/* +++Date last modified: 05-Jul-1997 */
/*
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 */
main()
{
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;
char buf[80];
printf( "Longitude (+ is east) and latitude (+ is north) : " );
fgets(buf, 80, stdin);
sscanf(buf, "%lf %lf", &lon, &lat );
for(;;)
{
printf( "Input date ( yyyy mm dd ) (ctrl-C exits): " );
fgets(buf, 80, stdin);
sscanf(buf, "%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;
}
return 0;
}
}
/* 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 compute */
/* 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 sidereal 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 altitude 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 altitude 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 unchanged */
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 Greenwich 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 generalized 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 */