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placalc.cpp
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placalc.cpp
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/*
** Astrolog (Version 7.40) File: placalc.cpp
**
** IMPORTANT NOTICE: Astrolog and all chart display routines and anything
** not enumerated below used in this program are Copyright (C) 1991-2022 by
** Walter D. Pullen ([email protected], http://www.astrolog.org/astrolog.htm).
** Permission is granted to freely use, modify, and distribute these
** routines provided these credits and notices remain unmodified with any
** altered or distributed versions of the program.
**
** The main ephemeris databases and calculation routines are from the
** library SWISS EPHEMERIS and are programmed and copyright 1997-2008 by
** Astrodienst AG. The use of that source code is subject to the license for
** Swiss Ephemeris Free Edition, available at http://www.astro.com/swisseph.
** This copyright notice must not be changed or removed by any user of this
** program.
**
** Additional ephemeris databases and formulas are from the calculation
** routines in the program PLACALC and are programmed and Copyright (C)
** 1989,1991,1993 by Astrodienst AG and Alois Treindl ([email protected]). The
** use of that source code is subject to regulations made by Astrodienst
** Zurich, and the code is not in the public domain. This copyright notice
** must not be changed or removed by any user of this program.
**
** The original planetary calculation routines used in this program have
** been copyrighted and the initial core of this program was mostly a
** conversion to C of the routines created by James Neely as listed in
** 'Manual of Computer Programming for Astrologers', by Michael Erlewine,
** available from Matrix Software.
**
** Atlas composed using data from https://www.geonames.org/ licensed under a
** Creative Commons Attribution 4.0 License. Time zone changes composed using
** public domain TZ database: https://data.iana.org/time-zones/tz-link.html
**
** The PostScript code within the core graphics routines are programmed
** and Copyright (C) 1992-1993 by Brian D. Willoughby ([email protected]).
**
** More formally: This program is free software; you can redistribute it
** and/or modify it under the terms of the GNU General Public License as
** published by the Free Software Foundation; either version 2 of the
** License, or (at your option) any later version. This program is
** distributed in the hope that it will be useful and inspiring, but
** WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
** General Public License for more details, a copy of which is in the
** LICENSE.HTM file included with Astrolog, and at http://www.gnu.org
**
** Initial programming 8/28-30/1991.
** X Window graphics initially programmed 10/23-29/1991.
** PostScript graphics initially programmed 11/29-30/1992.
** Last code change made 3/31/2022.
*/
#include "placalc.h"
#ifdef PLACALC
/*
** ---------------------------------------------------------------
** | Copyright Astrodienst AG and Alois Treindl, 1989,1991,1993 |
** | The use of this source code is subject to regulations made |
** | by Astrodienst Zurich. The code is NOT in the public domain.|
** | |
** | This copyright notice must not be changed or removed |
** | by any user of this program. |
** ---------------------------------------------------------------
**
** Important changes:
** 11-jun-93 revision 1.12: fixed error which affected Mercury between -2100
** and -3100 (it jumped wildly).
*/
/* function calc():
