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sunriset.c

/*

SUNRISET.C - computes Sun rise/set times, start/end of twilight, and
             the length of the day at any date and latitude

Written as DAYLEN.C, 1989-08-16

Modified to SUNRISET.C, 1992-12-01

(c) Paul Schlyter, 1989, 1992

Released to the public domain by Paul Schlyter, December 1992

*/


#include <stdio.h>
#include <math.h>


/* A macro to compute the number of days elapsed since 2000 Jan 0.0 */
/* (which is equal to 1999 Dec 31, 0h UT)                           */

#define days_since_2000_Jan_0(y,m,d) \
    (367L*(y)-((7*((y)+(((m)+9)/12)))/4)+((275*(m))/9)+(d)-730530L)

/* Some conversion factors between radians and degrees */

#ifndef PI
 #define PI        3.1415926535897932384
#endif

#define RADEG     ( 180.0 / PI )
#define DEGRAD    ( PI / 180.0 )

/* The trigonometric functions in degrees */

#define sind(x)  sin((x)*DEGRAD)
#define cosd(x)  cos((x)*DEGRAD)
#define tand(x)  tan((x)*DEGRAD)

#define atand(x)    (RADEG*atan(x))
#define asind(x)    (RADEG*asin(x))
#define acosd(x)    (RADEG*acos(x))
#define atan2d(y,x) (RADEG*atan2(y,x))


/* Following are some macros around the "workhorse" function __daylen__ */
/* They mainly fill in the desired values for the reference altitude    */
/* below the horizon, and also selects whether this altitude should     */
/* refer to the Sun's center or its upper limb.                         */


/* This macro computes the length of the day, from sunrise to sunset. */
/* Sunrise/set is considered to occur when the Sun's upper limb is    */
/* 35 arc minutes below the horizon (this accounts for the refraction */
/* of the Earth's atmosphere).                                        */
#define day_length(year,month,day,lon,lat)  \
        __daylen__( year, month, day, lon, lat, -35.0/60.0, 1 )

/* This macro computes the length of the day, including civil twilight. */
/* Civil twilight starts/ends when the Sun's center is 6 degrees below  */
/* the horizon.                                                         */
#define day_civil_twilight_length(year,month,day,lon,lat)  \
        __daylen__( year, month, day, lon, lat, -6.0, 0 )

/* This macro computes the length of the day, incl. nautical twilight.  */
/* Nautical twilight starts/ends when the Sun's center is 12 degrees    */
/* below the horizon.                                                   */
#define day_nautical_twilight_length(year,month,day,lon,lat)  \
        __daylen__( year, month, day, lon, lat, -12.0, 0 )

/* This macro computes the length of the day, incl. astronomical twilight. */
/* Astronomical twilight starts/ends when the Sun's center is 18 degrees   */
/* below the horizon.                                                      */
#define day_astronomical_twilight_length(year,month,day,lon,lat)  \
        __daylen__( year, month, day, lon, lat, -18.0, 0 )


/* This macro computes times for sunrise/sunset.                      */
/* Sunrise/set is considered to occur when the Sun's upper limb is    */
/* 35 arc minutes below the horizon (this accounts for the refraction */
/* of the Earth's atmosphere).                                        */
#define sun_rise_set(year,month,day,lon,lat,rise,set)  \
        __sunriset__( year, month, day, lon, lat, -35.0/60.0, 1, rise, set )

/* This macro computes the start and end times of civil twilight.       */
/* Civil twilight starts/ends when the Sun's center is 6 degrees below  */
/* the horizon.                                                         */
#define civil_twilight(year,month,day,lon,lat,start,end)  \
        __sunriset__( year, month, day, lon, lat, -6.0, 0, start, end )

/* This macro computes the start and end times of nautical twilight.    */
/* Nautical twilight starts/ends when the Sun's center is 12 degrees    */
/* below the horizon.                                                   */
#define nautical_twilight(year,month,day,lon,lat,start,end)  \
        __sunriset__( year, month, day, lon, lat, -12.0, 0, start, end )

