154359Sroberto/* propdelay.c,v 3.1 1993/07/06 01:05:24 jbj Exp
254359Sroberto * propdelay - compute propagation delays
354359Sroberto *
454359Sroberto * cc -o propdelay propdelay.c -lm
554359Sroberto *
654359Sroberto * "Time and Frequency Users' Manual", NBS Technical Note 695 (1977).
754359Sroberto */
854359Sroberto
954359Sroberto/*
1054359Sroberto * This can be used to get a rough idea of the HF propagation delay
1154359Sroberto * between two points (usually between you and the radio station).
1254359Sroberto * The usage is
1354359Sroberto *
1454359Sroberto * propdelay latitudeA longitudeA latitudeB longitudeB
1554359Sroberto *
1654359Sroberto * where points A and B are the locations in question.  You obviously
1754359Sroberto * need to know the latitude and longitude of each of the places.
1854359Sroberto * The program expects the latitude to be preceded by an 'n' or 's'
1954359Sroberto * and the longitude to be preceded by an 'e' or 'w'.  It understands
2054359Sroberto * either decimal degrees or degrees:minutes:seconds.  Thus to compute
2154359Sroberto * the delay between the WWVH (21:59:26N, 159:46:00W) and WWV (40:40:49N,
2254359Sroberto * 105:02:27W) you could use:
2354359Sroberto *
2454359Sroberto * propdelay n21:59:26 w159:46 n40:40:49 w105:02:27
2554359Sroberto *
2654359Sroberto * By default it prints out a summer (F2 average virtual height 350 km) and
2754359Sroberto * winter (F2 average virtual height 250 km) number.  The results will be
2854359Sroberto * quite approximate but are about as good as you can do with HF time anyway.
2954359Sroberto * You might pick a number between the values to use, or use the summer
3054359Sroberto * value in the summer and switch to the winter value when the static
3154359Sroberto * above 10 MHz starts to drop off in the fall.  You can also use the
3254359Sroberto * -h switch if you want to specify your own virtual height.
3354359Sroberto *
3454359Sroberto * You can also do a
3554359Sroberto *
3654359Sroberto * propdelay -W n45:17:47 w75:45:22
3754359Sroberto *
3854359Sroberto * to find the propagation delays to WWV and WWVH (from CHU in this
3954359Sroberto * case), a
4054359Sroberto *
4154359Sroberto * propdelay -C n40:40:49 w105:02:27
4254359Sroberto *
4354359Sroberto * to find the delays to CHU, and a
4454359Sroberto *
4554359Sroberto * propdelay -G n52:03:17 w98:34:18
4654359Sroberto *
4754359Sroberto * to find delays to GOES via each of the three satellites.
4854359Sroberto */
4954359Sroberto
5054359Sroberto#include <stdio.h>
5154359Sroberto#include <string.h>
5254359Sroberto
5354359Sroberto#include "ntp_stdlib.h"
5454359Sroberto
5554359Srobertoextern	double	sin	(double);
5654359Srobertoextern	double	cos	(double);
5754359Srobertoextern	double	acos	(double);
5854359Srobertoextern	double	tan	(double);
5954359Srobertoextern	double	atan	(double);
6054359Srobertoextern	double	sqrt	(double);
6154359Sroberto
6254359Sroberto#define	STREQ(a, b)	(*(a) == *(b) && strcmp((a), (b)) == 0)
6354359Sroberto
6454359Sroberto/*
6554359Sroberto * Program constants
6654359Sroberto */
6754359Sroberto#define	EARTHRADIUS	(6370.0)	/* raduis of earth (km) */
6854359Sroberto#define	LIGHTSPEED	(299800.0)	/* speed of light, km/s */
6954359Sroberto#define	PI		(3.1415926536)
7054359Sroberto#define	RADPERDEG	(PI/180.0)	/* radians per degree */
7154359Sroberto#define MILE		(1.609344)      /* km in a mile */
7254359Sroberto
7354359Sroberto#define	SUMMERHEIGHT	(350.0)		/* summer height in km */
