreviousLightTravelTime) > 2E-6); //2E-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - LightTravelTime;
PreviousLightTravelTime = LightTravelTime;
}
}
//Calculate Saturn's Longitude and Latitude
double lambda0 = Math.Atan2(y, x);
lambda0 = CAACoordinateTransformation.RadiansToDegrees(lambda0);
double beta0 = Math.Atan(z / Math.Sqrt(x * x + y * y));
beta0 = CAACoordinateTransformation.RadiansToDegrees(beta0);
//Precess the longtitude and Latitutude to B1950.0
CAA2DCoordinate Saturn1950 = CAAPrecession.PrecessEcliptic(lambda0, beta0, JD, 2433282.4235);
lambda0 = Saturn1950.X;
double lambda0rad = CAACoordinateTransformation.DegreesToRadians(lambda0);
beta0 = Saturn1950.Y;
double beta0rad = CAACoordinateTransformation.DegreesToRadians(beta0);
double JDE = JD - LightTravelTime;
double t1 = JDE - 2411093.0;
double t2 = t1 / 365.25;
double t3 = ((JDE - 2433282.423) / 365.25) + 1950.0;
double t4 = JDE - 2411368.0;
double t5 = t4 / 365.25;
double t6 = JDE - 2415020.0;
double t7 = t6 / 36525.0;
double t8 = t6 / 365.25;
double t9 = (JDE - 2442000.5) / 365.25;
double t10 = JDE - 2409786.0;
double t11 = t10 / 36525.0;
double t112 = t11 * t11;
double t113 = t112 * t11;
double W0 = CAACoordinateTransformation.MapTo0To360Range(5.095 * (t3 - 1866.39));
double W0rad = CAACoordinateTransformation.DegreesToRadians(W0);
double W1 = CAACoordinateTransformation.MapTo0To360Range(74.4 + 32.39 * t2);
double W1rad = CAACoordinateTransformation.DegreesToRadians(W1);
double W2 = CAACoordinateTransformation.MapTo0To360Range(134.3 + 92.62 * t2);
double W2rad = CAACoordinateTransformation.DegreesToRadians(W2);
double W3 = CAACoordinateTransformation.MapTo0To360Range(42.0 - 0.5118 * t5);
double W3rad = CAACoordinateTransformation.DegreesToRadians(W3);
double W4 = CAACoordinateTransformation.MapTo0To360Range(276.59 + 0.5118 * t5);
double W4rad = CAACoordinateTransformation.DegreesToRadians(W4);
double W5 = CAACoordinateTransformation.MapTo0To360Range(267.2635 + 1222.1136 * t7);
double W5rad = CAACoordinateTransformation.DegreesToRadians(W5);
double W6 = CAACoordinateTransformation.MapTo0To360Range(175.4762 + 1221.5515 * t7);
double W6rad = CAACoordinateTransformation.DegreesToRadians(W6);
double W7 = CAACoordinateTransformation.MapTo0To360Range(2.4891 + 0.002435 * t7);
double W7rad = CAACoordinateTransformation.DegreesToRadians(W7);
double W8 = CAACoordinateTransformation.MapTo0To360Range(113.35 - 0.2597 * t7);
double W8rad = CAACoordinateTransformation.DegreesToRadians(W8);
double s1 = Math.Sin(CAACoordinateTransformation.DegreesToRadians(28.0817));
double s2 = Math.Sin(CAACoordinateTransformation.DegreesToRadians(168.8112));
double c1 = Math.Cos(CAACoordinateTransformation.DegreesToRadians(28.0817));
double c2 = Math.Cos(CAACoordinateTransformation.DegreesToRadians(168.8112));
double e1 = 0.05589 - 0.000346 * t7;
//Satellite 1
double L = CAACoordinateTransformation.MapTo0To360Range(127.64 + 381.994497 * t1 - 43.57 * Math.Sin(W0rad) - 0.720 * Math.Sin(3 * W0rad) - 0.02144 * Math.Sin(5 * W0rad));
double p = 106.1 + 365.549 * t2;
double M = L - p;
double Mrad = CAACoordinateTransformation.DegreesToRadians(M);
double C = 2.18287 * Math.Sin(Mrad) + 0.025988 * Math.Sin(2 * Mrad) + 0.00043 * Math.Sin(3 * Mrad);
double Crad = CAACoordinateTransformation.DegreesToRadians(C);
double lambda1 = CAACoordinateTransformation.MapTo0To360Range(L + C);
double r1 = 3.06879 / (1 + 0.01905 * Math.Cos(Mrad + Crad));
double gamma1 = 1.563;
double omega1 = CAACoordinateTransformation.MapTo0To360Range(54.5 - 365.072 * t2);
