-
Notifications
You must be signed in to change notification settings - Fork 1
/
equation_of_time.mc
323 lines (292 loc) · 13.2 KB
/
equation_of_time.mc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
/* equation_of_time.mc Copyright 2016 Nicholas C. Strauss (strauss@positive-internet.com)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>
Low precision ephemeris for the Sun.
Source: Explanatory Supplement to the Astronomical Almanac
P. Kenneth Seidelmann, United States Naval Observatory.
Nautical Almanac Office, Great Britain. Nautical Almanac Office
*/
load("julian.mc");
/* T is julian day in unit of centuries
UT is universal time
output
dec is declination degrees
E is equation of time minutes
lambda is ecliptic longitude (position of earth along orbit) degrees
*/
equation_of_time_full(T, UT):= block([lambda, dec, L, G, epsilon, E],
numer:true,
keepfloat:true,
T:T + UT/(24*36525),
L:280.460 + 36000.770 * T,
G:357.528 + 35999.050 * T,
lambda:L + 1.915 * sind(G) + 0.020 * sind(2*G),
lambda:mod(lambda,360),
epsilon:23.4393 - 0.01300*T,
E:-1.915*sind(G) - 0.020*sind(2*G) + 2.466*sind(2*lambda) - 0.053*sind(4*lambda),
E:60.0/15.0*E,
dec:180.0/%pi*asin(sind(epsilon)*sind(lambda)),
[dec,E,lambda]);
/* T is julian day in unit of centuries
UT is universal time
output
declination degrees
E equation of time minutes
*/
equation_of_time(T, UT):=block([eot:equation_of_time_full(T, UT)], [eot[1],eot[2]])$
/* equation of time
tzi is time zone
ds is daylight savings
*/
analemma(day,month,year,tzi,ds):=equation_of_time(centuries_j2000(julian(day,month,year)), 12-tzi-ds);
/* for day:1 thru 30 do print(day,julian(day,10,1582),calendar(julian(day, 10, 1582)));*/
/* for jd:0 thru 5 do print(jd,calendar(jd),calendar8601(jd));*/
/* New York, NY example
*/
example_title:"New York, NY";
example_day:6;
example_month:8;
example_year:2016;
example_julian_date:julian(6,8,2016);
example_timezone:5;
example_daylight_savings:1;
example_observer_latitude: 40.708;
example_observer_longitude: -74.;
example_observer_altitude:3;
/* Las Vegas NV example
*/
example_title:"Las Vegas NV";
example_day:30;
example_month:7;
example_year:2016;
example_julian_date:julian(30,7,2016);
example_timezone:8;
example_daylight_savings:1;
example_observer_latitude: 36.048152;
example_observer_longitude: -114.951;
example_observer_altitude:1000;
analemma_start:julian(1,1,example_year);
timezone:example_timezone;
daylightsavings:0;
analemma_matrix:[];
label_matrix:[];
for day:1 thru 365 do analemma_matrix:cons(equation_of_time(centuries_j2000(analemma_start+day), 12-timezone-daylightsavings),analemma_matrix);
for month:1 thru 12 do label_matrix:cons(append([month_string_array[month]],analemma(1,month,example_year,timezone,daylightsavings)),label_matrix);
plot2d([discrete,analemma_matrix],[ylabel,"equation of time"],[xlabel,"declination"],cons(label,label_matrix),[title,"Analemma"],[png_file,"analemma.png"]);
/* value is in degrees
E is equation of time (see equation_of_time(double T)
UT is universal time
*/
greenwich_hour_angle(UT, E):=15*UT - 180 + 15*E/60.$
/* H is observer elevation AGL meters
phi is observer latitude degrees north positive (also gp, lat)
dec is sun's declination degrees
t is sun hour angle
*/
sun_hour_angle(phi, h, dec):=block([cost],
numer:true,
keepfloat:true,
h:-50./60. - 0.0353*sqrt(h),
cost:( sind(h) - sind(phi)*sind(dec) )/( cosd(phi)*cosd(dec) ),
if (cost > 1) then 0 else (
if (cost < -1) then 180.
else 180./%pi*acos(cost)))$
/* T is time centuries (see j2000)
lat is observer latitude degrees (+N)
lon is observer longitude degress (+E)
sgn is sign rise +1, sign set -1
H is observer altitude meters
(gdb) p GHA = -1.6324222262473047
(gdb) p SHA = 105.64753057341048
(gdb) p E = -6.5296889049892188
(gdb) p dec = 19.005791043318244
(gdb) p lambda = 125.0371808285275
*/
calculate_rise_time(T, lat, lon, sgn, h):=block([UT:12+8, UTZ:0, i:0, E, lambda, dec, GHA, SHA],
numer:true,
keepfloat:true,
while (abs(UT - UTZ) > 0.008 and i < 5) do (
i:i+1,
/* print(i, UT, UTZ),*/
eot:equation_of_time_full(T, UT),
dec:eot[1],
E:eot[2],
lambda:eot[3],
GHA:greenwich_hour_angle(UT, E),
SHA:sun_hour_angle(lat, h, dec),
UTZ:UT,
UT:UT - (GHA + lon + sgn*SHA)/15,
if (UT<0) then UT:UT + 24 else (if (UT > 24) then UT:UT - 24)),
UT)$
/* dow is day of week
returns julian day of nth dow.