/* This macro computes the start and end times of astronomical twilight.   */
/* Astronomical twilight starts/ends when the Sun's center is 18 degrees   */
/* below the horizon.                                                      */
#define astronomical_twilight(year,month,day,lon,lat,start,end)  \
        __sunriset__( year, month, day, lon, lat, -18.0, 0, start, end )


/* Function prototypes */

double __daylen__( int year, int month, int day, double lon, double lat,
                   double altit, int upper_limb );

int __sunriset__( int year, int month, int day, double lon, double lat,
                  double altit, int upper_limb, double *rise, double *set );

void sunpos( double d, double *lon, double *r );

void sun_RA_dec( double d, double *RA, double *dec, double *r );

double revolution( double x );

double rev180( double x );

double GMST0( double d );



/* A small test program */

void main(void)
{
      int year,month,day;
      double lon, lat;
      double daylen, civlen, nautlen, astrlen;
      double rise, set, civ_start, civ_end, naut_start, naut_end,
             astr_start, astr_end;
      int    rs, civ, naut, astr;

      printf( "Longitude (+ is east) and latitude (+ is north) : " );
      scanf( "%lf %lf", &lon, &lat );

      for(;;)
      {
            printf( "Input date ( yyyy mm dd ) (ctrl-C exits): " );
            scanf( "%d %d %d", &year, &month, &day );

            daylen  = day_length(year,month,day,lon,lat);
            civlen  = day_civil_twilight_length(year,month,day,lon,lat);
            nautlen = day_nautical_twilight_length(year,month,day,lon,lat);
            astrlen = day_astronomical_twilight_length(year,month,day,
                  lon,lat);

            printf( "Day length:                 %5.2f hours\n", daylen );
            printf( "With civil twilight         %5.2f hours\n", civlen );
            printf( "With nautical twilight      %5.2f hours\n", nautlen );
            printf( "With astronomical twilight  %5.2f hours\n", astrlen );
            printf( "Length of twilight: civil   %5.2f hours\n",
                  (civlen-daylen)/2.0);
            printf( "                  nautical  %5.2f hours\n",
                  (nautlen-daylen)/2.0);
            printf( "              astronomical  %5.2f hours\n",
                  (astrlen-daylen)/2.0);

            rs   = sun_rise_set         ( year, month, day, lon, lat,
                                          &rise, &set );
            civ  = civil_twilight       ( year, month, day, lon, lat,
                                          &civ_start, &civ_end );
            naut = nautical_twilight    ( year, month, day, lon, lat,
                                          &naut_start, &naut_end );
            astr = astronomical_twilight( year, month, day, lon, lat,
                                          &astr_start, &astr_end );

            printf( "Sun at south %5.2fh UT\n", (rise+set)/2.0 );

            switch( rs )
            {
                case 0:
                    printf( "Sun rises %5.2fh UT, sets %5.2fh UT\n",
                             rise, set );
                    break;
                case +1:
                    printf( "Sun above horizon\n" );
                    break;
                case -1:
                    printf( "Sun below horizon\n" );
                    break;
            }

            switch( civ )
            {
                case 0:
                    printf( "Civil twilight starts %5.2fh, "
                            "ends %5.2fh UT\n", civ_start, civ_end );
                    break;
                case +1:
                    printf( "Never darker than civil twilight\n" );
                    break;
                case -1:
                    printf( "Never as bright as civil twilight\n" );
                    break;
            }

            switch( naut )
            {
                case 0:
                    printf( "Nautical twilight starts %5.2fh, "
                            "ends %5.2fh UT\n", naut_start, naut_end );
                    break;
                case +1:
                    printf( "Never darker than nautical twilight\n" );
                    break;
                case -1:
                    printf( "Never as bright as nautical twilight\n" );
                    break;
            }

            switch( astr )
            {
                case 0:
                    printf( "Astronomical twilight starts %5.2fh, "
                            "ends %5.2fh UT\n", astr_start, astr_end );
                    break;
                case +1:
                    printf( "Never darker than astronomical twilight\n" );
                    break;
                case -1:
                    printf( "Never as bright as astronomical twilight\n" );
                    break;
            }

