/* 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 #include /* 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 */