//Satellite 2
L = CAACoordinateTransformation.MapTo0To360Range(200.317 + 262.7319002 * t1 + 0.25667 * Math.Sin(W1rad) + 0.20883 * Math.Sin(W2rad));
p = 309.107 + 123.44121 * t2;
M = L - p;
Mrad = CAACoordinateTransformation.DegreesToRadians(M);
C = 0.55577 * Math.Sin(Mrad) + 0.00168 * Math.Sin(2 * Mrad);
Crad = CAACoordinateTransformation.DegreesToRadians(C);
double lambda2 = CAACoordinateTransformation.MapTo0To360Range(L + C);
double r2 = 3.94118 / (1 + 0.00485 * Math.Cos(Mrad + Crad));
double gamma2 = 0.0262;
double omega2 = CAACoordinateTransformation.MapTo0To360Range(348 - 151.95 * t2);
//Satellite 3
double lambda3 = CAACoordinateTransformation.MapTo0To360Range(285.306 + 190.69791226 * t1 + 2.063 * Math.Sin(W0rad) + 0.03409 * Math.Sin(3 * W0rad) + 0.001015 * Math.Sin(5 * W0rad));
double r3 = 4.880998;
double gamma3 = 1.0976;
double omega3 = CAACoordinateTransformation.MapTo0To360Range(111.33 - 72.2441 * t2);
//Satellite 4
L = CAACoordinateTransformation.MapTo0To360Range(254.712 + 131.53493193 * t1 - 0.0215 * Math.Sin(W1rad) - 0.01733 * Math.Sin(W2rad));
p = 174.8 + 30.820 * t2;
M = L - p;
Mrad = CAACoordinateTransformation.DegreesToRadians(M);
C = 0.24717 * Math.Sin(Mrad) + 0.00033 * Math.Sin(2 * Mrad);
Crad = CAACoordinateTransformation.DegreesToRadians(C);
double lambda4 = CAACoordinateTransformation.MapTo0To360Range(L + C);
double r4 = 6.24871 / (1 + 0.002157 * Math.Cos(Mrad + Crad));
double gamma4 = 0.0139;
double omega4 = CAACoordinateTransformation.MapTo0To360Range(232 - 30.27 * t2);
//Satellite 5
double pdash = 342.7 + 10.057 * t2;
double pdashrad = CAACoordinateTransformation.DegreesToRadians(pdash);
double a1 = 0.000265 * Math.Sin(pdashrad) + 0.001 * Math.Sin(W4rad); //Note the book uses the incorrect constant 0.01*sin(W4rad);
double a2 = 0.000265 * Math.Cos(pdashrad) + 0.001 * Math.Cos(W4rad); //Note the book uses the incorrect constant 0.01*cos(W4rad);
double e = Math.Sqrt(a1 * a1 + a2 * a2);
p = CAACoordinateTransformation.RadiansToDegrees(Math.Atan2(a1, a2));
double N = 345 - 10.057 * t2;
double Nrad = CAACoordinateTransformation.DegreesToRadians(N);
double lambdadash = CAACoordinateTransformation.MapTo0To360Range(359.244 + 79.69004720 * t1 + 0.086754 * Math.Sin(Nrad));
double i = 28.0362 + 0.346898 * Math.Cos(Nrad) + 0.01930 * Math.Cos(W3rad);
double omega = 168.8034 + 0.736936 * Math.Sin(Nrad) + 0.041 * Math.Sin(W3rad);
double a = 8.725924;
double lambda5 = 0;
double gamma5 = 0;
double omega5 = 0;
double r5 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r5, ref lambda5, ref gamma5, ref omega5);
//Satellite 6
L = 261.1582 + 22.57697855 * t4 + 0.074025 * Math.Sin(W3rad);
double idash = 27.45141 + 0.295999 * Math.Cos(W3rad);
double idashrad = CAACoordinateTransformation.DegreesToRadians(idash);
double omegadash = 168.66925 + 0.628808 * Math.Sin(W3rad);
double omegadashrad = CAACoordinateTransformation.DegreesToRadians(omegadash);
a1 = Math.Sin(W7rad) * Math.Sin(omegadashrad - W8rad);
a2 = Math.Cos(W7rad) * Math.Sin(idashrad) - Math.Sin(W7rad) * Math.Cos(idashrad) * Math.Cos(omegadashrad - W8rad);
double g0 = CAACoordinateTransformation.DegreesToRadians(102.8623);
double psi = Math.Atan2(a1, a2);
if (a2 < 0)
{
psi += CAACoordinateTransformation.PI();
}
double psideg = CAACoordinateTransformation.RadiansToDegrees(psi);
double s = Math.Sqrt(a1 * a1 + a2 * a2);
double g = W4 - omegadash - psideg;
double w_ = 0;
for (int j = 0; j < 3; j++)
{
w_ = W4 + 0.37515 * (Math.Sin(2 * CAACoordinateTransformation.DegreesToRadians(g)) - Math.Sin(2 * g0));
