519 lines
16 KiB
Plaintext
519 lines
16 KiB
Plaintext
#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#define RADS 0.0174532925199433
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#define DEGS 57.2957795130823
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#define TPI 6.28318530717959
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#define PI 3.1415927
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/* ratio of earth radius to astronomical unit */
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#define ER_OVER_AU 0.0000426352325194252
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/* all prototypes here */
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double getcoord(int coord);
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void getargs(int argc, char *argv[], int *y, int *m, double *tz, double *glong, double *glat);
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double range(double y);
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double rangerad(double y);
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double days(int y, int m, int dn, double hour);
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double days_(int *y, int *m, int *dn, double *hour);
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void moonpos(double, double *, double *, double *);
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void sunpos(double , double *, double *, double *);
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double moontransit(int y, int m, int d, double timezone, double glat, double glong, int *nt);
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double atan22(double y, double x);
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double epsilon(double d);
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void equatorial(double d, double *lon, double *lat, double *r);
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void ecliptic(double d, double *lon, double *lat, double *r);
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double gst(double d);
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void topo(double lst, double glat, double *alp, double *dec, double *r);
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double alt(double glat, double ha, double dec);
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void libration(double day, double lambda, double beta, double alpha, double *l, double *b, double *p);
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void illumination(double day, double lra, double ldec, double dr, double sra, double sdec, double *pabl, double *ill);
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int daysinmonth(int y, int m);
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int isleap(int y);
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void tmoonsub_(double *day, double *glat, double *glong, double *moonalt,
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double *mrv, double *l, double *b, double *paxis);
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static const char
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usage[] = " Usage: tmoon date[yyyymm] timz[+/-h.hh] long[+/-dddmm] lat[+/-ddmm]\n"
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"example: tmoon 200009 0 -00155 5230\n";
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/*
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getargs() gets the arguments from the command line, does some basic error
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checking, and converts arguments into numerical form. Arguments are passed
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back in pointers. Error messages print to stderr so re-direction of output
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to file won't leave users blind. Error checking prints list of all errors
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in a command line before quitting.
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*/
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void getargs(int argc, char *argv[], int *y, int *m, double *tz,
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double *glong, double *glat) {
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int date, latitude, longitude;
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int mflag = 0, yflag = 0, longflag = 0, latflag = 0, tzflag = 0;
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int longminflag = 0, latminflag = 0, dflag = 0;
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/* if not right number of arguments, then print example command line */
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if (argc !=5) {
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fprintf(stderr, usage);
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exit(EXIT_FAILURE);
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}
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date = atoi(argv[1]);
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*y = date / 100;
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*m = date - *y * 100;
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*tz = (double) atof(argv[2]);
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longitude = atoi(argv[3]);
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latitude = atoi(argv[4]);
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*glong = RADS * getcoord(longitude);
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*glat = RADS * getcoord(latitude);
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/* set a flag for each error found */
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if (*m > 12 || *m < 1) mflag = 1;
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if (*y > 2500) yflag = 1;
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if (date < 150001) dflag = 1;
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if (fabs((float) *glong) > 180 * RADS) longflag = 1;
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if (abs(longitude) % 100 > 59) longminflag = 1;
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if (fabs((float) *glat) > 90 * RADS) latflag = 1;
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if (abs(latitude) % 100 > 59) latminflag = 1;
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if (fabs((float) *tz) > 12) tzflag = 1;
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/* print all the errors found */
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if (dflag == 1) {
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fprintf(stderr, "date: dates must be in form yyyymm, gregorian, and later than 1500 AD\n");
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}
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if (yflag == 1) {
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fprintf(stderr, "date: too far in future - accurate from 1500 to 2500\n");
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}
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if (mflag == 1) {
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fprintf(stderr, "date: month must be in range 0 to 12, eg - August 2000 is entered as 200008\n");
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}
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if (tzflag == 1) {
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fprintf(stderr, "timz: must be in range +/- 12 hours, eg -6 for Chicago\n");
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}
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if (longflag == 1) {
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fprintf(stderr, "long: must be in range +/- 180 degrees\n");
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}
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if (longminflag == 1) {
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fprintf(stderr, "long: last two digits are arcmin - max 59\n");
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}
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if (latflag == 1) {
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fprintf(stderr, " lat: must be in range +/- 90 degrees\n");
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}
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if (latminflag == 1) {
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fprintf(stderr, " lat: last two digits are arcmin - max 59\n");
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}
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/* quits if one or more flags set */
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if (dflag + mflag + yflag + longflag + latflag + tzflag + longminflag + latminflag > 0) {
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exit(EXIT_FAILURE);
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}
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}
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/*
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returns coordinates in decimal degrees given the
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coord as a ddmm value stored in an integer.
