/*! \fn double ln_solve_kepler (double E, double M);
* \param E Orbital eccentricity
* \param M Mean anomaly
* \return Eccentric anomaly
*
* Calculate the eccentric anomaly.
* This method was devised by Roger Sinnott. (Sky and Telescope, Vol 70, pg 159)
*/
double ln_solve_kepler (double e, double M)
{
double Eo = M_PI_2;
double F, M1;
double D = M_PI_4;
int i;
/* covert to radians */
M = ln_deg_to_rad (M);
F = sgn (M);
M = fabs (M) / (2.0 * M_PI);
M = (M - (int)M) * 2.0 * M_PI * F;
if (M < 0)
M = M + 2.0 * M_PI;
F = 1.0;
if (M > M_PI)
F = -1.0;
if (M > M_PI)
M = 2.0 * M_PI - M;
for (i = 0; i < KEPLER_STEPS; i++) {
M1 = Eo - e * sin (Eo);
Eo = Eo + D * sgn (M - M1);
D /= 2.0;
}
Eo *= F;
/* back to degrees */
Eo = ln_rad_to_deg (Eo);
return Eo;
}
/*! \fn double ln_get_refraction_adj (double altitude, double atm_pres, double temp)
* \param altitude The altitude of the object above the horizon in degrees
* \param atm_pres Atmospheric pressure in milibars
* \param temp Temperature in degrees C.
* \return Adjustment in objects altitude in degrees.
*
* Calculate the adjustment in altitude of a body due to atmosphric
* refraction. This value varies over altitude, pressure and temperature.
*
* Note: Default values for pressure and teperature are 1010 mBar and 10C
* respectively.
*/
double ln_get_refraction_adj (double altitude, double atm_pres, double temp)
{
long double R;
/* equ 16.3 */
R = 1.0 / tan (ln_deg_to_rad (altitude + (7.31 / (altitude + 4.4))));
R -= 0.06 * sin (ln_deg_to_rad (14.7 * (R / 60.0) + 13.0));
/* take into account of atm press and temp */
R *= ((atm_pres / 1010) * (283 / (273 + temp)));
/* convert from arcminutes to degrees */
R /= 60.0;
return R;
}
/* Equ 20.2, 20.4 pg 126 */
void ln_get_equ_prec2 (struct ln_equ_posn * mean_position, double fromJD, double toJD, struct ln_equ_posn * position)
{
long double t, t2, t3, A, B, C, zeta, eta, theta, ra, dec, mean_ra, mean_dec, T, T2;
/* change original ra and dec to radians */
mean_ra = ln_deg_to_rad (mean_position->ra);
mean_dec = ln_deg_to_rad (mean_position->dec);
/* calc t, T, zeta, eta and theta Equ 20.2 */
T = ((long double) (fromJD - JD2000)) / 36525.0;
T *= 1.0 / 3600.0;
t = ((long double) (toJD - fromJD)) / 36525.0;
t *= 1.0 / 3600.0;
T2 = T * T;
t2 = t * t;
t3 = t2 *t;
zeta = (2306.2181 + 1.39656 * T - 0.000139 * T2) * t + (0.30188 - 0.000344 * T) * t2 + 0.017998 * t3;
eta = (2306.2181 + 1.39656 * T - 0.000139 * T2) * t + (1.09468 + 0.000066 * T) * t2 + 0.018203 * t3;
theta = (2004.3109 - 0.85330 * T - 0.000217 * T2) * t - (0.42665 + 0.000217 * T) * t2 - 0.041833 * t3;
zeta = ln_deg_to_rad (zeta);
eta = ln_deg_to_rad (eta);
theta = ln_deg_to_rad (theta);
/* calc A,B,C equ 20.4 */
A = cosl (mean_dec) * sinl (mean_ra + zeta);
B = cosl (theta) * cosl (mean_dec) * cosl (mean_ra + zeta) - sinl (theta) * sinl (mean_dec);
C = sinl (theta) * cosl (mean_dec) * cosl (mean_ra + zeta) + cosl (theta) * sinl (mean_dec);
ra = atan2l (A,B) + eta;
/* check for object near celestial pole */
if (mean_dec > (0.4 * M_PI) || mean_dec < (-0.4 * M_PI)) {
/* close to pole */
dec = acosl (sqrt(A * A + B * B));
if (mean_dec < 0.)
