/// <summary>
/// Calculates angular separation between two points with geographical coordinates
/// </summary>
/// <param name="p1">Geographical coordinates of the first point</param>
/// <param name="p2">Geographical coordinates of the second point</param>
/// <returns>Angular separation in degrees</returns>
public static double Separation(CrdsGeographical p1, CrdsGeographical p2)
{
double a1 = ToRadians(p1.Latitude);
double a2 = ToRadians(p2.Latitude);
double A1 = To360(p1.Longitude);
double A2 = To360(p2.Longitude);
double a = Math.Acos(
Math.Sin(a1) * Math.Sin(a2) +
Math.Cos(a1) * Math.Cos(a2) * Math.Cos(ToRadians(A1 - A2)));
return(double.IsNaN(a) ? 0 : ToDegrees(a));
}
/// <summary>
/// Converts local horizontal coordinates to equatorial coordinates.
/// </summary>
/// <param name="hor">Pair of local horizontal coordinates.</param>
/// <param name="geo">Geographical of the observer</param>
/// <param name="theta0">Local sidereal time.</param>
/// <returns>Pair of equatorial coordinates</returns>
public static CrdsEquatorial ToEquatorial(this CrdsHorizontal hor, CrdsGeographical geo, double theta0)
{
CrdsEquatorial eq = new CrdsEquatorial();
double A = Angle.ToRadians(hor.Azimuth);
double h = Angle.ToRadians(hor.Altitude);
double phi = Angle.ToRadians(geo.Latitude);
double Y = Math.Sin(A);
double X = Math.Cos(A) * Math.Sin(phi) + Math.Tan(h) * Math.Cos(phi);
double H = Angle.ToDegrees(Math.Atan2(Y, X));
eq.Alpha = Angle.To360(theta0 - geo.Longitude - H);
eq.Delta = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(h) - Math.Cos(phi) * Math.Cos(h) * Math.Cos(A)));
return(eq);
}
/// <summary>
/// Converts equatorial coodinates to local horizontal
/// </summary>
/// <param name="eq">Pair of equatorial coodinates</param>
/// <param name="geo">Geographical coordinates of the observer</param>
/// <param name="theta0">Local sidereal time</param>
/// <remarks>
/// Implementation is taken from AA(I), formulae 12.5, 12.6.
/// </remarks>
public static CrdsHorizontal ToHorizontal(this CrdsEquatorial eq, CrdsGeographical geo, double theta0)
{
double H = Angle.ToRadians(HourAngle(theta0, geo.Longitude, eq.Alpha));
double phi = Angle.ToRadians(geo.Latitude);
double delta = Angle.ToRadians(eq.Delta);
CrdsHorizontal hor = new CrdsHorizontal();
double Y = Math.Sin(H);
double X = Math.Cos(H) * Math.Sin(phi) - Math.Tan(delta) * Math.Cos(phi);
hor.Altitude = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(delta) + Math.Cos(phi) * Math.Cos(delta) * Math.Cos(H)));
hor.Azimuth = Angle.ToDegrees(Math.Atan2(Y, X));
hor.Azimuth = Angle.To360(hor.Azimuth);
return(hor);
}
/// <summary>
/// Calculates topocentric equatorial coordinates of celestial body
/// with taking into account correction for parallax.
/// </summary>
/// <param name="eq">Geocentric equatorial coordinates of the body</param>
/// <param name="geo">Geographical coordinates of the body</param>
/// <param name="theta0">Apparent sidereal time at Greenwich</param>
/// <param name="pi">Parallax of a body</param>
/// <returns>Topocentric equatorial coordinates of the celestial body</returns>
/// <remarks>
/// Method is taken from AA(II), formulae 40.6-40.7.
/// </remarks>
public static CrdsEquatorial ToTopocentric(this CrdsEquatorial eq, CrdsGeographical geo, double theta0, double pi)
{
double H = Angle.ToRadians(HourAngle(theta0, geo.Longitude, eq.Alpha));
double delta = Angle.ToRadians(eq.Delta);
double sinPi = Math.Sin(Angle.ToRadians(pi));
double A = Math.Cos(delta) * Math.Sin(H);
double B = Math.Cos(delta) * Math.Cos(H) - geo.RhoCosPhi * sinPi;
double C = Math.Sin(delta) - geo.RhoSinPhi * sinPi;
double q = Math.Sqrt(A * A + B * B + C * C);
double H_ = Angle.ToDegrees(Math.Atan2(A, B));
double alpha_ = Angle.To360(theta0 - geo.Longitude - H_);
double delta_ = Angle.ToDegrees(Math.Asin(C / q));
return(new CrdsEquatorial(alpha_, delta_));
}
public CrdsGeographical(CrdsGeographical other)
: this(other.Longitude, other.Latitude, other.UtcOffset, other.Elevation, other.TimeZoneId, other.LocationName)
{
}
/// <summary>
/// Calculates instants of rising, transit and setting for non-stationary celestial body for the desired date.