      }
}


/* The "workhorse" function for sun rise/set times */

int __sunriset__( int year, int month, int day, double lon, double lat,
                  double altit, int upper_limb, double *trise, double *tset )
/***************************************************************************/
/* Note: year,month,date = calendar date, 1801-2099 only.             */
/*       Eastern longitude positive, Western longitude negative       */
/*       Northern latitude positive, Southern latitude negative       */
/*       The longitude value IS critical in this function!            */
/*       altit = the altitude which the Sun should cross              */
/*               Set to -35/60 degrees for rise/set, -6 degrees       */
/*               for civil, -12 degrees for nautical and -18          */
/*               degrees for astronomical twilight.                   */
/*         upper_limb: non-zero -> upper limb, zero -> center         */
/*               Set to non-zero (e.g. 1) when computing rise/set     */
/*               times, and to zero when computing start/end of       */
/*               twilight.                                            */
/*        *rise = where to store the rise time                        */
/*        *set  = where to store the set  time                        */
/*                Both times are relative to the specified altitude,  */
/*                and thus this function can be used to comupte       */
/*                various twilight times, as well as rise/set times   */
/* Return value:  0 = sun rises/sets this day, times stored at        */
/*                    *trise and *tset.                               */
/*               +1 = sun above the specified "horizon" 24 hours.     */
/*                    *trise set to time when the sun is at south,    */
/*                    minus 12 hours while *tset is set to the south  */
/*                    time plus 12 hours. "Day" length = 24 hours     */
/*               -1 = sun is below the specified "horizon" 24 hours   */
/*                    "Day" length = 0 hours, *trise and *tset are    */
/*                    both set to the time when the sun is at south.  */
/*                                                                    */
/**********************************************************************/
{
      double  d,  /* Days since 2000 Jan 0.0 (negative before) */
      sr,         /* Solar distance, astronomical units */
      sRA,        /* Sun's Right Ascension */
      sdec,       /* Sun's declination */
      sradius,    /* Sun's apparent radius */
      t,          /* Diurnal arc */
      tsouth,     /* Time when Sun is at south */
      sidtime;    /* Local sidereal time */

      int rc = 0; /* Return cde from function - usually 0 */

      /* Compute d of 12h local mean solar time */
      d = days_since_2000_Jan_0(year,month,day) + 0.5 - lon/360.0;

      /* Compute local sideral time of this moment */
      sidtime = revolution( GMST0(d) + 180.0 + lon );

      /* Compute Sun's RA + Decl at this moment */
      sun_RA_dec( d, &sRA, &sdec, &sr );

      /* Compute time when Sun is at south - in hours UT */
      tsouth = 12.0 - rev180(sidtime - sRA)/15.0;

      /* Compute the Sun's apparent radius, degrees */
      sradius = 0.2666 / sr;

      /* Do correction to upper limb, if necessary */
      if ( upper_limb )
            altit -= sradius;

      /* Compute the diurnal arc that the Sun traverses to reach */
      /* the specified altitide altit: */
      {
            double cost;
            cost = ( sind(altit) - sind(lat) * sind(sdec) ) /
                  ( cosd(lat) * cosd(sdec) );
            if ( cost >= 1.0 )
                  rc = -1, t = 0.0;       /* Sun always below altit */
            else if ( cost <= -1.0 )
                  rc = +1, t = 12.0;      /* Sun always above altit */
            else
                  t = acosd(cost)/15.0;   /* The diurnal arc, hours */
      }