dec *= -1; /* 0 <= acos() <= PI */
} else {
/* not close to pole */
dec = asinl (C);
}
/* change to degrees */
position->ra = ln_range_degrees (ln_rad_to_deg (ra));
position->dec = ln_rad_to_deg (dec);
}
/* equ 30.1 */
double ln_get_ell_true_anomaly (double e, double E)
{
double v;
E = ln_deg_to_rad (E);
v = sqrt ((1.0 + e) / (1.0 - e)) * tan (E / 2.0);
v = 2.0 * atan (v);
v = ln_range_degrees (ln_rad_to_deg (v));
return v;
}
/* Equ 20.3, 20.4 pg 126
*/
void ln_get_equ_prec (struct ln_equ_posn * mean_position, double JD, struct ln_equ_posn * position)
{
long double t, t2, t3, A, B, C, zeta, eta, theta, ra, dec, mean_ra, mean_dec;
/* change original ra and dec to radians */
mean_ra = ln_deg_to_rad (mean_position->ra);
mean_dec = ln_deg_to_rad (mean_position->dec);
/* calc t, zeta, eta and theta for J2000.0 Equ 20.3 */
t = (JD - JD2000) / 36525.0;
t *= 1.0 / 3600.0;
t2 = t * t;
t3 = t2 *t;
zeta = 2306.2181 * t + 0.30188 * t2 + 0.017998 * t3;
eta = 2306.2181 * t + 1.09468 * t2 + 0.041833 * t3;
theta = 2004.3109 * t - 0.42665 * t2 - 0.041833 * t3;
zeta = ln_deg_to_rad (zeta);
eta = ln_deg_to_rad (eta);
theta = ln_deg_to_rad (theta);
/* calc A,B,C equ 20.4 */
A = cosl (mean_dec) * sinl (mean_ra + zeta);
B = cosl (theta) * cosl (mean_dec) * cosl (mean_ra + zeta) - sinl (theta) * sinl (mean_dec);
C = sinl (theta) * cosl (mean_dec) * cosl (mean_ra + zeta) + cosl (theta) * sinl (mean_dec);
ra = atan2l (A,B) + eta;
/* check for object near celestial pole */
if (mean_dec > (0.4 * M_PI) || mean_dec < (-0.4 * M_PI)) {
/* close to pole */
dec = acosl (sqrt(A * A + B * B));
if (mean_dec < 0.)
dec *= -1; /* 0 <= acos() <= PI */
} else {
/* not close to pole */
dec = asinl (C);
}
/* change to degrees */
position->ra = ln_range_degrees (ln_rad_to_deg (ra));
position->dec = ln_rad_to_deg (dec);
}
/*! \fn double ln_get_heliocentric_time_diff (double JD, struct ln_equ_posn * object)
* \param JD Julian day
* \param object Pointer to object (RA, DEC) for which heliocentric correction will be caculated
*
* \return Heliocentric correction in fraction of day
*
* Calculate heliocentric corection for object at given coordinates and on given
* date.
*/
double ln_get_heliocentric_time_diff (double JD, struct ln_equ_posn *object)
{
double theta, ra, dec, c_dec, obliq;
struct ln_nutation nutation;
struct ln_helio_posn earth;
ln_get_nutation (JD, &nutation);
ln_get_earth_helio_coords (JD, &earth);
theta = ln_deg_to_rad (ln_range_degrees (earth.L + 180));
ra = ln_deg_to_rad (object->ra);
dec = ln_deg_to_rad (object->dec);
c_dec = cos (dec);
obliq = ln_deg_to_rad (nutation.ecliptic);
/* L.Binnendijk Properties of Double Stars, Philadelphia, University of Pennselvania Press, pp. 228-232, 1960 */
return -0.0057755 * earth.R * (
cos (theta) * cos (ra) * c_dec
+ sin (theta) * (sin (obliq) * sin (dec) + cos (obliq) * c_dec * sin (ra)));
}
/*! \fn void ln_get_ell_helio_rect_posn (struct ln_ell_orbit* orbit, double JD, struct ln_rect_posn* posn);
* \param orbit Orbital parameters of object.
* \param JD Julian day
* \param posn Position pointer to store objects position
*
* Calculate the objects rectangular heliocentric position given it's orbital
* elements for the given julian day.