7454359Sroberto#define	WINTERHEIGHT	(250.0)		/* winter height in km */
7554359Sroberto
7654359Sroberto#define SATHEIGHT	(6.6110 * 6378.0) /* geosync satellite height in km
7754359Sroberto					     from centre of earth */
7854359Sroberto
7954359Sroberto#define WWVLAT  "n40:40:49"
8054359Sroberto#define WWVLONG "w105:02:27"
8154359Sroberto
8254359Sroberto#define WWVHLAT  "n21:59:26"
8354359Sroberto#define WWVHLONG "w159:46:00"
8454359Sroberto
8554359Sroberto#define CHULAT	"n45:17:47"
8654359Sroberto#define	CHULONG	"w75:45:22"
8754359Sroberto
8854359Sroberto#define GOES_UP_LAT  "n37:52:00"
8954359Sroberto#define GOES_UP_LONG "w75:27:00"
9054359Sroberto#define GOES_EAST_LONG "w75:00:00"
9154359Sroberto#define GOES_STBY_LONG "w105:00:00"
9254359Sroberto#define GOES_WEST_LONG "w135:00:00"
9354359Sroberto#define GOES_SAT_LAT "n00:00:00"
9454359Sroberto
9554359Srobertochar *wwvlat = WWVLAT;
9654359Srobertochar *wwvlong = WWVLONG;
9754359Sroberto
9854359Srobertochar *wwvhlat = WWVHLAT;
9954359Srobertochar *wwvhlong = WWVHLONG;
10054359Sroberto
10154359Srobertochar *chulat = CHULAT;
10254359Srobertochar *chulong = CHULONG;
10354359Sroberto
10454359Srobertochar *goes_up_lat = GOES_UP_LAT;
10554359Srobertochar *goes_up_long = GOES_UP_LONG;
10654359Srobertochar *goes_east_long = GOES_EAST_LONG;
10754359Srobertochar *goes_stby_long = GOES_STBY_LONG;
10854359Srobertochar *goes_west_long = GOES_WEST_LONG;
10954359Srobertochar *goes_sat_lat = GOES_SAT_LAT;
11054359Sroberto
11154359Srobertoint hflag = 0;
11254359Srobertoint Wflag = 0;
11354359Srobertoint Cflag = 0;
11454359Srobertoint Gflag = 0;
11554359Srobertoint height;
11654359Sroberto
11754359Srobertochar *progname;
118182007Srobertovolatile int debug;
11954359Sroberto
12054359Srobertostatic	void	doit		(double, double, double, double, double, char *);
12154359Srobertostatic	double	latlong		(char *, int);
12254359Srobertostatic	double	greatcircle	(double, double, double, double);
12354359Srobertostatic	double	waveangle	(double, double, int);
12454359Srobertostatic	double	propdelay	(double, double, int);
12554359Srobertostatic	int	finddelay	(double, double, double, double, double, double *);
12654359Srobertostatic	void	satdoit		(double, double, double, double, double, double, char *);
12754359Srobertostatic	void	satfinddelay	(double, double, double, double, double *);
12854359Srobertostatic	double	satpropdelay	(double);
12954359Sroberto
13054359Sroberto/*
13154359Sroberto * main - parse arguments and handle options
13254359Sroberto */
13354359Srobertoint
13454359Srobertomain(
13554359Sroberto	int argc,
13654359Sroberto	char *argv[]
13754359Sroberto	)
13854359Sroberto{
13954359Sroberto	int c;
14054359Sroberto	int errflg = 0;
14154359Sroberto	double lat1, long1;
14254359Sroberto	double lat2, long2;
14354359Sroberto	double lat3, long3;
14454359Sroberto
14554359Sroberto	progname = argv[0];
14654359Sroberto	while ((c = ntp_getopt(argc, argv, "dh:CWG")) != EOF)
14754359Sroberto	    switch (c) {
14854359Sroberto		case 'd':
14954359Sroberto		    ++debug;
15054359Sroberto		    break;
15154359Sroberto		case 'h':
15254359Sroberto		    hflag++;
15354359Sroberto		    height = atof(ntp_optarg);
15454359Sroberto		    if (height <= 0.0) {
15554359Sroberto			    (void) fprintf(stderr, "height %s unlikely\n",
15654359Sroberto					   ntp_optarg);
15754359Sroberto			    errflg++;
15854359Sroberto		    }
15954359Sroberto		    break;
16054359Sroberto		case 'C':