** This is the main routine for computing a planets position.
** The function has several modes, which are controlled by bits in
** the parameter 'flag'. The normal mode (flag == 0) computes
** a planets apparent geocentric position in ecliptic coordinates relative to
** the true equinox of date, without speed
**
** Explanation of the arguments: see the functions header.
**
** Returns OK or ERR (if some planet out of time range). OK and ERR are
** defined in ourdef.h and must not be confused with TRUE and FALSE.
** OK and ERR are of type int, not of type PLABOOL.
**
** Bits used in flag:
** CALC_BIT_HELIO 0 = geocentric, 1 = heliocentric
** CALC_BIT_NOAPP 0 = apparent positions, 1 = true positions
** CALC_BIT_NONUT 0 = do nutation (true equinox of date)
** 1 = don't do nutation (mean equinox of date).
**
** CALC_BIT_SPEED 0 = don't calc speed,
** 1 = calc speed, takes quite long for moon
** (is observed only for moon, with other
** planets speed is cheap)
**
** Side effects and local memory:
** For doing heliocentric positions the fucntion must know the
** earth's position for the desired time t. It remembers the earth
** position so it does not have to recompute it each time a planet
** position is wanted for the same time t.
** It calls helup(t), which leaves as a side effect the global
** variables meanekl, ekl and nut for the time t.
**
** Functions called by calc():
** helup(t)
** hel(t)
** moon(t)
** togeo()
**
** Time range:
** The function can be used savely in the time range 5000 BC to
** 3000 AD. The stored ephemeris is available only for this time
** range, so Jupiter ... Pluto cannot be computed outside. The
** function will return results for the other planets also outside
** of this time range, but they become meaningless pretty soon
** before 5000 BC, because Newcombs time series expansions for the
** elements will not work anymore.
**
** pointers to the return variables:
** alng = ecliptic longitude in degrees
** arad = radius vector in AU (astronomic units)
** alat = ecliptic latitude in degrees
** alngspeed = speed of planet in degrees per day
**
** !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
** The precision of the speed is quite limited.
** !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
**
** For Sun, Mercury, Venus and Mars we take only the speed from
** the undisturbed Kepler orbit. For the Moon there is no
** reasonable undisturbed orbit and we derive the speed from
** its position at t + dt and t - dt. We need these
** moon positions anyway for the true node calculation.
** For the outer planets and Chiron we derive the precise
** speed from the stored ephemeris by high order inter-
** polation; the precision is limited for the geocentric
** case due to the limited precision of the earth's/sun's speed.
** Applications who need precise speeds should
** get them by calling calc() with slightly different times.
**
** Comment 7 May 1991 by Alois Treindl:
** Center of Earth versus Barycenter Earth-Moon:
** Brown's theory of the moon gives the moon's coordinates relative
** to the center of the earth. Newcomb's theory of the Sun gives the
** coordinates of the earth's center relative to the center of the Sun.
** This is what we need.
**
** How about the Mean Lunar Node?
** The orbital elements of the Sun in Newcomb's theory are given
** relative to the barycenter Earth-Moon; the reduction to geocentric
** is only applied after doing the Kepler ellipse calculation.
** Are the Lunar elements also relative to the barycenter??
** If yes:
** When we use the moon's mean node out of the elements, it is still
** as seen from the barycenter. Because the node is close to the
** earth, we would have to apply a considerable correction, which is of
** the order of 4000/384000 km or 35' (minutes of arc).
** Nobody has ever applied such a correction to the mean node.
**
** And the True Node?
** When we calculate the osculating orbital elements of the Moon (true node),
** are they relative to the barycenter or to the Earth's center?
** Our derivation of true node from the actual Moon positions considers
** the earth's center as the focal point of the osculating lunar ellipse.
** A more correct approach would first reduce the lunar position from
** geocentric to barycentric, then compute the orbital elements from
** the reduced positions, and then reduce the desired items
** (node, apogaeum, 'dark moon') to geocentric positions.
** No known astrological ephemeris has ever used such a correction, which is
** of the same order of magnitude as the correction to the meannode above.
** When the moon is going through the ecliptic, the geocenter, barycenter
** moon (and the node identical to the moon itself) line up; this is why
** the error does not show up in normal considerations.
*/
int calc(int planet, REAL8 jd_ad, int flag,
REAL8 *alng, REAL8 *arad, REAL8 *alat, REAL8 *alngspeed)
/* planet index as defined in placalc.h,
SUN = 0, MOON = 1 etc.
planet == -1 calc calculates only nut and ecl */
/* relative Astrodienst Juldate, ephemeris time.
Astrodienst Juldate is relative 31 Dec 1949, noon. */
/* See definition of flag bits above */
{
struct rememberdat /* time for which the datas are calculated */
{REAL8 calculation_time, lng, rad, zet, lngspeed, radspeed, zetspeed;};
static struct rememberdat earthrem =
{HUGE8, HUGE8, HUGE8, HUGE8, HUGE8, HUGE8, HUGE8};
static struct rememberdat moonrem =
{HUGE8, HUGE8, HUGE8, HUGE8, HUGE8, HUGE8, HUGE8};
REAL8 c, s, x, knn, knv;
REAL8 rp, zp; /* needed to call hel! */
REAL8 *azet = alat;
PLABOOL calc_geo, calc_helio, calc_apparent, calc_speed,
calc_nut;
/* helup checks whether it was already called with same time */
helup (jd_ad);
/* we could return now if we only wanted to compute ecl and nut */
calc_helio = flag & CALC_BIT_HELIO;
calc_geo = ! calc_helio;
calc_apparent = ! (flag & CALC_BIT_NOAPP);