For example 1st Sunday in November julian_dow(1,1,11,2016)
2nd Sunday of March julian_dow(1,2,3,2016) */
julian_dow(dow,week,month,year):=block([jd,cal,dowz,beginning],
numer:true,
keepfloat:true,
jd:julian(1,month,year),
cal:calendar(jd),
dowz:cal[2],
/* beginning:(week-1)*7+dow-dowz,
if (beginning < 0) then 7+beginning+1 else beginning+1,
7+beginning+1,*/
julian(week*7+dow-dowz+1, month, year)
);
day_of_year(day,month,year):=julian(day,month,year)-julian(1,1,year)+1$
/* DST begins on the second Sunday of March and ends on the first Sunday of November. */
DST(jd,ds):=block([dst_beg:julian_dow(1,2,3,example_year),dst_end:julian_dow(1,1,11,example_year)],
if (dst_beg<jd and jd<dst_end) then ds else 0);
UT_to_local_time(UT,jd,tz,ds):=block([],ds:DST(jd,ds),mod(UT-tz+ds,24))$
local_to_UT_time(LT,jd,tz,ds):=block([],ds:DST(jd,ds),mod(LT+tz-ds,24))$
T:centuries_j2000(example_julian_date);
rise:calculate_rise_time(T, example_observer_latitude,example_observer_longitude, 1, example_observer_altitude);
rise_local:UT_to_local_time(rise,example_julian_date,example_timezone, example_daylight_savings);
set:calculate_rise_time(T, example_observer_latitude, example_observer_longitude, -1, example_observer_altitude);
set_local:UT_to_local_time(set,example_julian_date,example_timezone, example_daylight_savings);
day_duration(T, jd, lat, lon, h):=block([delta,rise,set],
rise:UT_to_local_time(calculate_rise_time(T, lat, lon, 1, h),jd,example_timezone, example_daylight_savings),
set:UT_to_local_time(calculate_rise_time(T, lat, lon, -1, h),jd,example_timezone, example_daylight_savings),
[rise,set])$
/* one years duration list 2016 Las Vegas, NV */
day_length:[]$
for i:0 thru 365 do block([aday:day_duration(centuries_j2000(analemma_start+i), analemma_start+i, example_observer_latitude, example_observer_longitude, 0)], day_length:cons(aday[2]-aday[1],day_length));
/* 12 months duration list */
month_rise:[];
month_set:[];
label_matrix:[];
block([jd, T, lon:example_observer_longitude, lat:example_observer_latitude,
h:example_observer_altitude, tz:example_timezone, ds:example_daylight_savings],
for month:1 thru 12 do (
jd:julian(1,month,example_year),
T:centuries_j2000(jd),
month_rise:cons(UT_to_local_time(calculate_rise_time(T, lat, lon, 1, h), jd, tz, ds), month_rise),
month_set:cons(UT_to_local_time(calculate_rise_time(T, lat, lon, -1, h), jd, tz, ds), month_set)),
for month:1 thru 12 do label_matrix:cons([month_string_array[month], julian(1,month,example_year)-julian(1,1,example_year),
month_set[month]-month_rise[month]],
label_matrix));
/* Plot of Year 2016 Day's duration in Las Vegas, NV
*/
plot2d([discrete,day_length],[xlabel,"year"],[ylabel,"duration day"],cons(label,label_matrix),[title,example_title],[png_file,"duration_day.png"]);
/* 12 months dayup list */
dayup:[]$
for i:0 thru 365 do block([aday:day_duration(centuries_j2000(analemma_start+i), analemma_start+i, example_observer_latitude, example_observer_longitude, 0)], dayup:cons(aday[1],dayup));
/* 12 months daydown list */
daydown:[]$
for i:0 thru 365 do block([aday:day_duration(centuries_j2000(analemma_start+i), analemma_start+i, example_observer_latitude, example_observer_longitude, 0)], daydown:cons(aday[2],daydown));
month_rise:reverse(month_rise);
day_length:reverse(day_length);
dayup:reverse(dayup);
daydown:reverse(daydown);
plot2d([[discrete,day_length],[discrete,dayup],[discrete,daydown]],[xlabel,"days/year"],[ylabel,"hours/local time"],cons(label,label_matrix),[legend,"duration","sunup","sundown"],[title,example_title],[png_file,"day_duration_up_down.png"]);
/* convert observation local hour angle and declination
to azimuth and altitude.