16154359Sroberto		    Cflag++;
16254359Sroberto		    break;
16354359Sroberto		case 'W':
16454359Sroberto		    Wflag++;
16554359Sroberto		    break;
16654359Sroberto		case 'G':
16754359Sroberto		    Gflag++;
16854359Sroberto		    break;
16954359Sroberto		default:
17054359Sroberto		    errflg++;
17154359Sroberto		    break;
17254359Sroberto	    }
17354359Sroberto	if (errflg || (!(Cflag || Wflag || Gflag) && ntp_optind+4 != argc) ||
17454359Sroberto	    ((Cflag || Wflag || Gflag) && ntp_optind+2 != argc)) {
17554359Sroberto		(void) fprintf(stderr,
17654359Sroberto			       "usage: %s [-d] [-h height] lat1 long1 lat2 long2\n",
17754359Sroberto			       progname);
17854359Sroberto		(void) fprintf(stderr," - or -\n");
17954359Sroberto		(void) fprintf(stderr,
18054359Sroberto			       "usage: %s -CWG [-d] lat long\n",
18154359Sroberto			       progname);
18254359Sroberto		exit(2);
18354359Sroberto	}
18454359Sroberto
18554359Sroberto
18654359Sroberto	if (!(Cflag || Wflag || Gflag)) {
18754359Sroberto		lat1 = latlong(argv[ntp_optind], 1);
18854359Sroberto		long1 = latlong(argv[ntp_optind + 1], 0);
18954359Sroberto		lat2 = latlong(argv[ntp_optind + 2], 1);
19054359Sroberto		long2 = latlong(argv[ntp_optind + 3], 0);
19154359Sroberto		if (hflag) {
19254359Sroberto			doit(lat1, long1, lat2, long2, height, "");
19354359Sroberto		} else {
19454359Sroberto			doit(lat1, long1, lat2, long2, (double)SUMMERHEIGHT,
19554359Sroberto			     "summer propagation, ");
19654359Sroberto			doit(lat1, long1, lat2, long2, (double)WINTERHEIGHT,
19754359Sroberto			     "winter propagation, ");
19854359Sroberto		}
19954359Sroberto	} else if (Wflag) {
20054359Sroberto		/*
20154359Sroberto		 * Compute delay from WWV
20254359Sroberto		 */
20354359Sroberto		lat1 = latlong(argv[ntp_optind], 1);
20454359Sroberto		long1 = latlong(argv[ntp_optind + 1], 0);
20554359Sroberto		lat2 = latlong(wwvlat, 1);
20654359Sroberto		long2 = latlong(wwvlong, 0);
20754359Sroberto		if (hflag) {
20854359Sroberto			doit(lat1, long1, lat2, long2, height, "WWV  ");
20954359Sroberto		} else {
21054359Sroberto			doit(lat1, long1, lat2, long2, (double)SUMMERHEIGHT,
21154359Sroberto			     "WWV  summer propagation, ");
21254359Sroberto			doit(lat1, long1, lat2, long2, (double)WINTERHEIGHT,
21354359Sroberto			     "WWV  winter propagation, ");
21454359Sroberto		}
21554359Sroberto
21654359Sroberto		/*
21754359Sroberto		 * Compute delay from WWVH
21854359Sroberto		 */
21954359Sroberto		lat2 = latlong(wwvhlat, 1);
22054359Sroberto		long2 = latlong(wwvhlong, 0);
22154359Sroberto		if (hflag) {
22254359Sroberto			doit(lat1, long1, lat2, long2, height, "WWVH ");
22354359Sroberto		} else {
22454359Sroberto			doit(lat1, long1, lat2, long2, (double)SUMMERHEIGHT,
22554359Sroberto			     "WWVH summer propagation, ");
22654359Sroberto			doit(lat1, long1, lat2, long2, (double)WINTERHEIGHT,
22754359Sroberto			     "WWVH winter propagation, ");
22854359Sroberto		}
22954359Sroberto	} else if (Cflag) {
23054359Sroberto		lat1 = latlong(argv[ntp_optind], 1);
23154359Sroberto		long1 = latlong(argv[ntp_optind + 1], 0);
23254359Sroberto		lat2 = latlong(chulat, 1);
23354359Sroberto		long2 = latlong(chulong, 0);
23454359Sroberto		if (hflag) {
23554359Sroberto			doit(lat1, long1, lat2, long2, height, "CHU ");
23654359Sroberto		} else {
23754359Sroberto			doit(lat1, long1, lat2, long2, (double)SUMMERHEIGHT,
23854359Sroberto			     "CHU summer propagation, ");