calc_nut = ! (flag & CALC_BIT_NONUT);
calc_speed = flag & CALC_BIT_SPEED;
/*
** it is necessary to compute EARTH in the following cases:
** heliocentric MOON or EARTH
** geocentric any planet except MOON or nodes or LILITH
*/
if (calc_helio && (planet == MOON || planet == EARTH)
|| calc_geo && planet != MOON
&& planet != MEAN_NODE
&& planet != TRUE_NODE
&& planet != LILITH) {
if (earthrem.calculation_time != jd_ad) {
hel (EARTH, jd_ad, alng, arad, azet, alngspeed, &rp, &zp);
/* store earthdata for geocentric calculation: */
earthrem.lng = *alng;
earthrem.rad = *arad;
earthrem.zet = *azet;
earthrem.lngspeed = *alngspeed;
earthrem.radspeed = rp;
earthrem.zetspeed = zp;
earthrem.calculation_time = jd_ad;
}
}
switch(planet) {
case EARTH: /* has been already computed */
*alng = earthrem.lng;
*arad = earthrem.rad;
*azet = earthrem.zet;
*alngspeed = earthrem.lngspeed;
rp = earthrem.radspeed;
zp = earthrem.zetspeed;
if (calc_geo) { /* SUN seen from earth */
*alng = smod8360(*alng + 180.0);
*azet = - *azet;
}
if (calc_apparent)
*alng = *alng - 0.0057683 * (*arad) * (*alngspeed);
break;
case MOON:
moon(alng, arad, azet);
moonrem.lng = *alng; /* moonrem will be used for TRUE_NODE */
moonrem.rad = *arad;
moonrem.zet = *azet;
*alngspeed = 12;
moonrem.calculation_time = jd_ad;
if (calc_helio || calc_speed) {/* get a second moon position */
REAL8 lng2, _rad2, zet2;
helup(jd_ad + MOON_SPEED_INTERVAL);
moon(&lng2, &_rad2, &zet2);
helup(jd_ad);
if (calc_helio) { /* moon as seen from sun */
togeo(earthrem.lng, -earthrem.rad, moonrem.lng, moonrem.rad,
moonrem.zet, alng, arad);
togeo(earthrem.lng + MOON_SPEED_INTERVAL * earthrem.lngspeed,
-(earthrem.rad + MOON_SPEED_INTERVAL * earthrem.radspeed),
lng2, _rad2, zet2, &lng2, &_rad2);
}
*alngspeed = diff8360(lng2, *alng) / MOON_SPEED_INTERVAL;
/* rp = (rad2 - *arad) / MOON_SPEED_INTERVAL; */
/* zp = (zet2 - moonrem.zet) / MOON_SPEED_INTERVAL; */
}
*alat = RADTODEG * ASIN8(*azet / *arad);
/*
** light time correction, not applied for moon or nodes;
** moon would have only term of ca. 0.02", see Expl.Sup.1961 p.109
*/
break;
case MERCURY:
case VENUS:
case MARS:
case JUPITER:
case SATURN:
case URANUS:
case NEPTUNE:
case PLUTO:
case CHIRON:
case CERES:
case PALLAS:
case JUNO:
case VESTA:
if (hel(planet, jd_ad, alng, arad, azet, alngspeed, &rp, &zp) != OK)
return ERR; /* outer planets can fail if out of ephemeris range */
if (calc_geo) { /* geocentric */
REAL8 lng1, _rad1, lng2, _rad2;
togeo(earthrem.lng, earthrem.rad, *alng, *arad, *azet, &lng1, &_rad1);
togeo(earthrem.lng + earthrem.lngspeed,
earthrem.rad + earthrem.radspeed,
*alng + *alngspeed, *arad + rp, *azet + zp, &lng2, &_rad2);
*alng = lng1;
*arad = _rad1;
*alngspeed = diff8360(lng2, lng1);
/* rp = rad2 - rad1; */
}
*alat = RADTODEG * ASIN8(*azet / *arad);
if (calc_apparent)
*alng = *alng - 0.0057683 * (*arad) * (*alngspeed);
break;
case MEAN_NODE:
*alng = smod8360(el[MOON].kn);
/*
* the distance of the node is the 'orbital parameter' p = a (1-e^2);
* Our current use of the axis a is wrong, but is never used.
*/
*arad = pd[MOON].axis;
*alat = 0.0;
*alngspeed = -0.053;
break;
case TRUE_NODE: {
/* see comment 'Note 7 May 1991' above */
REAL8 ln, rn, zn,
lv, rv, zv,
l1, r1, z1,
xn, yn, xv, yv, r0, x0, y0;
helup(jd_ad + NODE_INTERVAL);
moon(&ln, &rn, &zn);
helup(jd_ad - NODE_INTERVAL);
moon(&lv, &rv, &zv);
helup(jd_ad);
if (moonrem.calculation_time != jd_ad)
moon(&l1, &r1, &z1);
else { /* moon is already calculated */
l1 = moonrem.lng;
r1 = moonrem.rad;
z1 = moonrem.zet;
}
rn = sqrt(rn * rn - zn * zn);
rv = sqrt(rv * rv - zv * zv);
r0 = sqrt(r1 * r1 - z1 * z1);
xn = rn * COS8(DEGTORAD * ln);
yn = rn * SIN8(DEGTORAD * ln);
xv = rv * COS8(DEGTORAD * lv);
yv = rv * SIN8(DEGTORAD * lv);
x0 = r0 * COS8(DEGTORAD * l1);
y0 = r0 * SIN8(DEGTORAD * l1);
x = test_near_zero(x0 * yn - xn * y0);
s = (y0 * zn - z1 * yn) / x;
c = test_near_zero((x0 * zn - z1 * xn) / x);
knn = smod8360(RADTODEG * ATAN28(s, c)); /* = ATAN8(s / c) */
x = test_near_zero(y0 * xv - x0 * yv);
s = (yv * z1 - zv * y0) / x;
c = test_near_zero((xv * z1 - zv * x0) / x);
knv = smod8360(RADTODEG * ATAN28(s, c));
*alng = smod8360((knv + knn) / 2);
/*
** the distance of the node is the 'orbital parameter' p = a (1-e^2);
** Our current use of the axis a is wrong.
*/
*arad = pd[MOON].axis;
*alat = 0.0;
*alngspeed = diff8360(knn, knv) / NODE_INTERVAL;
}
break;
case LILITH: {
/*
** Added 22-Jun-93
** Lilith or Dark Moon is the empty focal point of the mean lunar ellipse.
** This is 180 degrees from the perihel.
** Because the lunar orbit is not in the ecliptic, it must be
** projected onto the ecliptic in the same way as the planetary orbits
** are (see for example Montenbruck, Grundlagen der Ephemeridenrechnung).
**
** We compute the MEAN Lilith, not the TRUE one which would have to be
** derived in a similar way as the true node.
** For the radius vector of Lilith we use a simple formula;
** to get a precise value, the fact that the focal point of the ellipse
** is not at the center of the earth but at the barycenter moon-earth
** would have to be accounted for.
** For the speed we always return a constant: the T term from the
** lunar perihel.
** Joelle de Gravelaine publishes in her book "Lilith der schwarze Mond"
** (Astrodata, 1990) an ephemeris which gives noon (12.00) positions
** but does not project onto the ecliptic.
** This creates deviations
*/
double arg_lat, lon, cosi;
struct elements *e = &el[MOON];
arg_lat = degnorm(e->pe - e->kn + 180.0);
cosi = COSDEG(e->in);
if (e->in == 0 || ABS8(arg_lat - 90.0) < TANERRLIMIT
|| ABS8(arg_lat - 270.0) < TANERRLIMIT) {
lon = arg_lat;
} else {
lon = ATAN8(TANDEG(arg_lat) * cosi);
lon = RADTODEG * lon;
if (arg_lat > 90.0 && arg_lat < 270.0) lon += 180.0;
}
lon = degnorm(lon + e->kn);
*alng = lon;
*alngspeed = 0.111404; /* 6'41.05" per day */
*arad = 2 * pd[MOON].axis * e->ex;