*/
void ln_get_ell_helio_rect_posn (struct ln_ell_orbit* orbit, double JD, struct ln_rect_posn* posn)
{
double A,B,C;
double F,G,H;
double P,Q,R;
double sin_e, cos_e;
double a,b,c;
double sin_omega, sin_i, cos_omega, cos_i;
double M,v,E,r;
/* J2000 obliquity of the ecliptic */
sin_e = 0.397777156;
cos_e = 0.917482062;
/* equ 33.7 */
sin_omega = sin (ln_deg_to_rad (orbit->omega));
cos_omega = cos (ln_deg_to_rad (orbit->omega));
sin_i = sin (ln_deg_to_rad (orbit->i));
cos_i = cos (ln_deg_to_rad (orbit->i));
F = cos_omega;
G = sin_omega * cos_e;
H = sin_omega * sin_e;
P = -sin_omega * cos_i;
Q = cos_omega * cos_i * cos_e - sin_i * sin_e;
R = cos_omega * cos_i * sin_e + sin_i * cos_e;
/* equ 33.8 */
A = atan2 (F,P);
B = atan2 (G,Q);
C = atan2 (H,R);
a = sqrt (F * F + P * P);
b = sqrt (G * G + Q * Q);
c = sqrt (H * H + R * R);
/* get daily motion */
if (orbit->n == 0)
orbit->n = ln_get_ell_mean_motion (orbit->a);
/* get mean anomaly */
M = ln_get_ell_mean_anomaly (orbit->n, JD - orbit->JD);
/* get eccentric anomaly */
E = ln_solve_kepler (orbit->e, M);
/* get true anomaly */
v = ln_get_ell_true_anomaly (orbit->e, E);
/* get radius vector */
r = ln_get_ell_radius_vector (orbit->a, orbit->e, E);
/* equ 33.9 */
posn->X = r * a * sin (A + ln_deg_to_rad(orbit->w + v));
posn->Y = r * b * sin (B + ln_deg_to_rad(orbit->w + v));
posn->Z = r * c * sin (C + ln_deg_to_rad(orbit->w + v));
}
/*! \fn void ln_get_par_helio_rect_posn (struct ln_par_orbit* orbit, double JD, struct ln_rect_posn* posn);
* \param orbit Orbital parameters of object.
* \param JD Julian day
* \param posn Position pointer to store objects position
*
* Calculate the objects rectangular heliocentric position given it's orbital
* elements for the given julian day.
*/
void ln_get_par_helio_rect_posn (struct ln_par_orbit* orbit, double JD, struct ln_rect_posn* posn)
{
double A,B,C;
double F,G,H;
double P,Q,R;
double sin_e, cos_e;
double a,b,c;
double sin_omega, sin_i, cos_omega, cos_i;
double r,v,t;
/* time since perihelion */
t = JD - orbit->JD;
/* J2000 obliquity of the ecliptic */
sin_e = 0.397777156;
cos_e = 0.917482062;
/* equ 33.7 */
sin_omega = sin (ln_deg_to_rad (orbit->omega));
cos_omega = cos (ln_deg_to_rad (orbit->omega));
sin_i = sin (ln_deg_to_rad (orbit->i));
cos_i = cos (ln_deg_to_rad (orbit->i));
F = cos_omega;
G = sin_omega * cos_e;
H = sin_omega * sin_e;
P = -sin_omega * cos_i;
Q = cos_omega * cos_i * cos_e - sin_i * sin_e;
R = cos_omega * cos_i * sin_e + sin_i * cos_e;
/* equ 33.8 */
A = atan2 (F,P);
B = atan2 (G,Q);
C = atan2 (H,R);
a = sqrt (F * F + P * P);
b = sqrt (G * G + Q * Q);
c = sqrt (H * H + R * R);
/* get true anomaly */
v = ln_get_par_true_anomaly (orbit->q, t);
/* get radius vector */
r = ln_get_par_radius_vector (orbit->q, t);
/* equ 33.9 */
posn->X = r * a * sin (A + ln_deg_to_rad(orbit->w + v));
posn->Y = r * b * sin (B + ln_deg_to_rad(orbit->w + v));
posn->Z = r * c * sin (C + ln_deg_to_rad(orbit->w + v));
}
double ln_get_apparent_sidereal_time (double JD)
{
double correction, sidereal;
struct ln_nutation nutation;
/* get the mean sidereal time */
sidereal = ln_get_mean_sidereal_time (JD);
/* add corrections for nutation in longitude and for the true obliquity of
the ecliptic */
ln_get_nutation (JD, &nutation);
correction = (nutation.longitude / 15.0 * cos (ln_deg_to_rad(nutation.obliquity)));
sidereal += correction;
return sidereal;
}
/*! \fn double ln_get_ell_body_phase_angle (double JD, struct ln_ell_orbit * orbit);
* \param JD Julian day
* \param orbit Orbital parameters
* \return Phase angle.