23954359Sroberto			doit(lat1, long1, lat2, long2, (double)WINTERHEIGHT,
24054359Sroberto			     "CHU winter propagation, ");
24154359Sroberto		}
24254359Sroberto	} else if (Gflag) {
24354359Sroberto		lat1 = latlong(goes_up_lat, 1);
24454359Sroberto		long1 = latlong(goes_up_long, 0);
24554359Sroberto		lat3 = latlong(argv[ntp_optind], 1);
24654359Sroberto		long3 = latlong(argv[ntp_optind + 1], 0);
24754359Sroberto
24854359Sroberto		lat2 = latlong(goes_sat_lat, 1);
24954359Sroberto
25054359Sroberto		long2 = latlong(goes_west_long, 0);
25154359Sroberto		satdoit(lat1, long1, lat2, long2, lat3, long3,
25254359Sroberto			"GOES Delay via WEST");
25354359Sroberto
25454359Sroberto		long2 = latlong(goes_stby_long, 0);
25554359Sroberto		satdoit(lat1, long1, lat2, long2, lat3, long3,
25654359Sroberto			"GOES Delay via STBY");
25754359Sroberto
25854359Sroberto		long2 = latlong(goes_east_long, 0);
25954359Sroberto		satdoit(lat1, long1, lat2, long2, lat3, long3,
26054359Sroberto			"GOES Delay via EAST");
26154359Sroberto
26254359Sroberto	}
26354359Sroberto	exit(0);
26454359Sroberto}
26554359Sroberto
26654359Sroberto
26754359Sroberto/*
26854359Sroberto * doit - compute a delay and print it
26954359Sroberto */
27054359Srobertostatic void
27154359Srobertodoit(
27254359Sroberto	double lat1,
27354359Sroberto	double long1,
27454359Sroberto	double lat2,
27554359Sroberto	double long2,
27654359Sroberto	double h,
27754359Sroberto	char *str
27854359Sroberto	)
27954359Sroberto{
28054359Sroberto	int hops;
28154359Sroberto	double delay;
28254359Sroberto
28354359Sroberto	hops = finddelay(lat1, long1, lat2, long2, h, &delay);
28454359Sroberto	printf("%sheight %g km, hops %d, delay %g seconds\n",
28554359Sroberto	       str, h, hops, delay);
28654359Sroberto}
28754359Sroberto
28854359Sroberto
28954359Sroberto/*
29054359Sroberto * latlong - decode a latitude/longitude value
29154359Sroberto */
29254359Srobertostatic double
29354359Srobertolatlong(
29454359Sroberto	char *str,
29554359Sroberto	int islat
29654359Sroberto	)
29754359Sroberto{
29854359Sroberto	register char *cp;
29954359Sroberto	register char *bp;
30054359Sroberto	double arg;
301182007Sroberto	double divby;
30254359Sroberto	int isneg;
30354359Sroberto	char buf[32];
30454359Sroberto	char *colon;
30554359Sroberto
30654359Sroberto	if (islat) {
30754359Sroberto		/*
30854359Sroberto		 * Must be north or south
30954359Sroberto		 */
31054359Sroberto		if (*str == 'N' || *str == 'n')
31154359Sroberto		    isneg = 0;
31254359Sroberto		else if (*str == 'S' || *str == 's')
31354359Sroberto		    isneg = 1;
31454359Sroberto		else
31554359Sroberto		    isneg = -1;
31654359Sroberto	} else {
31754359Sroberto		/*
31854359Sroberto		 * East is positive, west is negative
31954359Sroberto		 */
32054359Sroberto		if (*str == 'E' || *str == 'e')
32154359Sroberto		    isneg = 0;
32254359Sroberto		else if (*str == 'W' || *str == 'w')
32354359Sroberto		    isneg = 1;
32454359Sroberto		else
32554359Sroberto		    isneg = -1;
32654359Sroberto	}
32754359Sroberto
32854359Sroberto	if (isneg >= 0)
32954359Sroberto	    str++;
33054359Sroberto
33154359Sroberto	colon = strchr(str, ':');
33254359Sroberto	if (colon != NULL) {
33354359Sroberto		/*
33454359Sroberto		 * in hhh:mm:ss form
33554359Sroberto		 */
33654359Sroberto		cp = str;
33754359Sroberto		bp = buf;
33854359Sroberto		while (cp < colon)
33954359Sroberto		    *bp++ = *cp++;
34054359Sroberto		*bp = '\0';
34154359Sroberto		cp++;
34254359Sroberto		arg = atof(buf);