/*
** To test Gravalaines error, return unprojected long in alat.
** the correct latitude would be:
** *alat = RADTODEG * ASIN8(SINDEG(arg_lat) * SINDEG(e->in));
*/
#ifdef ASTROLOG
*alat = RADTODEG * ASIN8(SINDEG(arg_lat) * SINDEG(e->in));
#else
*alat = degnorm(arg_lat + e->kn); /* unprojected longitude, no nut */
#endif
}
break;
default:
return ERR;
} /* end switch */
if (calc_nut)
*alng += nut;
*alng = smod8360(*alng); /* normalize to circle */
return OK;
}
/* helio to geocentric conversion */
void togeo(REAL8 lngearth, REAL8 radearth, REAL8 lng, REAL8 rad, REAL8 zet,
REAL8 *alnggeo, REAL8 *aradgeo)
{
REAL8 r1, x, y;
r1 = sqrt(rad * rad - zet * zet);
x = r1 * COS8(DEGTORAD * lng) - radearth * COS8(DEGTORAD * lngearth);
y = r1 * SIN8(DEGTORAD * lng) - radearth * SIN8(DEGTORAD * lngearth);
*aradgeo = sqrt(x * x + y * y + zet * zet);
x = test_near_zero(x);
*alnggeo = smod8360(RADTODEG * ATAN28(y, x));
}
/*
** helup()
** prepares the orbital elements and the disturbation arguments for the
** inner planets and the moon. helup(t) is called by hel() and by calc().
** helup() returns its results in global variables.
** helup() remembers the t it has been called with before and does
** not recalculate its results when it is called more than once with
** the same t.
*/
void helup(REAL8 jd_ad)
{
int i;
static REAL8 thelup = HUGE8; /* is initialized only once at load time */
struct elements *e = el; /* pointer to el[i] */
struct elements *ee = el; /* pointer to el[EARTH] */
struct eledata *d = pd; /* pointer to pd[i] */
REAL8 td, ti, ti2, tj1, tj2, tj3;
if (thelup == jd_ad)
return; /* if already calculated then return */
for (i = SUN; i <= MARS; i++, d++, e++) {
td = jd_ad - d->epoch;
ti = e->tj = td / 36525.0; /* julian centuries from epoch */
ti2 = ti * ti;
tj1 = ti / 3600.0; /* used when coefficients are in seconds of arc */
tj2 = ti * tj1;
tj3 = ti * tj2;
e->lg = mod8360(d->lg0 + d->lg1 * td + d->lg2 * tj2 + d->lg3 * tj3);
/* also with moon lg1 *td is exact to 10e-8 degrees within 5000 years */
e->pe = mod8360(d->pe0 + d->pe1 * tj1 + d->pe2 * tj2 + d->pe3 * tj3);
e->ex = d->ex0 + d->ex1 * ti + d->ex2 * ti2;
e->kn = mod8360(d->kn0 + d->kn1 * tj1 + d->kn2 * tj2 + d->kn3 * tj3);
e->in = d->in0 + d->in1 * tj1 + d->in2 * tj2;
e->ma = smod8360(e->lg - e->pe);
if (i == MOON) {
/* calculate ekliptic according Newcomb, APAE VI,
** and nutation according Exp.Suppl. 1961, identical
** with Mark Potttenger elemnut()
** all terms >= 0.01" only .
** The 1984 IAU Theory of Nutation, as published in
** AE 1984 suppl. has not yet been implemented
** because it would mean to use other elements of
** moon and sun */
REAL8 mnode, mlong2, slong2, mg, sg, d2;
mnode = DEGTORAD * e->kn; /* moon's mean node */
mlong2 = DEGTORAD * 2.0 * e->lg; /* 2 x moon's mean longitude */
mg = DEGTORAD * e->ma; /* moon's mean anomaly (g1) */
slong2 = DEGTORAD * 2.0 * ee->lg; /* 2 x sun's mean longitude (L), with
the phase 180 deg earth-sun irrelevant
because 2 x 180 = 360 deg */
sg = DEGTORAD * ee->ma; /* sun's mean anomaly = earth's */
d2 = mlong2 - slong2; /* 2 x elongation of moon from sun */
meanekl = ekld[0] + ekld[1] * tj1 + ekld[2] * tj2 + ekld[3] * tj3;
ekl = meanekl +
(9.2100 * COS8(mnode)
- 0.0904 * COS8(2.0 * mnode)
+ 0.0183 * COS8(mlong2 - mnode)
+ 0.0884 * COS8(mlong2)
+ 0.0113 * COS8(mlong2 + mg)
+ 0.5522 * COS8(slong2)
+ 0.0216 * COS8(slong2 + sg)) / 3600.0;
nut = ((-17.2327 - 0.01737 * ti) * SIN8(mnode)
+ 0.2088 * SIN8(2.0 * mnode)
+ 0.0675 * SIN8(mg)
- 0.0149 * SIN8(mg - d2)
- 0.0342 * SIN8(mlong2 - mnode)
+ 0.0114 * SIN8(mlong2 - mg)
- 0.2037 * SIN8(mlong2)
- 0.0261 * SIN8(mlong2 + mg)
+ 0.0124 * SIN8(slong2 - mnode)
+ 0.0214 * SIN8(slong2 - sg)
- 1.2729 * SIN8(slong2)
- 0.0497 * SIN8(slong2 + sg)
+ 0.1261 * SIN8(sg)) / 3600.0;
}
}
/* calculate the arguments sa[] for the disturbation terms */
ti = (jd_ad - EPOCH1850) / 365.25; /* julian years from 1850 */
for (i = 0; i < SDNUM; i++)
sa [i] = mod8360(_sd [i].sd0 + _sd [i].sd1 * ti);