hour_angle is hour angle (gha) in degrees
dec is declination in degrees
lat is observer latitude in degrees
output
az is azimuth degrees clockwise from north (pilot's coords)
alt is altitude degrees
*/
observer_coord(hour_angle, dec, lat):=block([sh : sind(hour_angle),ch : cosd(hour_angle),
sd : sind(dec),cd : cosd(dec),sl : sind(lat),cl : cosd(lat),x,y,z,r,az,alt],
numer:true,
keepfloat:true,
x : - ch * cd * sl + sd * cl,
y : - sh * cd,
z : ch * cd * cl + sd * sl,
r : sqrt(x^2 + y^2),
/* now get Alt, Az */
az :180/%pi * atan2(y,x),
alt :180/%pi* atan2(z,r),
/* correct for negative AZ */
if (az < 0) then az : az + 360,
[az,alt])$
/* convert observation greenwich hour angle and declination
to azimuth and altitude.
gha is greenwich hour angle (gha) in degrees
dec is declination in degrees
lat is observer latitude in degrees
lon is observer lonitude in degrees (-West)
note: formula lha=gha-lon is corrected for west positive convention yielding lha=gha+lon
*/
observer_coord_gha(gha, dec, lat, lon):=block([lha:gha+lon],observer_coord(lha, dec, lat))$
/* plot alt, az during the day for the sun
inputs: jd is julian day
tz is time zone (+west)
ds is day light savings (applied automatically be procedure).
lat is observer latitude (degrees +north)
lon is observer longitude (degrees -west)
h is observer height (meters)
output: list of observations (altaz) and labels for plot2
az is azimuth degrees clockwise from north (pilot's coords)
alt is altitude degrees
*/
sun_alt_az(jd,tz,ds,lat, lon, h):=block([T,LT,UT, UTZ:0, i:0, E, lambda, dec, GHA, SHA,altaz:[],sun_labels:[],observe,alt_old,alt_new],
numer:true,
keepfloat:true,
T:centuries_j2000(jd),
for LT:0 thru 24*60 do (
UT:local_to_UT_time(LT/60,jd,tz,ds),
eot:equation_of_time_full(T, UT),
dec:eot[1],
E:eot[2],
lambda:eot[3],
GHA:greenwich_hour_angle(UT, E),
observe:observer_coord_gha(GHA, dec, lat, lon),
alt_old:alt_new,
alt_new:observe[2],
if (alt_old<0 and alt_new>0) then sun_labels:cons(cons(string(truncate(LT/60*100)/100),observe),sun_labels),
if (alt_old>0 and alt_new<0) then sun_labels:cons(cons(string(truncate(LT/60*100)/100),observe),sun_labels),
if (mod(LT,60)=0 and alt_new>0) then sun_labels:cons(cons(string(LT/60),observe),sun_labels),
if (alt_new >= 0) then
altaz:cons(cons(LT/60, observe),altaz)),
[altaz,sun_labels])$
sun_alt_az_onepoint(jd,ut,lat, lon, h):=block([T,eot, dec, E, lambda, GHA],
numer:true,
keepfloat:true,
T:centuries_j2000(jd),
eot:equation_of_time_full(T, ut),
dec:eot[1],
E:eot[2],
lambda:eot[3],
GHA:greenwich_hour_angle(ut, E),
observe:observer_coord_gha(GHA, dec, lat, lon))$
sun_jan:sun_alt_az(
julian(1,1,example_year),
example_timezone,
example_daylight_savings,
example_observer_latitude,
example_observer_longitude,
example_observer_altitude);
sun_jun:sun_alt_az(
julian(1,6,example_year),
example_timezone,
example_daylight_savings,
example_observer_latitude,
example_observer_longitude,
example_observer_altitude);
sun_sep:sun_alt_az(
julian(1,9,example_year),
example_timezone,
example_daylight_savings,
example_observer_latitude,
example_observer_longitude,
example_observer_altitude);
/* Sun altitude azimuth example for Las Vegas, Nevada */
/*for mo:1 thru 12 do (*/
plot2d([[discrete,map(lambda([x],[x[2],x[3]]),sun_jan[1])],
[discrete,map(lambda([x],[x[2],x[3]]),sun_jun[1])],
[discrete,map(lambda([x],[x[2],x[3]]),sun_sep[1])]],
[legend,"jan","jun","sep"],
[ylabel,"Altitude (deg)"],[xlabel,"Azimuth (deg) degrees clockwise from north."],
cons(label,append(sun_jan[2],append(sun_jun[2],sun_sep[2]))),
[title,example_title], [png_file,"sun_position_day.png"]);