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*/
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double getcoord(int coord) {
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int west = 1;
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double glg, deg;
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if (coord < 0) west = -1;
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glg = fabs((double) coord/100);
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deg = floor(glg);
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glg = west* (deg + (glg - deg)*100 / 60);
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return(glg);
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}
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/*
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days() takes the year, month, day in the month and decimal hours
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in the day and returns the number of days since J2000.0.
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Assumes Gregorian calendar.
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*/
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double days(int y, int m, int d, double h) {
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int a, b;
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double day;
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/*
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The lines below work from 1900 march to feb 2100
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a = 367 * y - 7 * (y + (m + 9) / 12) / 4 + 275 * m / 9 + d;
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day = (double)a - 730531.5 + hour / 24;
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*/
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/* These lines work for any Gregorian date since 0 AD */
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if (m ==1 || m==2) {
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m +=12;
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y -= 1;
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}
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a = y / 100;
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b = 2 - a + a/4;
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day = floor(365.25*(y + 4716)) + floor(30.6001*(m + 1))
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+ d + b - 1524.5 - 2451545 + h/24;
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return(day);
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}
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double days_(int *y0, int *m0, int *d0, double *h0)
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{
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return days(*y0,*m0,*d0,*h0);
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}
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/*
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Returns 1 if y a leap year, and 0 otherwise, according
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to the Gregorian calendar
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*/
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int isleap(int y) {
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int a = 0;
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if(y % 4 == 0) a = 1;
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if(y % 100 == 0) a = 0;
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if(y % 400 == 0) a = 1;
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return(a);
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}
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/*
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Given the year and the month, function returns the
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number of days in the month. Valid for Gregorian
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calendar.
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*/
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int daysinmonth(int y, int m) {
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int b = 31;
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if(m == 2) {
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if(isleap(y) == 1) b= 29;
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else b = 28;
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}
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if(m == 4 || m == 6 || m == 9 || m == 11) b = 30;
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return(b);
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}
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/*
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moonpos() takes days from J2000.0 and returns ecliptic coordinates
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of moon in the pointers. Note call by reference.
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This function is within a couple of arcminutes most of the time,
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and is truncated from the Meeus Ch45 series, themselves truncations of
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ELP-2000. Returns moon distance in earth radii.
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Terms have been written out explicitly rather than using the
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table based method as only a small number of terms is
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retained.