/*
** sa[2] += 0.3315 * SIN8 (DEGTORAD *(133.9099 + 38.39365 * el[SUN].tj));
**
** correction of jupiter perturbation argument for sun from Pottenger;
** creates only .03" and 1e-7 rad, not applied because origin unclear */
thelup = jd_ad; /* note the last helup time */
}
/*
** hel()
** Computes the heliocentric positions for all planets except the moon.
** The outer planets from Jupiter onwards, including Chiron, are
** actually done by a subsequent call to outer_hel() which takes
** exactly the same parameters.
** hel() does true position relative to the mean ecliptic and equinox
** of date. Nutation is not added and must be done so by the caller.
** The latitude of the Sun (max. 0.5") is neglected and always returned
** as zero.
**
** return: OK or ERR
*/
int hel(int planet, REAL8 t, REAL8 *al, REAL8 *ar, REAL8 *az, REAL8 *alp,
REAL8 *arp, REAL8 *azp)
/* planet index as defined by placalc.h */
/* relative juliand date, ephemeris time */
/* Now come 6 pointers to return values. */
/* longitude in degrees */
/* radius in AU */
/* distance from ecliptic in AU */
/* speed in longitude, degrees per day */
/* speed in radius, AU per day */
/* speed in z, AU per day */
{
register struct elements *e;
register struct eledata *d;
REAL8 lk = 0.0;
REAL8 rk = 0.0;
REAL8 b, h1, sini, sinv, cosi, cosu, cosv, man, truanom, esquare,
k8, u, up, v, vp;
if (planet >= JUPITER)
return (outer_hel(planet, t, al, ar, az, alp, arp, azp));
if (planet < SUN || planet == MOON)
return ERR;
e = &el[planet];
d = &pd[planet];
sini = SIN8(DEGTORAD * e->in);
cosi = COS8(DEGTORAD * e->in);
esquare = sqrt((1.0 + e->ex) / (1.0 - e->ex)); /* H6 in old version */
man = e->ma;
if (planet == EARTH) /* some longperiodic terms in mean longitude */
man += (0.266 * SIN8 (DEGTORAD * (31.8 + 119.0 * e->tj))
+ 6.40 * SIN8(DEGTORAD * (231.19 + 20.2 * e->tj))
+ (1.882-0.016*e->tj) * SIN8(DEGTORAD * (57.24 + 150.27 * e->tj))
) / 3600.0;
if (planet == MARS) /* some longperiodic terms */
man += (0.606 * SIN8(DEGTORAD * (212.87 + e->tj * 119.051))
+ 52.490 * SIN8(DEGTORAD * (47.48 + e->tj * 19.771))
+ 0.319 * SIN8(DEGTORAD * (116.88 + e->tj * 773.444))
+ 0.130 * SIN8(DEGTORAD * (74 + e->tj * 163))
+ 0.280 * SIN8(DEGTORAD * (300 + e->tj * 40.8))
- (37.05 +13.5 * e->tj)
) / 3600.0;
u = fnu(man, e->ex, 0.0000003); /* error 0.001" returns radians */
cosu = COS8(u);
h1 = 1 - e->ex * cosu;
*ar = d->axis * h1;
if (ABS8(rPi - u) < TANERRLIMIT)
truanom = u; /* very close to aphel */
else
truanom = 2.0 * ATAN8(esquare * TAN8(u * 0.5)); /* true anomaly, rad*/
v = smod8360(truanom * RADTODEG + e->pe - e->kn); /* argument of latitude */
if (sini == 0.0 || ABS8(v - 90.0) < TANERRLIMIT
|| ABS8(v - 270.0) < TANERRLIMIT) {
*al = v;
} else {
*al = RADTODEG * ATAN8(TAN8(v * DEGTORAD) * cosi);
if (v > 90.0 && v < 270.0) *al += 180.0;
}
*al = smod8360(*al + e->kn);
sinv = SIN8(v * DEGTORAD);
cosv = COS8(v * DEGTORAD);
*az = *ar * sinv * sini;
b = ASIN8(sinv * sini); /* latitude in radians */
k8 = cosv / COS8(b) * sini;
up = 360.0 / d->period / h1; /* du/dt degrees/day */
if (ABS8(rPi - u) < TANERRLIMIT)
vp = up / esquare; /* speed at aphel */
else
vp = up * esquare * (1 + COS8 (truanom)) / (1 + cosu);
/* dv/dt degrees/day */
*arp = d->axis * up * DEGTORAD * SIN8(u) * e->ex;
/* dr/dt AU/day */
*azp = *arp * sinv * sini + *ar * vp * DEGTORAD * cosv * sini; /* dz/dt */
*alp = vp / cosi * (1 - k8 * k8);
/* now come the disturbations */
switch (planet) {
REAL8 am, mma, ema, u2;
case EARTH:
/*
** earth has some special moon values and a disturbation series due to the
** planets. The moon stuff is due to the fact, that the mean elements
** give the coordinates of the earth-moon barycenter. By adding the
** corrections we effectively reduce to the center of the earth.
** We neglect the correction in latitude, which is about 0.5", because
** for astrological purposes we want the Sun to have latitude zero.
*/
am = DEGTORAD * smod8360(el[MOON].lg - e->lg + 180.0); /* degrees */
mma = DEGTORAD * el[MOON].ma;
ema = DEGTORAD * e->ma;
u2 = 2.0 * DEGTORAD * (e->lg - 180.0 - el[MOON].kn); /* 2u' */
lk = 6.454 * SIN8(am)
+ 0.013 * SIN8(3.0 * am)
+ 0.177 * SIN8(am + mma)
- 0.424 * SIN8(am - mma)
+ 0.039 * SIN8(3.0 * am - mma)
- 0.064 * SIN8(am + ema)
+ 0.172 * SIN8(am - ema)
- 0.013 * SIN8(am - mma - ema)
- 0.013 * SIN8(u2);
rk = 13360 * COS8(am)
+ 30 * COS8(3.0 * am)
+ 370 * COS8(am + mma)
- 1330 * COS8(am - mma)
+ 80 * COS8(3.0 * am - mma)
- 140 * COS8(am + ema)
+ 360 * COS8(am - ema)
- 30 * COS8(am - mma - ema)
+ 30 * COS8(u2);
/* long periodic term from mars 15g''' - 8g'', Vol 6 p19, p24 */
lk += 0.202 * SIN8(DEGTORAD * (315.6 + 893.3 * e->tj));
disturb(earthkor, al, ar, lk, rk, man);
break;
case MERCURY: /* only normal disturbation series */
disturb(mercurykor, al, ar, 0.0, 0.0, man);
break;
case VENUS: /* some longperiod terms and normal series */
lk = (2.761 - 0.22*e->tj) * SIN8(DEGTORAD * (237.24 + 150.27 * e->tj))
+ 0.269 * SIN8(DEGTORAD * (212.2 + 119.05 * e->tj))
- 0.208 * SIN8(DEGTORAD * (175.8 + 1223.5 * e->tj));
/* make seconds */
disturb(venuskor, al, ar, lk, 0.0, man);
break;
case MARS: /* only normal disturbation series */
disturb(marskor, al, ar, 0.0, 0.0, man);
break;
}
return OK;
}
void disturb(register struct kor *k, REAL8 *al, REAL8 *ar, REAL8 lk, REAL8 rk,
REAL8 man)
/* ENDMARK-terminated array of struct kor */
/* longitude in degrees, use a pointer to return value */
/* radius in AU */
/* longitude correction in SECONDS OF ARC
function can be called with an lk and rk already
!= 0, but no value is returned */
/* radius correction in units of 9th place of log r */
/* mean anomaly of planet */
{
REAL8 arg;
while (k->j != ENDMARK) {
arg = k->j * sa[k->k] + k->i * man;
lk += k->lampl * COS8(DEGTORAD * (k->lphase - arg));
rk += k->rampl * COS8(DEGTORAD * (k->rphase - arg));
k++;
}
*ar *= EXP10(rk * 1.0E-9); /* 10^rk */
*al += lk / 3600.0;
}
int moon(REAL8 *al, REAL8 *ar, REAL8 *az) /* return OK or ERR */
{
REAL8 a1,a2,a3,a4,a5,a6,a7,a8,a9,c2,c4,arg,b,d,f,dgc,dlm,dpm,dkm,dls;
REAL8 ca, cb, cd, f_2d, f_4d, g1c,lk,lk1,man,ms,nib,s,sinarg,sinp,sk;
REAL8 t, tb, t2c, r2rad, i1corr, i2corr, dlid;
int i;
struct elements *e;
struct m45dat *mp;
#if MOON_TEST_CORR
struct m5dat *m5p;
#endif
e = &el[MOON];
t = e->tj * 36525; /* days from epoch 1900 */
/* new format table II, parameters in full rotations of 360 degrees */
r2rad = 360.0 * DEGTORAD;
tb = t * 1e-12; /* units of 10^12 */
t2c = t * t * 1e-16; /* units of 10^16 */
a1 = SIN8(r2rad * (0.53733431 - 10104982 * tb + 191 * t2c));
a2 = SIN8(r2rad * (0.71995354 - 147094228 * tb + 43 * t2c));
c2 = COS8(r2rad * (0.71995354 - 147094228 * tb + 43 * t2c));
a3 = SIN8(r2rad * (0.14222222 + 1536238 * tb));
a4 = SIN8(r2rad * (0.48398132 - 147269147 * tb + 43 * t2c));
c4 = COS8(r2rad * (0.48398132 - 147269147 * tb + 43 * t2c));
a5 = SIN8(r2rad * (0.52453688 - 147162675 * tb + 43 * t2c));
a6 = SIN8(r2rad * (0.84536324 - 11459387 * tb));
a7 = SIN8(r2rad * (0.23363774 + 1232723 * tb + 191 * t2c));
a8 = SIN8(r2rad * (0.58750000 + 9050118 * tb));
a9 = SIN8(r2rad * (0.61043085 - 67718733 * tb));
dlm = 0.84 * a3 + 0.31 * a7 + 14.27 * a1 + 7.261 * a2 + 0.282 * a4
+ 0.237 * a6;
dpm = -2.1 * a3 - 2.076 * a2 - 0.840 * a4 - 0.593 * a6;
