/*

This module contains function calls to calculate the positions of

the sun and planets. It follows the method given in Chapter 32

of Jean Meeus's book Astronomical Algorythms. However, unlike that

book, this code uses *all* of the terms in the VSOP87 model, so the

result is more accurate than what one gets using Meeus's truncated

tables. There are few comments in this code, because it pretty

closely follows the steps given in Meeus's book, and uses similar

variable names, so the book is the documentation for the code.

The full VSOP87 model, for all planets in the Solar System, contains

nearly 100,000 coefficients. These coefficients are available via

FTP, as ASCII tables. A standalone program was written to read

those files and write out the coefficients as binary files (mostly

double precision floats, with a few integers specifying table sizes).

The code here reads those files into heap storage, the first time the

function is called. Obviously the file read only occurs once - the

heap storage is never freed.

*/

#include <stdio.h>

#include <stdlib.h>

#include <sys/types.h>

#include <unistd.h>

#include <sys/stat.h>

#include <fcntl.h>

#include <math.h>

#define TRUE (1)

#define FALSE (0)

#define DEGREES_TO_RADIANS (M_PI/180.0)

#define ARCSEC_TO_RADIANS (M_PI/(180.0*3600.0))

#define N_PLANETS (8)

#define SUN (2)

static double *vSOPCoef[N_PLANETS][3][6][3];

static unsigned short nVSOPCoef[N_PLANETS][3][6];

static char *planetName[N_PLANETS] = {"mercury", "venus", "earth",

"mars", "jupiter", "saturn",

"uranus", "neptune"};

void nutation(double T, double *deltaPhi, double *deltaEps, double *eps);

void doubleNormalize0to2pi(double *angle);

void heliocentricEclipticCoordinates(char *dataDir, double tJD, int planet,

double *lHelio, double *bHelio, double *rHelio)

{

static int dataNeeded = TRUE;

int i, j;

double tau, L[6], B[6], R[6], Ltotal, Btotal, Rtotal;

if (dataNeeded) {

/*

Read the binary files containing the VSOP87 coefficients

*/

int p, fD, done, power, coef, nRead;

int nDoubles = 0;

char fileName[100];

/*

We aren't going to use this function for Mercury, Uranus and Neptune

right away, so don't bother reading the data for them into

RAM.

*/

for (p = 1; p < N_PLANETS-2; p++) {

sprintf(fileName, "%s/%sVSOPData.bin", dataDir, planetName[p]);

fD = open(fileName, O_RDONLY);

if (fD < 0) {

perror(fileName);

exit(-1);

}

done = FALSE;

power = coef = 0;

while (!done) {

nRead = read(fD, &nVSOPCoef[p][coef][power], 4);

if (nRead != 4) {

fprintf(stderr, "rRead = %d for read of nVSOPCoef[%d][%d][%d]\n",

nRead, p, coef, power);

exit(-1);

}

for (i = 0; i < 3; i++) {

vSOPCoef[p][coef][power][i] =

(double *)malloc(sizeof(double)*nVSOPCoef[p][coef][power]);

nDoubles += nVSOPCoef[p][coef][power];

if (vSOPCoef[p][coef][power][i] == NULL) {

perror("malloc of vSOPCoef[p][coef][power]");

fprintf(stderr, "Wanted %d doubles\n", nVSOPCoef[p][coef][power]);

fprintf(stderr, "p = %d, coef = %d, power = %d\n",

p, coef, power);

exit(-1);

}

}

for (i = 0; i < nVSOPCoef[p][coef][power]; i++)

for (j = 0; j < 3; j++)

read(fD, &vSOPCoef[p][coef][power][j][i], 8);

power++;

if (power > 5) {

coef++;

if (coef > 2)

done = TRUE;

else

power = 0;

}

}

}

dataNeeded = FALSE;

}

tau = (tJD - 2451545.0) / 365250.0;

for (i = 0; i <= 5; i++) {

L[i] = 0.0;

for (j = 0; j < nVSOPCoef[planet][0][i]; j++) {

L[i] += vSOPCoef[planet][0][i][0][j]*cos(vSOPCoef[planet][0][i][1][j] +

vSOPCoef[planet][0][i][2][j]*tau);

}

}

Ltotal = L[0]