g = w_ - omegadash - psideg;
}
double grad = CAACoordinateTransformation.DegreesToRadians(g);
double edash = 0.029092 + 0.00019048 * (Math.Cos(2 * grad) - Math.Cos(2 * g0));
double q = CAACoordinateTransformation.DegreesToRadians(2 * (W5 - w_));
double b1 = Math.Sin(idashrad) * Math.Sin(omegadashrad - W8rad);
double b2 = Math.Cos(W7rad) * Math.Sin(idashrad) * Math.Cos(omegadashrad - W8rad) - Math.Sin(W7rad) * Math.Cos(idashrad);
double atanb1b2 = Math.Atan2(b1, b2);
double theta = atanb1b2 + W8rad;
e = edash + 0.002778797 * edash * Math.Cos(q);
p = w_ + 0.159215 * Math.Sin(q);
double u = 2 * W5rad - 2 * theta + psi;
double h = 0.9375 * edash * edash * Math.Sin(q) + 0.1875 * s * s * Math.Sin(2 * (W5rad - theta));
lambdadash = CAACoordinateTransformation.MapTo0To360Range(L - 0.254744 * (e1 * Math.Sin(W6rad) + 0.75 * e1 * e1 * Math.Sin(2 * W6rad) + h));
i = idash + 0.031843 * s * Math.Cos(u);
omega = omegadash + (0.031843 * s * Math.Sin(u)) / Math.Sin(idashrad);
a = 20.216193;
double lambda6 = 0;
double gamma6 = 0;
double omega6 = 0;
double r6 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r6, ref lambda6, ref gamma6, ref omega6);
//Satellite 7
double eta = 92.39 + 0.5621071 * t6;
double etarad = CAACoordinateTransformation.DegreesToRadians(eta);
double zeta = 148.19 - 19.18 * t8;
double zetarad = CAACoordinateTransformation.DegreesToRadians(zeta);
theta = CAACoordinateTransformation.DegreesToRadians(184.8 - 35.41 * t9);
double thetadash = theta - CAACoordinateTransformation.DegreesToRadians(7.5);
double @as = CAACoordinateTransformation.DegreesToRadians(176 + 12.22 * t8);
double bs = CAACoordinateTransformation.DegreesToRadians(8 + 24.44 * t8);
double cs = bs + CAACoordinateTransformation.DegreesToRadians(5);
w_ = 69.898 - 18.67088 * t8;
double phi = 2 * (w_ - W5);
double phirad = CAACoordinateTransformation.DegreesToRadians(phi);
double chi = 94.9 - 2.292 * t8;
double chirad = CAACoordinateTransformation.DegreesToRadians(chi);
a = 24.50601 - 0.08686 * Math.Cos(etarad) - 0.00166 * Math.Cos(zetarad + etarad) + 0.00175 * Math.Cos(zetarad - etarad);
e = 0.103458 - 0.004099 * Math.Cos(etarad) - 0.000167 * Math.Cos(zetarad + etarad) + 0.000235 * Math.Cos(zetarad - etarad) + 0.02303 * Math.Cos(zetarad) - 0.00212 * Math.Cos(2 * zetarad) + 0.000151 * Math.Cos(3 * zetarad) + 0.00013 * Math.Cos(phirad);
p = w_ + 0.15648 * Math.Sin(chirad) - 0.4457 * Math.Sin(etarad) - 0.2657 * Math.Sin(zetarad + etarad) + -0.3573 * Math.Sin(zetarad - etarad) - 12.872 * Math.Sin(zetarad) + 1.668 * Math.Sin(2 * zetarad) + -0.2419 * Math.Sin(3 * zetarad) - 0.07 * Math.Sin(phirad);
lambdadash = CAACoordinateTransformation.MapTo0To360Range(177.047 + 16.91993829 * t6 + 0.15648 * Math.Sin(chirad) + 9.142 * Math.Sin(etarad) + 0.007 * Math.Sin(2 * etarad) - 0.014 * Math.Sin(3 * etarad) + 0.2275 * Math.Sin(zetarad + etarad) + 0.2112 * Math.Sin(zetarad - etarad) - 0.26 * Math.Sin(zetarad) - 0.0098 * Math.Sin(2 * zetarad) + -0.013 * Math.Sin(@as) + 0.017 * Math.Sin(bs) - 0.0303 * Math.Sin(phirad));
i = 27.3347 + 0.643486 * Math.Cos(chirad) + 0.315 * Math.Cos(W3rad) + 0.018 * Math.Cos(theta) - 0.018 * Math.Cos(cs);
omega = 168.6812 + 1.40136 * Math.Cos(chirad) + 0.68599 * Math.Sin(W3rad) - 0.0392 * Math.Sin(cs) + 0.0366 * Math.Sin(thetadash);
double lambda7 = 0;
double gamma7 = 0;
double omega7 = 0;
double r7 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r7, ref lambda7, ref gamma7, ref omega7);
//Satellite 8