*
* Calculate the phase angle of the body. The angle Sun - body - Earth.
*/
double ln_get_ell_body_phase_angle (double JD, struct ln_ell_orbit * orbit)
{
double r,R,d;
double E,M;
double phase;
/* get mean anomaly */
if (orbit->n == 0)
orbit->n = ln_get_ell_mean_motion (orbit->a);
M = ln_get_ell_mean_anomaly (orbit->n, JD - orbit->JD);
/* get eccentric anomaly */
E = ln_solve_kepler (orbit->e, M);
/* get radius vector */
r = ln_get_ell_radius_vector (orbit->a, orbit->e, E);
/* get solar and Earth distances */
R = ln_get_ell_body_earth_dist (JD, orbit);
d = ln_get_ell_body_solar_dist (JD, orbit);
phase = (r * r + d * d - R * R) / ( 2.0 * r * d );
return ln_range_degrees(acos (ln_deg_to_rad (phase)));
}
int ln_get_object_rst_horizon_offset (double JD, struct ln_lnlat_posn * observer,
struct ln_equ_posn * object, long double horizon, struct ln_rst_time * rst, double ut_offset)
{
int jd;
long double O, JD_UT, H0, H1;
double Hat, Har, Has, altr, alts;
double mt, mr, ms, mst, msr, mss;
double dmt, dmr, dms;
int ret, i;
if (isnan (ut_offset))
{
JD_UT = JD;
}
else
{
/* convert local sidereal time into degrees
for 0h of UT on day JD */
jd = (int)JD;
JD_UT = jd + ut_offset;
}
O = ln_get_apparent_sidereal_time (JD_UT);
O *= 15.0;
/* equ 15.1 */
H0 = (sin (ln_deg_to_rad (horizon)) -
sin (ln_deg_to_rad (observer->lat)) * sin (ln_deg_to_rad (object->dec)));
H1 = (cos (ln_deg_to_rad (observer->lat)) * cos (ln_deg_to_rad (object->dec)));
H1 = H0 / H1;
ret = check_coords (observer, H1, horizon, object);
if (ret)
return ret;
H0 = acos (H1);
H0 = ln_rad_to_deg (H0);
/* equ 15.2 */
mt = (object->ra - observer->lng - O) / 360.0;
mr = mt - H0 / 360.0;
ms = mt + H0 / 360.0;
for (i = 0; i < 3; i++)
{
/* put in correct range */
if (mt > 1.0)
mt--;
else if (mt < 0)
mt++;
if (mr > 1.0)
mr--;
else if (mr < 0)
mr++;
if (ms > 1.0)
ms--;
else if (ms < 0)
ms++;
/* find sidereal time at Greenwich, in degrees, for each m */
mst = O + 360.985647 * mt;
msr = O + 360.985647 * mr;
mss = O + 360.985647 * ms;
/* find local hour angle */
Hat = mst + observer->lng - object->ra;
Har = msr + observer->lng - object->ra;
Has = mss + observer->lng - object->ra;
/* find altitude for rise and set */
altr = sin (ln_deg_to_rad (observer->lat)) * sin (ln_deg_to_rad (object->dec)) +
cos (ln_deg_to_rad (observer->lat)) * cos (ln_deg_to_rad (object->dec)) *
cos (ln_deg_to_rad (Har));
alts = sin (ln_deg_to_rad (observer->lat)) * sin (ln_deg_to_rad (object->dec)) +
cos (ln_deg_to_rad (observer->lat)) * cos (ln_deg_to_rad (object->dec)) *
cos (ln_deg_to_rad (Has));
/* must be in degrees */
altr = ln_rad_to_deg (altr);
alts = ln_rad_to_deg (alts);
/* corrections for m */
ln_range_degrees (Hat);
if (Hat > 180.0)
Hat -= 360;
dmt = -(Hat / 360.0);
dmr = (altr - horizon) / (360 * cos (ln_deg_to_rad (object->dec)) * cos (ln_deg_to_rad (observer->lat)) * sin (ln_deg_to_rad (Har)));