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*/
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void moonpos(double d, double *lambda, double *beta, double *rvec) {
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double dl, dB, dR, L, D, M, M1, F, e, lm, bm, rm, t;
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t = d / 36525;
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L = range(218.3164591 + 481267.88134236 * t) * RADS;
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D = range(297.8502042 + 445267.1115168 * t) * RADS;
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M = range(357.5291092 + 35999.0502909 * t) * RADS;
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M1 = range(134.9634114 + 477198.8676313 * t - .008997 * t * t) * RADS;
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F = range(93.27209929999999 + 483202.0175273 * t - .0034029*t*t)*RADS;
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e = 1 - .002516 * t;
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dl = 6288774 * sin(M1);
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dl += 1274027 * sin(2 * D - M1);
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dl += 658314 * sin(2 * D);
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dl += 213618 * sin(2 * M1);
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dl -= e * 185116 * sin(M);
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dl -= 114332 * sin(2 * F) ;
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dl += 58793 * sin(2 * D - 2 * M1);
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dl += e * 57066 * sin(2 * D - M - M1) ;
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dl += 53322 * sin(2 * D + M1);
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dl += e * 45758 * sin(2 * D - M);
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dl -= e * 40923 * sin(M - M1);
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dl -= 34720 * sin(D) ;
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dl -= e * 30383 * sin(M + M1) ;
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dl += 15327 * sin(2 * D - 2 * F) ;
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dl -= 12528 * sin(M1 + 2 * F);
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dl += 10980 * sin(M1 - 2 * F);
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lm = rangerad(L + dl / 1000000 * RADS);
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dB = 5128122 * sin(F);
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dB += 280602 * sin(M1 + F);
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dB += 277693 * sin(M1 - F);
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dB += 173237 * sin(2 * D - F);
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dB += 55413 * sin(2 * D - M1 + F);
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dB += 46271 * sin(2 * D - M1 - F);
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dB += 32573 * sin(2 * D + F);
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dB += 17198 * sin(2 * M1 + F);
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dB += 9266 * sin(2 * D + M1 - F);
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dB += 8822 * sin(2 * M1 - F);
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dB += e * 8216 * sin(2 * D - M - F);
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dB += 4324 * sin(2 * D - 2 * M1 - F);
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bm = dB / 1000000 * RADS;
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dR = -20905355 * cos(M1);
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dR -= 3699111 * cos(2 * D - M1);
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dR -= 2955968 * cos(2 * D);
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dR -= 569925 * cos(2 * M1);
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dR += e * 48888 * cos(M);
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dR -= 3149 * cos(2 * F);
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dR += 246158 * cos(2 * D - 2 * M1);
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dR -= e * 152138 * cos(2 * D - M - M1) ;
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dR -= 170733 * cos(2 * D + M1);
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dR -= e * 204586 * cos(2 * D - M);
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dR -= e * 129620 * cos(M - M1);
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dR += 108743 * cos(D);
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dR += e * 104755 * cos(M + M1);
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dR += 79661 * cos(M1 - 2 * F);
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rm = 385000.56 + dR / 1000;
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*lambda = lm;
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*beta = bm;
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/* distance to Moon must be in Earth radii */
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*rvec = rm / 6378.14;
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}
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/*
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topomoon() takes the local siderial time, the geographical
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latitude of the observer, and pointers to the geocentric
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equatorial coordinates. The function overwrites the geocentric
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coordinates with topocentric coordinates on a simple spherical
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earth model (no polar flattening). Expects Moon-Earth distance in
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Earth radii. Formulas scavenged from Astronomical Almanac 'low
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precision formulae for Moon position' page D46.
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*/
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void topo(double lst, double glat, double *alp, double *dec, double *r) {
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double x, y, z, r1;
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x = *r * cos(*dec) * cos(*alp) - cos(glat) * cos(lst);
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y = *r * cos(*dec) * sin(*alp) - cos(glat) * sin(lst);
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z = *r * sin(*dec) - sin(glat);
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r1 = sqrt(x*x + y*y + z*z);
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*alp = atan22(y, x);
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*dec = asin(z / r1);
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*r = r1;
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}
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/*
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moontransit() takes date, the time zone and geographic longitude
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of observer and returns the time (decimal hours) of lunar transit
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on that day if there is one, and sets the notransit flag if there
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isn't. See Explanatory Supplement to Astronomical Almanac
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section 9.32 and 9.31 for the method.