/// Non-stationary in this particular case means that body has fastly changing celestial coordinates during the day.
/// </summary>
/// <param name="eq">Array of three equatorial coordinates of the celestial body correspoding to local midnight, local noon, and local midnight of the following day after the desired date respectively.</param>
/// <param name="location">Geographical location of the observation point.</param>
/// <param name="theta0">Apparent sidereal time at Greenwich for local midnight of the desired date.</param>
/// <param name="pi">Horizontal equatorial parallax of the body.</param>
/// <param name="sd">Visible semidiameter of the body, expressed in degrees.</param>
/// <returns>Instants of rising, transit and setting for the celestial body for the desired date.</returns>
public static RTS RiseTransitSet(CrdsEquatorial[] eq, CrdsGeographical location, double theta0, double pi = 0, double sd = 0)
{
if (eq.Length != 3)
{
throw new ArgumentException("Number of equatorial coordinates in the array should be equal to 3.");
}
double[] alpha = new double[3];
double[] delta = new double[3];
for (int i = 0; i < 3; i++)
{
alpha[i] = eq[i].Alpha;
delta[i] = eq[i].Delta;
}
Angle.Align(alpha);
Angle.Align(delta);
List <CrdsHorizontal> hor = new List <CrdsHorizontal>();
for (int i = 0; i <= 24; i++)
{
double n = i / 24.0;
CrdsEquatorial eq0 = InterpolateEq(alpha, delta, n);
var sidTime = InterpolateSiderialTime(theta0, n);
hor.Add(eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime));
}
var result = new RTS();
for (int i = 0; i < 24; i++)
{
double n = (i + 0.5) / 24.0;
CrdsEquatorial eq0 = InterpolateEq(alpha, delta, n);
var sidTime = InterpolateSiderialTime(theta0, n);
var hor0 = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime);
if (double.IsNaN(result.Transit) && hor0.Altitude > 0)
{
double r = SolveParabola(Math.Sin(Angle.ToRadians(hor[i].Azimuth)), Math.Sin(Angle.ToRadians(hor0.Azimuth)), Math.Sin(Angle.ToRadians(hor[i + 1].Azimuth)));
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
eq0 = InterpolateEq(alpha, delta, t);
sidTime = InterpolateSiderialTime(theta0, t);
result.Transit = t;
result.TransitAltitude = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Altitude;
}
}
if (double.IsNaN(result.Rise) || double.IsNaN(result.Set))
{
double r = SolveParabola(hor[i].Altitude + sd, hor0.Altitude + sd, hor[i + 1].Altitude + sd);
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
eq0 = InterpolateEq(alpha, delta, t);
sidTime = InterpolateSiderialTime(theta0, t);
if (double.IsNaN(result.Rise) && hor[i].Altitude + sd < 0 && hor[i + 1].Altitude + sd > 0)
{
result.Rise = t;
result.RiseAzimuth = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Azimuth;
}
if (double.IsNaN(result.Set) && hor[i].Altitude + sd > 0 && hor[i + 1].Altitude + sd < 0)
{
result.Set = t;
result.SetAzimuth = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Azimuth;
}
if (!double.IsNaN(result.Transit) && !double.IsNaN(result.Rise) && !double.IsNaN(result.Set))
{
break;
}
}
}
}
return(result);
}
/// <summary>
/// Calculates visibity details for the celestial body,
/// </summary>
/// <param name="eqBody">Mean equatorial coordinates of the body for the desired day.</param>
/// <param name="eqSun">Mean equatorial coordinates of the Sun for the desired day.</param>
/// <param name="minAltitude">Minimal altitude of the body, in degrees, to be considered as approproate for observations. By default it's 5 degrees for planet.</param>
/// <returns><see cref="VisibilityDetails"/> instance describing details of visibility.</returns>
// TODO: tests
public static VisibilityDetails Details(CrdsEquatorial eqBody, CrdsEquatorial eqSun, CrdsGeographical location, double theta0, double minAltitude = 5)
{
var details = new VisibilityDetails();
// period when the planet is above the horizon and its altitude is larger than "minAltitude"
RTS body = RiseTransitSet(eqBody, location, theta0, minAltitude);
// period when the Sun is above the horizon
RTS sun = RiseTransitSet(eqSun, location, theta0);
// body reaches minimal altitude but Sun does not rise at all (polar night)
if (body.TransitAltitude > minAltitude && sun.TransitAltitude <= 0)
{
details.Period = VisibilityPeriod.WholeNight;
details.Duration = body.Duration * 24;
}
// body does not reach the minimal altitude during the day
else if (body.TransitAltitude <= minAltitude)
{
details.Period = VisibilityPeriod.Invisible;
details.Duration = 0;
}
// there is a day/night change during the day and body reaches minimal altitude
else if (body.TransitAltitude > minAltitude)
{
// "Sun is below horizon" time range, expressed in degrees (0 is midnight, 180 is noon)
var r1 = new AngleRange(sun.Set * 360, (1 - sun.Duration) * 360);
// "body is above horizon" time range, expressed in degrees (0 is midnight, 180 is noon)
var r2 = new AngleRange(body.Rise * 360, body.Duration * 360);
// find the intersections of two ranges
var ranges = r1.Overlaps(r2);
// no intersections of time ranges
if (!ranges.Any())
{
details.Period = VisibilityPeriod.Invisible;
details.Duration = 0;
details.Begin = double.NaN;
details.End = double.NaN;
}
// the body is observable during the day
else
{
// duration of visibility
details.Duration = ranges.Sum(i => i.Range / 360 * 24);
// beginning of visibility
details.Begin = ranges.First().Start / 360;
// end of visibility
details.End = (details.Begin + details.Duration / 24) % 1;
// Evening time range, expressed in degrees
// Start is a sunset time, range is a timespan from sunset to midnight.
