# sidetrack [was Re: 'at now' not working as expected]

Michael Butler imb at protected-networks.net
Fri Oct 10 00:17:05 UTC 2008

```I wrote:
> The attached program (not mine - credits in the header) does this
> effectively given your current position as input,

Inserted as text since it got stripped last time ..

> ------------------------------------------------------------------------

/*

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

This program may be used by anyone for any purpose, iff:
1. it is not being sold for profit
2. this notice is not removed

*/

#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 */

/* 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 ): ");
if (scanf ("%d %d %d", &year, &month, &day) != 3)
exit (0);

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 */
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)

/* 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 */
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)

/* 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 */
```