343182007Sroberto		divby = 60.0;
34454359Sroberto		colon = strchr(cp, ':');
34554359Sroberto		if (colon != NULL) {
34654359Sroberto			bp = buf;
34754359Sroberto			while (cp < colon)
34854359Sroberto			    *bp++ = *cp++;
34954359Sroberto			*bp = '\0';
35054359Sroberto			cp++;
351182007Sroberto			arg += atof(buf) / divby;
352182007Sroberto			divby = 3600.0;
35354359Sroberto		}
35454359Sroberto		if (*cp != '\0')
355182007Sroberto		    arg += atof(cp) / divby;
35654359Sroberto	} else {
35754359Sroberto		arg = atof(str);
35854359Sroberto	}
35954359Sroberto
36054359Sroberto	if (isneg == 1)
36154359Sroberto	    arg = -arg;
36254359Sroberto
36354359Sroberto	if (debug > 2)
36454359Sroberto	    (void) printf("latitude/longitude %s = %g\n", str, arg);
36554359Sroberto
36654359Sroberto	return arg;
36754359Sroberto}
36854359Sroberto
36954359Sroberto
37054359Sroberto/*
37154359Sroberto * greatcircle - compute the great circle distance in kilometers
37254359Sroberto */
37354359Srobertostatic double
37454359Srobertogreatcircle(
37554359Sroberto	double lat1,
37654359Sroberto	double long1,
37754359Sroberto	double lat2,
37854359Sroberto	double long2
37954359Sroberto	)
38054359Sroberto{
38154359Sroberto	double dg;
38254359Sroberto	double l1r, l2r;
38354359Sroberto
38454359Sroberto	l1r = lat1 * RADPERDEG;
38554359Sroberto	l2r = lat2 * RADPERDEG;
38654359Sroberto	dg = EARTHRADIUS * acos(
38754359Sroberto		(cos(l1r) * cos(l2r) * cos((long2-long1)*RADPERDEG))
38854359Sroberto		+ (sin(l1r) * sin(l2r)));
38954359Sroberto	if (debug >= 2)
39054359Sroberto	    printf(
39154359Sroberto		    "greatcircle lat1 %g long1 %g lat2 %g long2 %g dist %g\n",
39254359Sroberto		    lat1, long1, lat2, long2, dg);
39354359Sroberto	return dg;
39454359Sroberto}
39554359Sroberto
39654359Sroberto
39754359Sroberto/*
39854359Sroberto * waveangle - compute the wave angle for the given distance, virtual
39954359Sroberto *	       height and number of hops.
40054359Sroberto */
40154359Srobertostatic double
40254359Srobertowaveangle(
40354359Sroberto	double dg,
40454359Sroberto	double h,
40554359Sroberto	int n
40654359Sroberto	)
40754359Sroberto{
40854359Sroberto	double theta;
40954359Sroberto	double delta;
41054359Sroberto
41154359Sroberto	theta = dg / (EARTHRADIUS * (double)(2 * n));
41254359Sroberto	delta = atan((h / (EARTHRADIUS * sin(theta))) + tan(theta/2)) - theta;
41354359Sroberto	if (debug >= 2)
41454359Sroberto	    printf("waveangle dist %g height %g hops %d angle %g\n",
41554359Sroberto		   dg, h, n, delta / RADPERDEG);
41654359Sroberto	return delta;
41754359Sroberto}
41854359Sroberto
41954359Sroberto
42054359Sroberto/*
42154359Sroberto * propdelay - compute the propagation delay
42254359Sroberto */
42354359Srobertostatic double
42454359Srobertopropdelay(
42554359Sroberto	double dg,
42654359Sroberto	double h,
42754359Sroberto	int n
42854359Sroberto	)
42954359Sroberto{
43054359Sroberto	double phi;
43154359Sroberto	double theta;
43254359Sroberto	double td;
43354359Sroberto
43454359Sroberto	theta = dg / (EARTHRADIUS * (double)(2 * n));
43554359Sroberto	phi = (PI/2.0) - atan((h / (EARTHRADIUS * sin(theta))) + tan(theta/2));
43654359Sroberto	td = dg / (LIGHTSPEED * sin(phi));
43754359Sroberto	if (debug >= 2)
43854359Sroberto	    printf("propdelay dist %g height %g hops %d time %g\n",
43954359Sroberto		   dg, h, n, td);
44054359Sroberto	return td;
44154359Sroberto}
44254359Sroberto
44354359Sroberto
44454359Sroberto/*
44554359Sroberto * finddelay - find the propagation delay