var rE = new AngleRange(sun.Set * 360, (1 - sun.Set) * 360);
// Night time range, expressed in degrees
// Start is a midnight time, range is a half of timespan from midnight to sunrise
var rN = new AngleRange(0, sun.Rise / 2 * 360);
// Morning time range, expressed in degrees
// Start is a half of time from midnight to sunrise, range is a time to sunrise
var rM = new AngleRange(sun.Rise / 2 * 360, sun.Rise / 2 * 360);
foreach (var r in ranges)
{
var isEvening = r.Overlaps(rE);
if (isEvening.Any())
{
details.Period |= VisibilityPeriod.Evening;
}
var isNight = r.Overlaps(rN);
if (isNight.Any())
{
details.Period |= VisibilityPeriod.Night;
}
var isMorning = r.Overlaps(rM);
if (isMorning.Any())
{
details.Period |= VisibilityPeriod.Morning;
}
}
}
}
return(details);
}
/// <summary>
/// Calculates instants of rising, transit and setting for stationary celestial body for the desired date.
/// Stationary in this particular case means that body has unchanged (or slightly changing) celestial coordinates during the day.
/// </summary>
/// <param name="eq">Equatorial coordinates of the celestial body.</param>
/// <param name="location">Geographical location of the observation point.</param>
/// <param name="theta0">Apparent sidereal time at Greenwich for local midnight of the desired date.</param>
/// <param name="minAltitude">Minimal altitude of the body above the horizon, in degrees, to detect rise/set. Used only for calculating visibility conditions.</param>
/// <returns>Instants of rising, transit and setting for the celestial body for the desired date.</returns>
public static RTS RiseTransitSet(CrdsEquatorial eq, CrdsGeographical location, double theta0, double minAltitude = 0)
{
List <CrdsHorizontal> hor = new List <CrdsHorizontal>();
for (int i = 0; i <= 24; i++)
{
double n = i / 24.0;
var sidTime = InterpolateSiderialTime(theta0, n);
hor.Add(eq.ToHorizontal(location, sidTime));
}
var result = new RTS();
for (int i = 0; i < 24; i++)
{
double n = (i + 0.5) / 24.0;
var sidTime = InterpolateSiderialTime(theta0, n);
var hor0 = eq.ToHorizontal(location, sidTime);
if (double.IsNaN(result.Transit) && hor0.Altitude > 0)
{
double r = SolveParabola(Math.Sin(Angle.ToRadians(hor[i].Azimuth)), Math.Sin(Angle.ToRadians(hor0.Azimuth)), Math.Sin(Angle.ToRadians(hor[i + 1].Azimuth)));
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
sidTime = InterpolateSiderialTime(theta0, t);
result.Transit = t;
result.TransitAltitude = eq.ToHorizontal(location, sidTime).Altitude;
}
}
if (double.IsNaN(result.Rise) || double.IsNaN(result.Set))
{
double r = SolveParabola(hor[i].Altitude - minAltitude, hor0.Altitude - minAltitude, hor[i + 1].Altitude - minAltitude);
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
sidTime = InterpolateSiderialTime(theta0, t);
if (double.IsNaN(result.Rise) && hor[i].Altitude - minAltitude < 0 && hor[i + 1].Altitude - minAltitude > 0)
{
result.Rise = t;
result.RiseAzimuth = eq.ToHorizontal(location, sidTime).Azimuth;
}
if (double.IsNaN(result.Set) && hor[i].Altitude - minAltitude > 0 && hor[i + 1].Altitude - minAltitude < 0)
{
result.Set = t;
result.SetAzimuth = eq.ToHorizontal(location, sidTime).Azimuth;
}
if (!double.IsNaN(result.Transit) && !double.IsNaN(result.Rise) && !double.IsNaN(result.Set))
{
break;
}
}
}
}
return(result);
}