L = CAACoordinateTransformation.MapTo0To360Range(261.1582 + 22.57697855 * t4);
double w_dash = 91.796 + 0.562 * t7;
psi = 4.367 - 0.195 * t7;
double psirad = CAACoordinateTransformation.DegreesToRadians(psi);
theta = 146.819 - 3.198 * t7;
phi = 60.470 + 1.521 * t7;
phirad = CAACoordinateTransformation.DegreesToRadians(phi);
double PHI = 205.055 - 2.091 * t7;
edash = 0.028298 + 0.001156 * t11;
double w_0 = 352.91 + 11.71 * t11;
double mu = CAACoordinateTransformation.MapTo0To360Range(76.3852 + 4.53795125 * t10);
mu = CAACoordinateTransformation.MapTo0To360Range(189097.71668440815);
idash = 18.4602 - 0.9518 * t11 - 0.072 * t112 + 0.0054 * t113;
idashrad = CAACoordinateTransformation.DegreesToRadians(idash);
omegadash = 143.198 - 3.919 * t11 + 0.116 * t112 + 0.008 * t113;
l = CAACoordinateTransformation.DegreesToRadians(mu - w_0);
g = CAACoordinateTransformation.DegreesToRadians(w_0 - omegadash - psi);
double g1 = CAACoordinateTransformation.DegreesToRadians(w_0 - omegadash - phi);
double ls = CAACoordinateTransformation.DegreesToRadians(W5 - w_dash);
double gs = CAACoordinateTransformation.DegreesToRadians(w_dash - theta);
double lt = CAACoordinateTransformation.DegreesToRadians(L - W4);
double gt = CAACoordinateTransformation.DegreesToRadians(W4 - PHI);
double u1 = 2 * (l + g - ls - gs);
double u2 = l + g1 - lt - gt;
double u3 = l + 2 * (g - ls - gs);
double u4 = lt + gt - g1;
double u5 = 2 * (ls + gs);
a = 58.935028 + 0.004638 * Math.Cos(u1) + 0.058222 * Math.Cos(u2);
e = edash - 0.0014097 * Math.Cos(g1 - gt) + 0.0003733 * Math.Cos(u5 - 2 * g) + 0.0001180 * Math.Cos(u3) + 0.0002408 * Math.Cos(l) + 0.0002849 * Math.Cos(l + u2) + 0.0006190 * Math.Cos(u4);
double w = 0.08077 * Math.Sin(g1 - gt) + 0.02139 * Math.Sin(u5 - 2 * g) - 0.00676 * Math.Sin(u3) + 0.01380 * Math.Sin(l) + 0.01632 * Math.Sin(l + u2) + 0.03547 * Math.Sin(u4);
p = w_0 + w / edash;
lambdadash = mu - 0.04299 * Math.Sin(u2) - 0.00789 * Math.Sin(u1) - 0.06312 * Math.Sin(ls) + -0.00295 * Math.Sin(2 * ls) - 0.02231 * Math.Sin(u5) + 0.00650 * Math.Sin(u5 + psirad);
i = idash + 0.04204 * Math.Cos(u5 + psirad) + 0.00235 * Math.Cos(l + g1 + lt + gt + phirad) + 0.00360 * Math.Cos(u2 + phirad);
double wdash = 0.04204 * Math.Sin(u5 + psirad) + 0.00235 * Math.Sin(l + g1 + lt + gt + phirad) + 0.00358 * Math.Sin(u2 + phirad);
omega = omegadash + wdash / Math.Sin(idashrad);
double lambda8 = 0;
double gamma8 = 0;
double omega8 = 0;
double r8 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r8, ref lambda8, ref gamma8, ref omega8);
u = CAACoordinateTransformation.DegreesToRadians(lambda1 - omega1);
w = CAACoordinateTransformation.DegreesToRadians(omega1 - 168.8112);
double gamma1rad = CAACoordinateTransformation.DegreesToRadians(gamma1);
double X1 = r1 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma1rad) * Math.Sin(w));
double Y1 = r1 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma1rad) + Math.Cos(u) * Math.Sin(w));
double Z1 = r1 * Math.Sin(u) * Math.Sin(gamma1rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda2 - omega2);
w = CAACoordinateTransformation.DegreesToRadians(omega2 - 168.8112);
double gamma2rad = CAACoordinateTransformation.DegreesToRadians(gamma2);
double X2 = r2 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma2rad) * Math.Sin(w));
double Y2 = r2 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma2rad) + Math.Cos(u) * Math.Sin(w));
double Z2 = r2 * Math.Sin(u) * Math.Sin(gamma2rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda3 - omega3);