dms = (alts - horizon) / (360 * cos (ln_deg_to_rad (object->dec)) * cos (ln_deg_to_rad (observer->lat)) * sin (ln_deg_to_rad (Has)));
/* add corrections and change to JD */
mt += dmt;
mr += dmr;
ms += dms;
if (mt <= 1 && mt >= 0 && mr <= 1 && mr >= 0 && ms <= 1 && ms >= 0)
break;
}
rst->rise = JD_UT + mr;
rst->transit = JD_UT + mt;
rst->set = JD_UT + ms;
/* not circumpolar */
return 0;
}
int ln_get_motion_body_rst_horizon_offset (double JD, struct ln_lnlat_posn * observer, get_motion_body_coords_t get_motion_body_coords,
void * orbit, double horizon, struct ln_rst_time * rst, double ut_offset)
{
int jd;
double T, O, JD_UT, H0, H1;
double Hat, Har, Has, altr, alts;
double mt, mr, ms, mst, msr, mss, nt, nr, ns;
struct ln_equ_posn sol1, sol2, sol3, post, posr, poss;
double dmt, dmr, dms;
int ret, i;
/* dynamical time diff */
T = ln_get_dynamical_time_diff (JD);
if (isnan (ut_offset))
{
JD_UT = JD;
}
else
{
jd = (int)JD;
JD_UT = jd + ut_offset;
}
O = ln_get_apparent_sidereal_time (JD_UT);
O *= 15.0;
/* get body coords for JD_UT -1, JD_UT and JD_UT + 1 */
get_motion_body_coords (JD_UT - 1.0, orbit, &sol1);
get_motion_body_coords (JD_UT, orbit, &sol2);
get_motion_body_coords (JD_UT + 1.0, orbit, &sol3);
/* equ 15.1 */
H0 = (sin(ln_deg_to_rad (horizon)) - sin(ln_deg_to_rad(observer->lat)) * sin(ln_deg_to_rad(sol2.dec)));
H1 = (cos(ln_deg_to_rad(observer->lat)) * cos(ln_deg_to_rad(sol2.dec)));
H1 = H0 / H1;
ret = check_coords (observer, H1, horizon, &sol2);
if (ret)
return ret;
H0 = acos (H1);
H0 = ln_rad_to_deg (H0);
/* correct ra values for interpolation - put them to the same side of circle */
if ((sol1.ra - sol2.ra) > 180.0)
sol2.ra += 360;
if ((sol2.ra - sol3.ra) > 180.0)
sol3.ra += 360;
if ((sol3.ra - sol2.ra) > 180.0)
sol3.ra -= 360;
if ((sol2.ra - sol1.ra) > 180.0)
sol3.ra -= 360;
for (i = 0; i < 3; i++)
{
/* equ 15.2 */
mt = (sol2.ra - observer->lng - O) / 360.0;
mr = mt - H0 / 360.0;
ms = mt + H0 / 360.0;
/* put in correct range */
if (mt > 1.0 )
mt--;
else if (mt < 0.0)
mt++;
if (mr > 1.0 )
mr--;
else if (mr < 0.0)
mr++;
if (ms > 1.0 )
ms--;
else if (ms < 0.0)
ms++;
/* find sidereal time at Greenwich, in degrees, for each m*/
mst = O + 360.985647 * mt;
msr = O + 360.985647 * mr;
mss = O + 360.985647 * ms;
nt = mt + T / 86400.0;
nr = mr + T / 86400.0;
ns = ms + T / 86400.0;
/* interpolate ra and dec for each m, except for transit dec (dec2) */
posr.ra = ln_interpolate3 (nr, sol1.ra, sol2.ra, sol3.ra);
posr.dec = ln_interpolate3 (nr, sol1.dec, sol2.dec, sol3.dec);
post.ra = ln_interpolate3 (nt, sol1.ra, sol2.ra, sol3.ra);
poss.ra = ln_interpolate3 (ns, sol1.ra, sol2.ra, sol3.ra);
poss.dec = ln_interpolate3 (ns, sol1.dec, sol2.dec, sol3.dec);
/* find local hour angle */
Hat = mst + observer->lng - post.ra;
Har = msr + observer->lng - posr.ra;
Has = mss + observer->lng - poss.ra;
/* find altitude for rise and set */
altr = sin(ln_deg_to_rad(observer->lat)) * sin(ln_deg_to_rad(posr.dec)) +
