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Astronomical Algorithms
The motions of Earth and planets are usually computed in ecliptic
coordinates, based on the plane of the ecliptic. The position of an object
is defined by the ecliptic latitude (=0 for the sun), the ecliptic
longitude, and the distance.
The figure represents the elliptical orbit of a body K, the Sun
situated in the focus S:
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We consider a fictitious body K' describing
a circular orbit around S with constant velocity, with the same period as
the real body K, and situated at P' at the
instance when the real body is at the perihelion P. The angle PSK' is
called mean anomaly M, increasing linearly with
time. The problem consists in finding the true anomaly (angle PSK) at a
given instant, when the mean anomaly M and the eccentricity of the ellipse
are known.
Julian Day (valid from
1900/3/1 to 2100/2/28)
Julian day: 86400 s, Julian year: 365.25 d, Julian Century: 36525 d
double JulianDay (int date, int month, int year, double UT)
{
if (month<=2) {month=month+12; year=year-1;}
return
(int)(365.25*year) + (int)(30.6001*(month+1)) - 15 + 1720996.5 + date +
UT/24.0;
}
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Solar Coordinates
(according to: Jean
Meeus: Astronomical Algorithms), accuracy of 0.01 degree
k = 2*PI/360;
M = 357.52910 + 35999.05030*T - 0.0001559*T*T - 0.00000048*T*T*T; //
mean anomaly, degree
L0 = 280.46645 + 36000.76983*T + 0.0003032*T*T; // mean longitude,
degree
DL = (1.914600 - 0.004817*T - 0.000014*T*T)*sin(k*M)
+ (0.019993 -
0.000101*T)*sin(k*2*M) + 0.000290*sin(k*3*M);
L = L0 + DL; // true longitude, degree
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convert ecliptic longitude
L to right ascension RA and declination delta
X = cos(L); Y = cos(eps)*sin(L); Z = sin(eps)*sin(L); R =
Math.sqrt(1.0-Z*Z);
eps = 23.43999; // obliquity of ecliptic
delta = (180/PI)*arctan(Z/R); // in degrees
RA = (24/PI)*arctan(Y/(X+R)); // in hours
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compute sidereal time
at Greenwich (according to: Jean Meeus:
Astronomical Algorithms)
T = (JD - 2451545.0 ) / 36525;
theta0 = 280.46061837 + 360.98564736629*(JD-2451545.0) +
0.000387933*T*T - T*T*T/38710000.0;
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convert tau, delta to horizon
coordinates of the observer (altitude h, azimuth az)
sin h = sin beta sin delta + cos beta
cos delta cos tau
tan az = (- sin tau) / (cos beta tan delta - sin
beta cos tau)
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"Positional Astronomy" "Sun, Moon & Earth
Applet"
Last update: 11/01/2001 | 