w = CAACoordinateTransformation.DegreesToRadians(omega3 - 168.8112);
double gamma3rad = CAACoordinateTransformation.DegreesToRadians(gamma3);
double X3 = r3 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma3rad) * Math.Sin(w));
double Y3 = r3 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma3rad) + Math.Cos(u) * Math.Sin(w));
double Z3 = r3 * Math.Sin(u) * Math.Sin(gamma3rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda4 - omega4);
w = CAACoordinateTransformation.DegreesToRadians(omega4 - 168.8112);
double gamma4rad = CAACoordinateTransformation.DegreesToRadians(gamma4);
double X4 = r4 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma4rad) * Math.Sin(w));
double Y4 = r4 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma4rad) + Math.Cos(u) * Math.Sin(w));
double Z4 = r4 * Math.Sin(u) * Math.Sin(gamma4rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda5 - omega5);
w = CAACoordinateTransformation.DegreesToRadians(omega5 - 168.8112);
double gamma5rad = CAACoordinateTransformation.DegreesToRadians(gamma5);
double X5 = r5 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma5rad) * Math.Sin(w));
double Y5 = r5 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma5rad) + Math.Cos(u) * Math.Sin(w));
double Z5 = r5 * Math.Sin(u) * Math.Sin(gamma5rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda6 - omega6);
w = CAACoordinateTransformation.DegreesToRadians(omega6 - 168.8112);
double gamma6rad = CAACoordinateTransformation.DegreesToRadians(gamma6);
double X6 = r6 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma6rad) * Math.Sin(w));
double Y6 = r6 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma6rad) + Math.Cos(u) * Math.Sin(w));
double Z6 = r6 * Math.Sin(u) * Math.Sin(gamma6rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda7 - omega7);
w = CAACoordinateTransformation.DegreesToRadians(omega7 - 168.8112);
double gamma7rad = CAACoordinateTransformation.DegreesToRadians(gamma7);
double X7 = r7 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma7rad) * Math.Sin(w));
double Y7 = r7 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma7rad) + Math.Cos(u) * Math.Sin(w));
double Z7 = r7 * Math.Sin(u) * Math.Sin(gamma7rad);
u = CAACoordinateTransformation.DegreesToRadians(lambda8 - omega8);
w = CAACoordinateTransformation.DegreesToRadians(omega8 - 168.8112);
double gamma8rad = CAACoordinateTransformation.DegreesToRadians(gamma8);
double X8 = r8 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma8rad) * Math.Sin(w));
double Y8 = r8 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma8rad) + Math.Cos(u) * Math.Sin(w));
double Z8 = r8 * Math.Sin(u) * Math.Sin(gamma8rad);
double X9 = 0;
double Y9 = 0;
double Z9 = 1;
//Now do the rotations, first for the ficticious 9th satellite, so that we can calculate D
double A4 = 0;
double B4 = 0;
double C4 = 0;
Rotations(X9, Y9, Z9, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
double D = Math.Atan2(A4, C4);
//Now calculate the values for satellite 1
Rotations(X1, Y1, Z1, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite1.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite1.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite1.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 2
Rotations(X2, Y2, Z2, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite2.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite2.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite2.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 3