44654359Sroberto */
44754359Srobertostatic int
44854359Srobertofinddelay(
44954359Sroberto	double lat1,
45054359Sroberto	double long1,
45154359Sroberto	double lat2,
45254359Sroberto	double long2,
45354359Sroberto	double h,
45454359Sroberto	double *delay
45554359Sroberto	)
45654359Sroberto{
45754359Sroberto	double dg;	/* great circle distance */
45854359Sroberto	double delta;	/* wave angle */
45954359Sroberto	int n;		/* number of hops */
46054359Sroberto
46154359Sroberto	dg = greatcircle(lat1, long1, lat2, long2);
46254359Sroberto	if (debug)
46354359Sroberto	    printf("great circle distance %g km %g miles\n", dg, dg/MILE);
46454359Sroberto
46554359Sroberto	n = 1;
46654359Sroberto	while ((delta = waveangle(dg, h, n)) < 0.0) {
46754359Sroberto		if (debug)
46854359Sroberto		    printf("tried %d hop%s, no good\n", n, n>1?"s":"");
46954359Sroberto		n++;
47054359Sroberto	}
47154359Sroberto	if (debug)
47254359Sroberto	    printf("%d hop%s okay, wave angle is %g\n", n, n>1?"s":"",
47354359Sroberto		   delta / RADPERDEG);
47454359Sroberto
47554359Sroberto	*delay = propdelay(dg, h, n);
47654359Sroberto	return n;
47754359Sroberto}
47854359Sroberto
47954359Sroberto/*
48054359Sroberto * satdoit - compute a delay and print it
48154359Sroberto */
48254359Srobertostatic void
48354359Srobertosatdoit(
48454359Sroberto	double lat1,
48554359Sroberto	double long1,
48654359Sroberto	double lat2,
48754359Sroberto	double long2,
48854359Sroberto	double lat3,
48954359Sroberto	double long3,
49054359Sroberto	char *str
49154359Sroberto	)
49254359Sroberto{
49354359Sroberto	double up_delay,down_delay;
49454359Sroberto
49554359Sroberto	satfinddelay(lat1, long1, lat2, long2, &up_delay);
49654359Sroberto	satfinddelay(lat3, long3, lat2, long2, &down_delay);
49754359Sroberto
49854359Sroberto	printf("%s, delay %g seconds\n", str, up_delay + down_delay);
49954359Sroberto}
50054359Sroberto
50154359Sroberto/*
50254359Sroberto * satfinddelay - calculate the one-way delay time between a ground station
50354359Sroberto * and a satellite
50454359Sroberto */
50554359Srobertostatic void
50654359Srobertosatfinddelay(
50754359Sroberto	double lat1,
50854359Sroberto	double long1,
50954359Sroberto	double lat2,
51054359Sroberto	double long2,
51154359Sroberto	double *delay
51254359Sroberto	)
51354359Sroberto{
51454359Sroberto	double dg;	/* great circle distance */
51554359Sroberto
51654359Sroberto	dg = greatcircle(lat1, long1, lat2, long2);
51754359Sroberto
51854359Sroberto	*delay = satpropdelay(dg);
51954359Sroberto}
52054359Sroberto
52154359Sroberto/*
52254359Sroberto * satpropdelay - calculate the one-way delay time between a ground station
52354359Sroberto * and a satellite
52454359Sroberto */
52554359Srobertostatic double
52654359Srobertosatpropdelay(
52754359Sroberto	double dg
52854359Sroberto	)
52954359Sroberto{
53054359Sroberto	double k1, k2, dist;
53154359Sroberto	double theta;
53254359Sroberto	double td;
53354359Sroberto
53454359Sroberto	theta = dg / (EARTHRADIUS);
53554359Sroberto	k1 = EARTHRADIUS * sin(theta);
53654359Sroberto	k2 = SATHEIGHT - (EARTHRADIUS * cos(theta));
53754359Sroberto	if (debug >= 2)
53854359Sroberto	    printf("Theta %g k1 %g k2 %g\n", theta, k1, k2);
53954359Sroberto	dist = sqrt(k1*k1 + k2*k2);
54054359Sroberto	td = dist / LIGHTSPEED;
54154359Sroberto	if (debug >= 2)
54254359Sroberto	    printf("propdelay dist %g height %g time %g\n", dg, dist, td);
54354359Sroberto	return td;
54454359Sroberto}
545