cos(ln_deg_to_rad(observer->lat)) * cos(ln_deg_to_rad(posr.dec)) * cos(ln_deg_to_rad (Har));
alts = sin(ln_deg_to_rad(observer->lat)) * sin(ln_deg_to_rad(poss.dec)) +
cos(ln_deg_to_rad(observer->lat)) * cos(ln_deg_to_rad(poss.dec)) * cos(ln_deg_to_rad (Has));
/* corrections for m */
dmt = - (Hat / 360.0);
dmr = (altr - horizon) / (360 * cos(ln_deg_to_rad(posr.dec)) * cos(ln_deg_to_rad(observer->lat)) * sin(ln_deg_to_rad(Har)));
dms = (alts - horizon) / (360 * cos(ln_deg_to_rad(poss.dec)) * cos(ln_deg_to_rad(observer->lat)) * sin(ln_deg_to_rad(Has)));
/* add corrections and change to JD */
mt += dmt;
mr += dmr;
ms += dms;
if (mt <= 1 && mt >= 0 && mr <= 1 && mr >= 0 && ms <= 1 && ms >= 0)
break;
}
rst->rise = JD_UT + mr;
rst->transit = JD_UT + mt;
rst->set = JD_UT + ms;
/* not circumpolar */
return 0;
}
/* equ 30.2 */
double ln_get_ell_radius_vector (double a, double e, double E)
{
return a * ( 1.0 - e * cos (ln_deg_to_rad (E)));
}
void ln_get_nutation (double JD, struct ln_nutation * nutation)
{
long double D,M,MM,F,O,T,T2,T3,JDE;
long double coeff_sine, coeff_cos;
long double argument;
int i;
/* should we bother recalculating nutation */
if (fabs(JD - c_JD) > LN_NUTATION_EPOCH_THRESHOLD) {
/* set the new epoch */
c_JD = JD;
/* get julian ephemeris day */
JDE = ln_get_jde (JD);
/* calc T */
T = (JDE - 2451545.0)/36525;
T2 = T * T;
T3 = T2 * T;
/* calculate D,M,M',F and Omega */
D = 297.85036 + 445267.111480 * T - 0.0019142 * T2 + T3 / 189474.0;
M = 357.52772 + 35999.050340 * T - 0.0001603 * T2 - T3 / 300000.0;
MM = 134.96298 + 477198.867398 * T + 0.0086972 * T2 + T3 / 56250.0;
F = 93.2719100 + 483202.017538 * T - 0.0036825 * T2 + T3 / 327270.0;
O = 125.04452 - 1934.136261 * T + 0.0020708 * T2 + T3 / 450000.0;
/* convert to radians */
D = ln_deg_to_rad (D);
M = ln_deg_to_rad (M);
MM = ln_deg_to_rad (MM);
F = ln_deg_to_rad (F);
O = ln_deg_to_rad (O);
/* calc sum of terms in table 21A */
for (i=0; i< TERMS; i++) {
/* calc coefficients of sine and cosine */
coeff_sine = (coefficients[i].longitude1 + (coefficients[i].longitude2 * T));
coeff_cos = (coefficients[i].obliquity1 + (coefficients[i].obliquity2 * T));
argument = arguments[i].D * D
+ arguments[i].M * M
+ arguments[i].MM * MM
+ arguments[i].F * F
+ arguments[i].O * O;
c_longitude += coeff_sine * sin(argument);
c_obliquity += coeff_cos * cos(argument);
}
/* change to arcsecs */
c_longitude /= 10000;
c_obliquity /= 10000;
/* change to degrees */
c_longitude /= (60 * 60);
c_obliquity /= (60 * 60);
/* calculate mean ecliptic - Meeus 2nd edition, eq. 22.2 */
c_ecliptic = 23.0 + 26.0 / 60.0 + 21.448 / 3600.0
- 46.8150/3600 * T
- 0.00059/3600 * T2
+ 0.001813/3600 * T3;
/* c_ecliptic += c_obliquity; * Uncomment this if function should
return true obliquity rather than
mean obliquity */
}
/* return results */
nutation->longitude = c_longitude;
nutation->obliquity = c_obliquity;
nutation->ecliptic = c_ecliptic;
}