Rotations(X3, Y3, Z3, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite3.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite3.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite3.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 4
Rotations(X4, Y4, Z4, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite4.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite4.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite4.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 5
Rotations(X5, Y5, Z5, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite5.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite5.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite5.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 6
Rotations(X6, Y6, Z6, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite6.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite6.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite6.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 7
Rotations(X7, Y7, Z7, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite7.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite7.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite7.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 8
Rotations(X8, Y8, Z8, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite8.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite8.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite8.TrueRectangularCoordinates.Z = B4;
//apply the differential light-time correction
details.Satellite1.ApparentRectangularCoordinates.X = details.Satellite1.TrueRectangularCoordinates.X + Math.Abs(details.Satellite1.TrueRectangularCoordinates.Z) / 20947 * Math.Sqrt(1 - (details.Satellite1.TrueRectangularCoordinates.X / r1) * (details.Satellite1.TrueRectangularCoordinates.X / r1));
details.Satellite1.ApparentRectangularCoordinates.Y = details.Satellite1.TrueRectangularCoordinates.Y;
details.Satellite1.ApparentRectangularCoordinates.Z = details.Satellite1.TrueRectangularCoordinates.Z;
details.Satellite2.ApparentRectangularCoordinates.X = details.Satellite2.TrueRectangularCoordinates.X + Math.Abs(details.Satellite2.TrueRectangularCoordinates.Z) / 23715 * Math.Sqrt(1 - (details.Satellite2.TrueRectangularCoordinates.X / r2) * (details.Satellite2.TrueRectangularCoordinates.X / r2));
details.Satellite2.ApparentRectangularCoordinates.Y = details.Satellite2.TrueRectangularCoordinates.Y;
details.Satellite2.ApparentRectangularCoordinates.Z = details.Satellite2.TrueRectangularCoordinates.Z;
details.Satellite3.ApparentRectangularCoordinates.X = details.Satellite3.TrueRectangularCoordinates.X + Math.Abs(details.Satellite3.TrueRectangularCoordinates.Z) / 26382 * Math.Sqrt(1 - (details.Satellite3.TrueRectangularCoordinates.X / r3) * (details.Satellite3.TrueRectangularCoordinates.X / r3));
details.Satellite3.ApparentRectangularCoordinates.Y = details.Satellite3.TrueRectangularCoordinates.Y;
details.Satellite3.ApparentRectangularCoordinates.Z = details.Satellite3.TrueRectangularCoordinates.Z;
details.Satellite4.ApparentRectangularCoordinates.X = details.Satellite4.TrueRectangularCoordinates.X + Math.Abs(details.Satellite4.TrueRectangularCoordinates.Z) / 29876 * Math.Sqrt(1 - (details.Satellite4.TrueRectangularCoordinates.X / r4) * (details.Satellite4.TrueRectangularCoordinates.X / r4));
details.Satellite4.ApparentRectangularCoordinates.Y = details.Satellite4.TrueRectangularCoordinates.Y;
details.Satellite4.ApparentRectangularCoordinates.Z = details.Satellite4.TrueRectangularCoordinates.Z;