dkm = 0.63 * a3 + 95.96 * a2 + 15.58 * a4 + 1.86 * a5;
dls = -6.4 * a3 - 0.27 * a8 - 1.89 * a6 + 0.20 * a9;
dgc = (-4.318 * c2 - 0.698 * c4) / 3600.0 / 360.0; /* in revolutions */
dgc = (1.000002708 + 139.978 * dgc); /* in this form used later */
man = DEGTORAD * (e->ma + (dlm - dpm) / 3600.0);
/* man with periodic and secular corr. */
ms = DEGTORAD * (el[EARTH].ma + dls / 3600.0);
f = DEGTORAD * (e->lg - e->kn + (dlm - dkm) / 3600.0);
d = DEGTORAD * (e->lg + 180 - el[EARTH].lg + (dlm - dls) / 3600.0);
lk = lk1 = sk = sinp = nib = g1c = 0;
i1corr = 1.0 - 6.8320E-8 * t;
i2corr = dgc * dgc; /* i2 occurs only as -2, 2 */
for (i = 0, mp = m45; i < NUM_MOON_CORR; i++, mp++) {
/* arg = mp->i0 * man + mp->i1 * ms + mp->i2 * f + mp->i3 * d; */
arg = mp->i0 * man;
arg += mp->i3 * d;
arg += mp->i2 * f;
arg += mp->i1 * ms;
sinarg = SIN8(arg);
/*
** now apply corrections due to changes in constants;
** we correct only terms in l' (i1) and F (i2), not in l (i0), because
** the latter are < 0.05"
** We don't apply corrections for cos(arg), i.e. for parallax
*/
if (mp->i1 != 0) { /* i1 can be -2, -1, 0, 1, 2 */
sinarg *= i1corr;
if (mp->i1 == 2 || mp->i1 == -2)
sinarg *= i1corr;
}
if (mp->i2 != 0) /* i2 can be -2, 0, 2 */
sinarg *= i2corr;
lk += mp->lng * sinarg;
sk += mp->lat * sinarg;
sinp += mp->par * COS8 (arg) ;
}
#if MOON_TEST_CORR /* optionally add more lunar longitudes */
for (m5p = m5; m5p->i0 != 99; m5p++) { /* i0 = 99 is end mark */
arg = m5p->i0 * man + m5p->i1 * ms + m5p->i2 * f + m5p->i3 * d;
sinarg = SIN8(arg);
lk1 += m5p->lng * sinarg;
}
#endif
/*
** now compute some planetary terms in longitude, list i delta;
** we take all > 0.5" and neglect secular terms in the arguments. These
** produce phase errors > 10 degrees only after 3000 years.
*/
dlid = 0.822 * SIN8 (r2rad * (0.32480 - 0.0017125594 * t));
dlid += 0.307 * SIN8 (r2rad * (0.14905 - 0.0034251187 * t));
dlid += 0.348 * SIN8 (r2rad * (0.68266 - 0.0006873156 * t));
dlid += 0.662 * SIN8 (r2rad * (0.65162 + 0.0365724168 * t));
dlid += 0.643 * SIN8 (r2rad * (0.88098 - 0.0025069941 * t));
dlid += 1.137 * SIN8 (r2rad * (0.85823 + 0.0364487270 * t));
dlid += 0.436 * SIN8 (r2rad * (0.71892 + 0.0362179180 * t));
dlid += 0.327 * SIN8 (r2rad * (0.97639 + 0.0001734910 * t));
/* without nutation */
*al = smod8360(e->lg + (dlm + lk + lk1 + dlid) / 3600.0);
/* solar Terms in latitude Nibeta */
f_2d = f - 2.0 * d;
f_4d = f - 4.0 * d;
nib += -526.069 * SIN8( f_2d);
nib += -3.352 * SIN8( f_4d);
nib += 44.297 * SIN8( man + f_2d);
nib += -6.000 * SIN8( man + f_4d);
nib += 20.599 * SIN8(-man + f );
nib += -30.598 * SIN8(-man + f_2d);
nib += -24.649 * SIN8(-2*man + f );
nib += -2.000 * SIN8(-2*man + f_2d);
nib += -22.571 * SIN8( ms + f_2d);
nib += 10.985 * SIN8( -ms + f_2d);
/* new gamma1C from 29 Jul 88, all terms > 0.4 " in table III, code 2 */
g1c += -0.725 * COS8( d);
g1c += 0.601 * COS8( 2 * d);
g1c += 0.394 * COS8( 3 * d);
g1c += -0.445 * COS8(man + 4 * d);
g1c += 0.455 * COS8(man + 1 * d);
g1c += 5.679 * COS8(2 * man - 2 * d);
g1c += -1.300 * COS8(3 * man );
g1c += -1.302 * COS8( ms );
g1c += -0.416 * COS8( ms - 4 * d);
g1c += -0.740 * COS8( 2 * ms - 2 * d);
g1c += 0.787 * COS8( man + ms + 2 * d);
g1c += 0.461 * COS8( man + ms );
g1c += 2.056 * COS8( man + ms - 2 * d);
g1c += -0.471 * COS8( man + ms - 4 * d);
g1c += -0.443 * COS8( -man + ms + 2 * d);
g1c += 0.679 * COS8( -man + ms );
g1c += -1.540 * COS8( -man + ms - 2 * d);
s = f + sk / 3600.0 * DEGTORAD;
ca = 18519.7 + g1c;
cb = -0.000336992 * ca * dgc * dgc * dgc;
cd = ca / 18519.7;
b = (ca * SIN8(s) * dgc + cb * SIN8(3.0 * s) + cd * nib) / 3600.0;
/* we neglect the planetary terms in latitude, code 4 in table III */
sinp = (sinp + 3422.451);