      /* Store rise and set times - in hours UT */
      *trise = tsouth - t;
      *tset  = tsouth + t;

      return rc;
}  /* __sunriset__ */



/* The "workhorse" function */


double __daylen__( int year, int month, int day, double lon, double lat,
                   double altit, int upper_limb )
/**********************************************************************/
/* Note: year,month,date = calendar date, 1801-2099 only.             */
/*       Eastern longitude positive, Western longitude negative       */
/*       Northern latitude positive, Southern latitude negative       */
/*       The longitude value is not critical. Set it to the correct   */
/*       longitude if you're picky, otherwise set to to, say, 0.0     */
/*       The latitude however IS critical - be sure to get it correct */
/*       altit = the altitude which the Sun should cross              */
/*               Set to -35/60 degrees for rise/set, -6 degrees       */
/*               for civil, -12 degrees for nautical and -18          */
/*               degrees for astronomical twilight.                   */
/*         upper_limb: non-zero -> upper limb, zero -> center         */
/*               Set to non-zero (e.g. 1) when computing day length   */
/*               and to zero when computing day+twilight length.      */
/**********************************************************************/
{
      double  d,  /* Days since 2000 Jan 0.0 (negative before) */
      obl_ecl,    /* Obliquity (inclination) of Earth's axis */
      sr,         /* Solar distance, astronomical units */
      slon,       /* True solar longitude */
      sin_sdecl,  /* Sine of Sun's declination */
      cos_sdecl,  /* Cosine of Sun's declination */
      sradius,    /* Sun's apparent radius */
      t;          /* Diurnal arc */

      /* Compute d of 12h local mean solar time */
      d = days_since_2000_Jan_0(year,month,day) + 0.5 - lon/360.0;

      /* Compute obliquity of ecliptic (inclination of Earth's axis) */
      obl_ecl = 23.4393 - 3.563E-7 * d;

      /* Compute Sun's position */
      sunpos( d, &slon, &sr );

      /* Compute sine and cosine of Sun's declination */
      sin_sdecl = sind(obl_ecl) * sind(slon);
      cos_sdecl = sqrt( 1.0 - sin_sdecl * sin_sdecl );

      /* Compute the Sun's apparent radius, degrees */
      sradius = 0.2666 / sr;

      /* Do correction to upper limb, if necessary */
      if ( upper_limb )
            altit -= sradius;

      /* Compute the diurnal arc that the Sun traverses to reach */
      /* the specified altitide altit: */
      {
            double cost;
            cost = ( sind(altit) - sind(lat) * sin_sdecl ) /
                  ( cosd(lat) * cos_sdecl );
            if ( cost >= 1.0 )
                  t = 0.0;                      /* Sun always below altit */
            else if ( cost <= -1.0 )
                  t = 24.0;                     /* Sun always above altit */
            else  t = (2.0/15.0) * acosd(cost); /* The diurnal arc, hours */
      }
      return t;
}  /* __daylen__ */


/* This function computes the Sun's position at any instant */

void sunpos( double d, double *lon, double *r )
/******************************************************/
/* Computes the Sun's ecliptic longitude and distance */
/* at an instant given in d, number of days since     */
/* 2000 Jan 0.0.  The Sun's ecliptic latitude is not  */
/* computed, since it's always very near 0.           */
/******************************************************/
{
      double M,         /* Mean anomaly of the Sun */
             w,         /* Mean longitude of perihelion */
                        /* Note: Sun's mean longitude = M + w */
             e,         /* Eccentricity of Earth's orbit */
             E,         /* Eccentric anomaly */
             x, y,      /* x, y coordinates in orbit */
             v;         /* True anomaly */

      /* Compute mean elements */
      M = revolution( 356.0470 + 0.9856002585 * d );
      w = 282.9404 + 4.70935E-5 * d;
      e = 0.016709 - 1.151E-9 * d;