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*/
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double moontransit(int y, int m, int d, double tz, double glat, double glong, int *notransit) {
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double hm, ht, ht1, lon, lat, rv, dnew, lst;
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int itcount;
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ht1 = 180 * RADS;
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ht = 0;
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itcount = 0;
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*notransit = 0;
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do {
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ht = ht1;
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itcount++;
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dnew = days(y, m, d, ht * DEGS/15) - tz/24;
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lst = gst(dnew) + glong;
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/* find the topocentric Moon ra (hence hour angle) and dec */
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moonpos(dnew, &lon, &lat, &rv);
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equatorial(dnew, &lon, &lat, &rv);
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topo(lst, glat, &lon, &lat, &rv);
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hm = rangerad(lst - lon);
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ht1 = rangerad(ht - hm);
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/* if no convergence, then no transit on that day */
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if (itcount > 30) {
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*notransit = 1;
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break;
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}
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}
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while (fabs(ht - ht1) > 0.04 * RADS);
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return(ht1);
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}
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/*
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Calculates the selenographic coordinates of either the sub Earth point
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(optical libration) or the sub-solar point (selen. coords of centre of
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bright hemisphere). Based on Meeus chapter 51 but neglects physical
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libration and nutation, with some simplification of the formulas.
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*/
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void libration(double day, double lambda, double beta, double alpha, double *l, double *b, double *p) {
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double i, f, omega, w, y, x, a, t, eps;
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t = day / 36525;
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i = 1.54242 * RADS;
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eps = epsilon(day);
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f = range(93.2720993 + 483202.0175273 * t - .0034029 * t * t) * RADS;
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omega = range(125.044555 - 1934.1361849 * t + .0020762 * t * t) * RADS;
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w = lambda - omega;
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y = sin(w) * cos(beta) * cos(i) - sin(beta) * sin(i);
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x = cos(w) * cos(beta);
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a = atan22(y, x);
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*l = a - f;
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/* kludge to catch cases of 'round the back' angles */
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if (*l < -90 * RADS) *l += TPI;
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if (*l > 90 * RADS) *l -= TPI;
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*b = asin(-sin(w) * cos(beta) * sin(i) - sin(beta) * cos(i));
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/* pa pole axis - not used for Sun stuff */
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x = sin(i) * sin(omega);
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y = sin(i) * cos(omega) * cos(eps) - cos(i) * sin(eps);
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w = atan22(x, y);
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*p = rangerad(asin(sqrt(x*x + y*y) * cos(alpha - w) / cos(*b)));
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}
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/*
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Takes: days since J2000.0, eq coords Moon, ratio of moon to sun distance,
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eq coords Sun
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Returns: position angle of bright limb wrt NCP, percentage illumination
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of Sun
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*/
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void illumination(double day , double lra, double ldec, double dr, double sra, double sdec, double *pabl, double *ill) {
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double x, y, phi, i;
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(void)day;
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y = cos(sdec) * sin(sra - lra);
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x = sin(sdec) * cos(ldec) - cos(sdec) * sin(ldec) * cos (sra - lra);
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*pabl = atan22(y, x);
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phi = acos(sin(sdec) * sin(ldec) + cos(sdec) * cos(ldec) * cos(sra-lra));
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i = atan22(sin(phi) , (dr - cos(phi)));
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*ill = 0.5*(1 + cos(i));
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}
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/*
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sunpos() takes days from J2000.0 and returns ecliptic longitude
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of Sun in the pointers. Latitude is zero at this level of precision,
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but pointer left in for consistency in number of arguments.
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This function is within 0.01 degree (1 arcmin) almost all the time
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for a century either side of J2000.0. This is from the 'low precision
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fomulas for the Sun' from C24 of Astronomical Alamanac
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*/
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void sunpos(double d, double *lambda, double *beta, double *rvec) {
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double L, g, ls, bs, rs;
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L = range(280.461 + .9856474 * d) * RADS;
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g = range(357.528 + .9856003 * d) * RADS;
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ls = L + (1.915 * sin(g) + .02 * sin(2 * g)) * RADS;
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bs = 0;
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rs = 1.00014 - .01671 * cos(g) - .00014 * cos(2 * g);
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*lambda = ls;
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*beta = bs;
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*rvec = rs;
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}
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/*
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this routine returns the altitude given the days since J2000.0
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the hour angle and declination of the object and the latitude
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of the observer. Used to find the Sun's altitude to put a letter
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code on the transit time, and to find the Moon's altitude at
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transit just to make sure that the Moon is visible.
