protected override double AdjustAltitude(Body body)
{
/* Readjust moon altitude based on earth radius and refraction */
var horizon = 90.0;
var location = new NOVAS.OnSurface()
{
Latitude = Latitude,
Longitude = Longitude
};
var refraction = NOVAS.Refract(ref location, NOVAS.RefractionOption.StandardRefraction, horizon);;
var altitude = body.Altitude - Astrometry.ToDegree(Earth.Radius) / body.Distance + Astrometry.ToDegree(body.Radius) / body.Distance + refraction;
return(altitude);
}
public Task Calculate()
{
return(Task.Run(() => {
var jd = Astrometry.GetJulianDate(Date);
var deltaT = Astrometry.DeltaT(Date);
var location = new NOVAS.OnSurface()
{
Latitude = Latitude,
Longitude = Longitude
};
var observer = new NOVAS.Observer()
{
OnSurf = location,
Where = (short)NOVAS.ObserverLocation.EarthGeoCenter
};
var obj = new NOVAS.CelestialObject()
{
Name = Name,
Number = (short)BodyNumber,
Star = new NOVAS.CatalogueEntry(),
Type = (short)NOVAS.ObjectType.MajorPlanetSunOrMoon
};
var objPosition = new NOVAS.SkyPosition();
NOVAS.Place(jd + Astrometry.SecondsToDays(deltaT), obj, observer, deltaT, NOVAS.CoordinateSystem.EquinoxOfDate, NOVAS.Accuracy.Full, ref objPosition);
this.Distance = Astrometry.AUToKilometer(objPosition.Dis);
var siderealTime = Astrometry.GetLocalSiderealTime(Date, Longitude);
var hourAngle = Astrometry.HoursToDegrees(Astrometry.GetHourAngle(siderealTime, objPosition.RA));
this.Altitude = Astrometry.GetAltitude(hourAngle, Latitude, objPosition.Dec);
}));
}
/// <summary>
/// Calculates rise and set time
/// Caveat: does not consider more than one rise and one set event
/// </summary>
/// <returns></returns>
public Task <bool> Calculate()
{
return(Task.Run(async() => {
// Check rise and set events in two hour periods
var offset = 0;
do
{
// Shift date by offset
var offsetDate = Date.AddHours(offset);
// Get three body locations for date, date + 1 hour and date + 2 hours
var bodyAt0 = GetBody(offsetDate);
var bodyAt1 = GetBody(offsetDate.AddHours(1));
var bodyAt2 = GetBody(offsetDate.AddHours(2));
await Task.WhenAll(bodyAt0.Calculate(), bodyAt1.Calculate(), bodyAt2.Calculate());
var location = new NOVAS.OnSurface()
{
Latitude = Latitude,
Longitude = Longitude
};
// Adjust altitude for the three body parameters
var altitude0 = AdjustAltitude(bodyAt0);
var altitude1 = AdjustAltitude(bodyAt1);
var altitude2 = AdjustAltitude(bodyAt2);
// fit the three reference positions into a quadratic equation
//P1 (offsetDate | altitude0) => (0 | altitude0)
//P2 (offsetDate + 1 | altitude1) => (1 | altitude1)
//P3 (offsetDate + 2 | altitude2) => (2 | altitude2)
// ax² + bx + c
// Solve for c
// => altitude0 = 0 * x² + 0 * x + c => altitude0 = c
// Solve for b using c
// altitude1 = a * 1² + b * 1 + altitude0
// => altitude1 = a + b + altitude0
// => b = altitude1 - a - altitude0
// Solve for a using b and c
// altitude2 = a * 2² + b * 2 + altitude0
// => altitude2 = 4a + 2(altitude1 - a - altitude0) + altitude0
// => altitude2 = 4a + 2*altitude1 - 2a - 2*altitude0 + altitude0
// => altitude2 = 2a + 2*altitude1 - altitude0
// => 2a = altitude2 - 2*altitude1 + altitude0
// => a = 0.5 * altitude2 - altitude1 + 0.5 * altitude0
// => a = 0.5 * (altitude2 + altitude0) - altitude1
// Solve for b using a and c
// => b = altitude1 - (0.5 * (altitude2 + altitude0) - altitude1) - altitude0
// => b = altitude1 - 0.5 * altitude2 - 0.5 * altitude0 + altitude1 - altitude0
// => b = 2 * altitude1 - 0.5 * altitude2 - 1.5 * altitude0
var a = 0.5 * (altitude2 + altitude0) - altitude1;
var b = 2 * altitude1 - 0.5 * altitude2 - 1.5 * altitude0;
var c = altitude0;
// a-b-c formula
// x = -b +- Sqrt(b² - 4ac) / 2a
// Discriminant definition: b² - 4ac
var discriminant = (Math.Pow(b, 2)) - (4.0 * a * c);
var zeroPoint1 = double.NaN;
var zeroPoint2 = double.NaN;
var events = 0;
if (discriminant == 1)
{
zeroPoint1 = (-b + Math.Sqrt(discriminant)) / (2 * a);
if (zeroPoint1 >= 0 && zeroPoint1 <= 2)
{
events++;
}
}
else if (discriminant > 1)
{
zeroPoint1 = (-b + Math.Sqrt(discriminant)) / (2 * a);
zeroPoint2 = (-b - Math.Sqrt(discriminant)) / (2 * a);
// Check if zero point is inside the span of 0 to 2 (to be inside the checked timeframe)
if (zeroPoint1 >= 0 && zeroPoint1 <= 2)
{
events++;
}
if (zeroPoint2 >= 0 && zeroPoint2 <= 2)
{
events++;
}
if (zeroPoint1 < 0 || zeroPoint1 > 2)
{
zeroPoint1 = zeroPoint2;
}
}
//find the gradient at zeroPoint1. positive => rise event, negative => set event
var gradient = 2 * a * zeroPoint1 + b;
if (events == 1)
{
if (gradient > 0)
{
// rise
this.Rise = offsetDate.AddHours(zeroPoint1);
}
else
{
// set
this.Set = offsetDate.AddHours(zeroPoint1);
}
}
else if (events == 2)
{
if (gradient > 0)
{
// rise and set
this.Rise = offsetDate.AddHours(zeroPoint1);
this.Set = offsetDate.AddHours(zeroPoint2);
}
else
{
// set and rise
this.Rise = offsetDate.AddHours(zeroPoint2);
this.Set = offsetDate.AddHours(zeroPoint1);
}
}
offset += 2;
//Repeat until rise and set events are found, or after a whole day
} while (!((this.Rise != null && this.Set != null) || offset > 24));
return true;
}));
}