      /* Compute true longitude and radius vector */
      E = M + e * RADEG * sind(M) * ( 1.0 + e * cosd(M) );
            x = cosd(E) - e;
      y = sqrt( 1.0 - e*e ) * sind(E);
      *r = sqrt( x*x + y*y );              /* Solar distance */
      v = atan2d( y, x );                  /* True anomaly */
      *lon = v + w;                        /* True solar longitude */
      if ( *lon >= 360.0 )
            *lon -= 360.0;                   /* Make it 0..360 degrees */
}

void sun_RA_dec( double d, double *RA, double *dec, double *r )
{
      double lon, obl_ecl, x, y, z;

      /* Compute Sun's ecliptical coordinates */
      sunpos( d, &lon, r );

      /* Compute ecliptic rectangular coordinates (z=0) */
      x = *r * cosd(lon);
      y = *r * sind(lon);

      /* Compute obliquity of ecliptic (inclination of Earth's axis) */
      obl_ecl = 23.4393 - 3.563E-7 * d;

      /* Convert to equatorial rectangular coordinates - x is uchanged */
      z = y * sind(obl_ecl);
      y = y * cosd(obl_ecl);

      /* Convert to spherical coordinates */
      *RA = atan2d( y, x );
      *dec = atan2d( z, sqrt(x*x + y*y) );

}  /* sun_RA_dec */


/******************************************************************/
/* This function reduces any angle to within the first revolution */
/* by subtracting or adding even multiples of 360.0 until the     */
/* result is >= 0.0 and < 360.0                                   */
/******************************************************************/

#define INV360    ( 1.0 / 360.0 )

double revolution( double x )
/*****************************************/
/* Reduce angle to within 0..360 degrees */
/*****************************************/
{
      return( x - 360.0 * floor( x * INV360 ) );
}  /* revolution */

double rev180( double x )
/*********************************************/
/* Reduce angle to within +180..+180 degrees */
/*********************************************/
{
      return( x - 360.0 * floor( x * INV360 + 0.5 ) );
}  /* revolution */


/*******************************************************************/
/* This function computes GMST0, the Greenwhich Mean Sidereal Time */
/* at 0h UT (i.e. the sidereal time at the Greenwhich meridian at  */
/* 0h UT).  GMST is then the sidereal time at Greenwich at any     */
/* time of the day.  I've generelized GMST0 as well, and define it */
/* as:  GMST0 = GMST - UT  --  this allows GMST0 to be computed at */
/* other times than 0h UT as well.  While this sounds somewhat     */
/* contradictory, it is very practical:  instead of computing      */
/* GMST like:                                                      */
/*                                                                 */
/*  GMST = (GMST0) + UT * (366.2422/365.2422)                      */
/*                                                                 */
/* where (GMST0) is the GMST last time UT was 0 hours, one simply  */
/* computes:                                                       */
/*                                                                 */
/*  GMST = GMST0 + UT                                              */
/*                                                                 */
/* where GMST0 is the GMST "at 0h UT" but at the current moment!   */
/* Defined in this way, GMST0 will increase with about 4 min a     */
/* day.  It also happens that GMST0 (in degrees, 1 hr = 15 degr)   */
/* is equal to the Sun's mean longitude plus/minus 180 degrees!    */
/* (if we neglect aberration, which amounts to 20 seconds of arc   */
/* or 1.33 seconds of time)                                        */
/*                                                                 */
/*******************************************************************/

double GMST0( double d )
{
      double sidtim0;
      /* Sidtime at 0h UT = L (Sun's mean longitude) + 180.0 degr  */
      /* L = M + w, as defined in sunpos().  Since I'm too lazy to */
      /* add these numbers, I'll let the C compiler do it for me.  */
      /* Any decent C compiler will add the constants at compile   */
      /* time, imposing no runtime or code overhead.               */
      sidtim0 = revolution( ( 180.0 + 356.0470 + 282.9404 ) +
                          ( 0.9856002585 + 4.70935E-5 ) * d );
      return sidtim0;
}  /* GMST0 */

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