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*/
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double alt(double glat, double ha, double dec) {
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return(asin(sin(dec) * sin(glat) + cos(dec) * cos(glat) * cos(ha)));
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}
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/* returns an angle in degrees in the range 0 to 360 */
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double range(double x) {
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double a, b;
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b = x / 360;
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a = 360 * (b - floor(b));
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if (a < 0)
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a = 360 + a;
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return(a);
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}
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/* returns an angle in rads in the range 0 to two pi */
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double rangerad(double x) {
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double a, b;
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b = x / TPI;
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a = TPI * (b - floor(b));
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if (a < 0)
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a = TPI + a;
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return(a);
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}
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/*
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gets the atan2 function returning angles in the right
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order and range
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*/
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double atan22(double y, double x) {
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double a;
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a = atan2(y, x);
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if (a < 0) a += TPI;
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return(a);
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}
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/*
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returns mean obliquity of ecliptic in radians given days since
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J2000.0.
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*/
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double epsilon(double d) {
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double t = d/ 36525;
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return((23.4392911111111 - (t* (46.8150 + 0.00059*t)/3600)) *RADS);
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}
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/*
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replaces ecliptic coordinates with equatorial coordinates
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note: call by reference destroys original values
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R is unchanged.
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*/
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void equatorial(double d, double *lon, double *lat, double * r) {
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double eps, ceps, seps, l, b;
|
|
(void)r;
|
|
|
|
l = *lon;
|
|
b = * lat;
|
|
eps = epsilon(d);
|
|
ceps = cos(eps);
|
|
seps = sin(eps);
|
|
*lon = atan22(sin(l)*ceps - tan(b)*seps, cos(l));
|
|
*lat = asin(sin(b)*ceps + cos(b)*seps*sin(l));
|
|
}
|
|
|
|
/*
|
|
replaces equatorial coordinates with ecliptic ones. Inverse
|
|
of above, but used to find topocentric ecliptic coords.
|
|
*/
|
|
void ecliptic(double d, double *lon, double *lat, double * r) {
|
|
double eps, ceps, seps, alp, dec;
|
|
(void)r;
|
|
|
|
alp = *lon;
|
|
dec = *lat;
|
|
eps = epsilon(d);
|
|
ceps = cos(eps);
|
|
seps = sin(eps);
|
|
*lon = atan22(sin(alp)*ceps + tan(dec)*seps, cos(alp));
|
|
*lat = asin(sin(dec)*ceps - cos(dec)*seps*sin(alp));
|
|
}
|
|
|
|
/*
|
|
returns the siderial time at greenwich meridian as
|
|
an angle in radians given the days since J2000.0
|
|
*/
|
|
double gst( double d) {
|
|
double t = d / 36525;
|
|
double theta;
|
|
theta = range(280.46061837 + 360.98564736629 * d + 0.000387933 * t * t);
|
|
return(theta * RADS);
|
|
}
|
|
|
|
void tmoonsub_(double *day, double *glat, double *glong, double *moonalt,
|
|
double *mrv, double *l, double *b, double *paxis)
|
|
{
|
|
double mlambda, mbeta;
|
|
double malpha, mdelta;
|
|
double lst, mhr;
|
|
double tlambda, tbeta, trv;
|
|
|
|
lst = gst(*day) + *glong;
|
|
|
|
/* find Moon topocentric coordinates for libration calculations */
|
|
|
|
moonpos(*day, &mlambda, &mbeta, mrv);
|
|
malpha = mlambda;
|
|
mdelta = mbeta;
|
|
equatorial(*day, &malpha, &mdelta, mrv);
|
|
topo(lst, *glat, &malpha, &mdelta, mrv);
|
|
mhr = rangerad(lst - malpha);
|
|
*moonalt = alt(*glat, mhr, mdelta);
|
|
|
|
/* Optical libration and Position angle of the Pole */
|
|
|
|
tlambda = malpha;
|
|
tbeta = mdelta;
|
|
trv = *mrv;
|
|
ecliptic(*day, &tlambda, &tbeta, &trv);
|
|
libration(*day, tlambda, tbeta, malpha, l, b, paxis);
|
|
}
|