/*
** Improved lunar ephemeris and APAE until ca. 1970 had here
** 3422.54 as constant of moon's sine parallax.
** The difference can be applied by direct addition of 0.089" to
** our parallax results.
**
** To get the radius in A.U. from the sine parallax,
** we use 1964 IAU value 8.794" for solar parallax.
** sinp is still in seconds of arc.
** To calculate moon parallax in " it would be:
** p = sinp (1 + sinp * sinp * 3.917405E-12)
** based on the formula p = sinp + 1/6 sinp^3
** and taking into account the conversion of " to radians.
** The semidiameter of the moon is: (Expl.Suppl. 61, p 109)
** s = 0.0796 + 0.272446 * p
*/
*ar = 8.794 / sinp;
*az = *ar * SIN8(DEGTORAD * b);
return OK;
}
/*
** outer_hel()
** Computes the position of Jupiter, Saturn, Uranus, Neptune, Pluto and
** Chiron by reading our stored ephemeris in steps of 80 (!) days and
** applying a high order interpolation to it. The interpolation errors are
** less than 0.01" seconds of arc.
** The stored ephemeris is packed in a special format consisting of
** 32 bit numbers; it has been created on the Astrodienst Unix system
** by numerical integration with routines provided originally by Marc
** Pottenger, USA, which we improved for better long term precision.
** Because the Unix system uses a different byte order than the MSDOS
** systems, the bytes must be reordered for MSDOS after reading from
** the binary files.
**
** outer_hel() takes the same parameters as hel().
** It returns the same type of values.
**
** The access to the ephemeris files is done in the functions chi_file_posit()
** and lrz_file_posit().
*/
int outer_hel(int planet, REAL8 jd_ad, REAL8 *al, REAL8 *ar, REAL8 *az,
REAL8 *alp, REAL8 *arp, REAL8 *azp)
/* jd_ad Astrodienst relative Julian ephemeris time */
{
static FILE *outerfp = NULL, *chironfp = NULL, *asterfp = NULL;
static double last_j0_outer = HUGE8;
static double last_j0_chiron = HUGE8;
static double last_j0_aster = HUGE8;
static long icoord[6][5][3], chicoord[6][3], ascoord[6][4][3];
REAL8 j0, jd, jfrac;
REAL8 l[6], r[6], z[6];
int n, order, p;
if ((planet < JUPITER || planet > PLUTO) && planet != CHIRON &&
(planet < CERES || planet > VESTA))
return ERR;
jd = jd_ad + JUL_OFFSET;
j0 = RFloor((jd - 0.5) / EPHE_STEP) * EPHE_STEP + 0.5;
jfrac = (jd - j0) / EPHE_STEP;
if (planet == CHIRON) {
if (last_j0_chiron != j0) {
for (n = 0; n < 6; n++) { /* read 6 days */
jd = j0 + (n - 2) * EPHE_STEP;
if (chi_file_posit(jd, &chironfp) != OK)
return ERR;
fread(&chicoord[n][0], sizeof(word4), 3, chironfp);
longreorder((UCHAR *)&chicoord[n][0], 3*4);
}
last_j0_chiron = j0;
}
for (n = 0; n < 6; n++) {
l[n] = chicoord[n][0] / DEG2MSEC;
r[n] = chicoord[n][1] / AU2INT;
z[n] = chicoord[n][2] / AU2INT;
}
} else if (planet >= CERES && planet <= VESTA) {
if (last_j0_aster != j0) { /* read all 4 asteroids for 6 steps */
for (n = 0; n < 6; n++) {
jd = j0 + (n - 2) * EPHE_STEP;
if (ast_file_posit(jd, &asterfp) != OK)
return ERR;
fread(&ascoord[n][0][0], sizeof(word4), 12, asterfp);
longreorder((UCHAR *)&ascoord[n][0][0], 12*4);
}
last_j0_aster = j0;
}
p = planet - CERES;
for (n = 0; n < 6; n++) {
l[n] = ascoord[n][p][0] / DEG2MSEC;
r[n] = ascoord[n][p][1] / AU2INT;
z[n] = ascoord[n][p][2] / AU2INT;
}
} else { /* an outerplanet */
if (last_j0_outer != j0) { /* read all 5 planets for 6 steps */
for (n = 0; n < 6; n++) {
jd = j0 + (n - 2) * EPHE_STEP;
if (lrz_file_posit(jd, &outerfp) != OK)
return ERR;
fread(&icoord[n][0][0], sizeof(word4), 15, outerfp);
longreorder((UCHAR *)&icoord[n][0][0], 15*4);
}
last_j0_outer = j0;
}
p = planet - JUPITER;
for (n = 0; n < 6; n++) {
l[n] = icoord[n][p][0] / DEG2MSEC;
r[n] = icoord[n][p][1] / AU2INT;
z[n] = icoord[n][p][2] / AU2INT;
}
}
if (planet > SATURN)
order = 3;
else
order = 5;
inpolq(2, order, jfrac, l, al, alp);
*alp /= EPHE_STEP;
inpolq(2, order, jfrac, r, ar, arp);
*arp /= EPHE_STEP;
inpolq(2, order, jfrac, z, az, azp);
*azp /= EPHE_STEP;
return OK;
}
/*
** quicker Everett interpolation, after Pottenger
** version 9 Jul 1988 by Alois Treindl
** return OK or ERR.
*/
int inpolq(int n, int o, double p, double x[], double *axu, double *adxu)
/* interpolate between x[n] and x[n-1], at argument n+p */
/* order of interpolation, maximum 5 */
/* argument , intervall [0..1] */
/* array of function values, x[n-o]..x[n+o] must exist */
/* pointer for storage of result */
/* pointer for storage of dx/dt */
{
static double q, q2, q3, q4, q5, p2, p3, p4, p5, u, u0, u1, u2;
static double lastp = 9999;
double dm2, dm1, d0, dp1, dp2,
d2m1, d20, d2p1, d2p2, d30, d3p1, d3p2, d4p1, d4p2;
double offset = 0.0;
if (lastp != p) {
q = 1.0-p;
q2 = q*q;