+ L[1] * tau

+ L[2] * tau*tau

+ L[3] * tau*tau*tau

+ L[4] * tau*tau*tau*tau

+ L[5] * tau*tau*tau*tau*tau;

doubleNormalize0to2pi(&Ltotal);

for (i = 0; i <= 5; i++) {

B[i] = 0.0;

for (j = 0; j < nVSOPCoef[planet][1][i]; j++) {

B[i] += vSOPCoef[planet][1][i][0][j]*cos(vSOPCoef[planet][1][i][1][j] +

vSOPCoef[planet][1][i][2][j]*tau);

}

}

Btotal = B[0]

+ B[1] * tau

+ B[2] * tau*tau

+ B[3] * tau*tau*tau

+ B[4] * tau*tau*tau*tau

+ B[5] * tau*tau*tau*tau*tau;

doubleNormalize0to2pi(&Btotal);

for (i = 0; i <= 5; i++) {

R[i] = 0.0;

for (j = 0; j < nVSOPCoef[planet][2][i]; j++) {

R[i] += vSOPCoef[planet][2][i][0][j]*cos(vSOPCoef[planet][2][i][1][j] +

vSOPCoef[planet][2][i][2][j]*tau);

}

}

Rtotal = R[0]

+ R[1] * tau

+ R[2] * tau*tau

+ R[3] * tau*tau*tau

+ R[4] * tau*tau*tau*tau

+ R[5] * tau*tau*tau*tau*tau;

*lHelio = Ltotal;

*bHelio = Btotal;

*rHelio = Rtotal;

}

void vSOPPlanetInfo(char *dataDir, double tJD, int planet,

double *rA, double *dec, double *distance)

{

double L, B, R, L0, B0, R0, x, y, z, lambda, beta, delta, tau,

T, Lprime, deltaL, deltaB, deltaPhi, deltaEps, eps, tY, tX;

heliocentricEclipticCoordinates(dataDir, tJD, 2, &L0, &B0, &R0);

if (planet != SUN)

heliocentricEclipticCoordinates(dataDir, tJD, planet, &L, &B, &R);

else

L = B = R = 0.0;

x = R*cos(B)*cos(L) - R0*cos(B0)*cos(L0);

y = R*cos(B)*sin(L) - R0*cos(B0)*sin(L0);

z = R*sin(B) - R0*sin(B0);

delta = sqrt(x*x + y*y + z*z);

tau = 0.0057755183*delta;

heliocentricEclipticCoordinates(dataDir, tJD-tau, 2, &L0, &B0, &R0);

if (planet != SUN)

heliocentricEclipticCoordinates(dataDir, tJD-tau, planet, &L, &B, &R);

else

L = B = R = 0.0;

x = R*cos(B)*cos(L) - R0*cos(B0)*cos(L0);

y = R*cos(B)*sin(L) - R0*cos(B0)*sin(L0);

z = R*sin(B) - R0*sin(B0);

lambda = atan2(y, x);

doubleNormalize0to2pi(&lambda);

beta = atan2(z, sqrt(x*x + y*y));

T = (tJD - 2451545.0) / 36525.0;

Lprime = lambda - 1.397*DEGREES_TO_RADIANS*T - 0.00031*DEGREES_TO_RADIANS*T*T;

deltaL = -0.09033*ARCSEC_TO_RADIANS

+ 0.03916*ARCSEC_TO_RADIANS*(cos(Lprime) + sin(Lprime))*tan(beta);

deltaB = 0.03916*ARCSEC_TO_RADIANS*(cos(Lprime) - sin(Lprime));

lambda += deltaL;

beta += deltaB;

nutation(T, &deltaPhi, &deltaEps, &eps);

eps *= DEGREES_TO_RADIANS;

lambda += deltaPhi*ARCSEC_TO_RADIANS;

tY = sin(lambda)*cos(eps) - tan(beta)*sin(eps) + 1.0;

tX = cos(lambda) + 1.0;

*rA = atan2(sin(lambda)*cos(eps) - tan(beta)*sin(eps), cos(lambda));

doubleNormalize0to2pi(rA);

*dec = asin(sin(beta)*cos(eps) + cos(beta)*sin(eps)*sin(lambda));

*distance = sqrt(x*x + y*y + z*z);

}