details.Satellite5.ApparentRectangularCoordinates.X = details.Satellite5.TrueRectangularCoordinates.X + Math.Abs(details.Satellite5.TrueRectangularCoordinates.Z) / 35313 * Math.Sqrt(1 - (details.Satellite5.TrueRectangularCoordinates.X / r5) * (details.Satellite5.TrueRectangularCoordinates.X / r5));
details.Satellite5.ApparentRectangularCoordinates.Y = details.Satellite5.TrueRectangularCoordinates.Y;
details.Satellite5.ApparentRectangularCoordinates.Z = details.Satellite5.TrueRectangularCoordinates.Z;
details.Satellite6.ApparentRectangularCoordinates.X = details.Satellite6.TrueRectangularCoordinates.X + Math.Abs(details.Satellite6.TrueRectangularCoordinates.Z) / 53800 * Math.Sqrt(1 - (details.Satellite6.TrueRectangularCoordinates.X / r6) * (details.Satellite6.TrueRectangularCoordinates.X / r6));
details.Satellite6.ApparentRectangularCoordinates.Y = details.Satellite6.TrueRectangularCoordinates.Y;
details.Satellite6.ApparentRectangularCoordinates.Z = details.Satellite6.TrueRectangularCoordinates.Z;
details.Satellite7.ApparentRectangularCoordinates.X = details.Satellite7.TrueRectangularCoordinates.X + Math.Abs(details.Satellite7.TrueRectangularCoordinates.Z) / 59222 * Math.Sqrt(1 - (details.Satellite7.TrueRectangularCoordinates.X / r7) * (details.Satellite7.TrueRectangularCoordinates.X / r7));
details.Satellite7.ApparentRectangularCoordinates.Y = details.Satellite7.TrueRectangularCoordinates.Y;
details.Satellite7.ApparentRectangularCoordinates.Z = details.Satellite7.TrueRectangularCoordinates.Z;
details.Satellite8.ApparentRectangularCoordinates.X = details.Satellite8.TrueRectangularCoordinates.X + Math.Abs(details.Satellite8.TrueRectangularCoordinates.Z) / 91820 * Math.Sqrt(1 - (details.Satellite8.TrueRectangularCoordinates.X / r8) * (details.Satellite8.TrueRectangularCoordinates.X / r8));
details.Satellite8.ApparentRectangularCoordinates.Y = details.Satellite8.TrueRectangularCoordinates.Y;
details.Satellite8.ApparentRectangularCoordinates.Z = details.Satellite8.TrueRectangularCoordinates.Z;
//apply the perspective effect correction
double W = DELTA / (DELTA + details.Satellite1.TrueRectangularCoordinates.Z / 2475);
details.Satellite1.ApparentRectangularCoordinates.X *= W;
details.Satellite1.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite2.TrueRectangularCoordinates.Z / 2475);
details.Satellite2.ApparentRectangularCoordinates.X *= W;
details.Satellite2.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite3.TrueRectangularCoordinates.Z / 2475);
details.Satellite3.ApparentRectangularCoordinates.X *= W;
details.Satellite3.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite4.TrueRectangularCoordinates.Z / 2475);
details.Satellite4.ApparentRectangularCoordinates.X *= W;
details.Satellite4.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite5.TrueRectangularCoordinates.Z / 2475);
details.Satellite5.ApparentRectangularCoordinates.X *= W;
details.Satellite5.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite6.TrueRectangularCoordinates.Z / 2475);
details.Satellite6.ApparentRectangularCoordinates.X *= W;
details.Satellite6.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite7.TrueRectangularCoordinates.Z / 2475);
details.Satellite7.ApparentRectangularCoordinates.X *= W;
details.Satellite7.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite8.TrueRectangularCoordinates.Z / 2475);
details.Satellite8.ApparentRectangularCoordinates.X *= W;
details.Satellite8.ApparentRectangularCoordinates.Y *= W;
return(details);
}