Part Page
Calendar, yearly 4
Day of Week & Day Number of Year 5
Links Time signals Bowditch Terrestrial Almanac Pub. No. 249 Pub. No. 229 Sight Reduction Forms and Methods
6
Equation of Time curve 15
Moon Phases (includes Moon in graphic form) 16-17
Note! The Daily Page numbers are found at the bottom of each page
January 2
February 22
March 42
April 62
May 82
June 102
July 122
August 144
September 164
October 184
November 204
December 224
Note! Increments and Altitude Corrections are found on the pdf page numbers below
Tables of Increments and Corrections for Sun, planets, Aries, Moon (“the yellow pages”) 262
Conversion of Arc to Time 282
Altitude Corrections for Sun, Planets, Stars (includes Refraction and Dip) 283-284
Altitude Corrections for the Moon 285-286
Navigational Star Chart 287
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Copyright 2021 TheNauticalAlmanac.com You are free to copy and distribute this document in its entirety
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Acknowledgment and Credits
Dr. Enno Rodegerdts
The Nautical Almanac Daily Pages and Sun Almanacs found on our site were originally created from PyAlmanac written by the great Norwegian sailor Enno Rodegerdts. PyAlmanac used PyEphem to generate the almanacs and LaTex provided the final formatting. Visit Dr. Rodegerdts site and learn of his voyages at https://sv-inua.net/
Without his work TheNauticalAlmanac.com wouldn't exist.
Andrew Bauer
Mr. Bauer has taken the initial work of Dr. Rodegerdts and improved it to the excellence found in the following Daily Pages. Attending foremost to the accuracy of data and then formatting Mr. Bauer created SkyAlmanac which draws from Brandon Rhodes work Ephem and Skyfield and provides a clear arrangement of figures required for celestial navigation. To that end his work was determined, tireless and efficient. In our mutual writing across many lines of longitude he has always been pleasant, friendly and most affable.
As he has said, "The art of celestial navigation should be promoted, not discouraged, even in the modern day".
To both of these men we all owe a large debt of gratitude and thanks
Disclaimer and Warning
Prior to use verify the accuracy of The Nautical Almanac or data you download from our site. They SHOULD NOT and MUST NOT be relied upon for celestial navigation work of any sorts or any purpose whatsoever. You use them at your own risk or peril.
Errors & Corrections
Contact us if you find any significant errors and describe the correction that should be made.
Copyright 2021 TheNauticalAlmanac.com
You are free to copy and distribute this document in its entirety but never sell it.
freely ye received, freely give
2021 January February March
M Tu W Th F Sa Su M Tu W Th F Sa Su M Tu W Th F Sa Su 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 6 7
4 5 6 7 8 9 10 8 9 10 11 12 13 14 8 9 10 11 12 13 14 11 12 13 14 15 16 17 15 16 17 18 19 20 21 15 16 17 18 19 20 21 18 19 20 21 22 23 24 22 23 24 25 26 27 28 22 23 24 25 26 27 28 25 26 27 28 29 30 31 29 30 31
April May June M Tu W Th F Sa Su M Tu W Th F Sa Su M Tu W Th F Sa Su
1 2 3 4 1 2 1 2 3 4 5 6 5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13
12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30
31
July August September M Tu W Th F Sa Su M Tu W Th F Sa Su M Tu W Th F Sa Su
1 2 3 4 1 1 2 3 4 5 5 6 7 8 9 10 11 2 3 4 5 6 7 8 6 7 8 9 10 11 12
12 13 14 15 16 17 18 9 10 11 12 13 14 15 13 14 15 16 17 18 19 19 20 21 22 23 24 25 16 17 18 19 20 21 22 20 21 22 23 24 25 26 26 27 28 29 30 31 23 24 25 26 27 28 29 27 28 29 30
30 31
October November December M Tu W Th F Sa Su M Tu W Th F Sa Su M Tu W Th F Sa Su
1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12
11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19 18 19 20 21 22 23 24 22 23 24 25 26 27 28 20 21 22 23 24 25 26 25 26 27 28 29 30 31 29 30 27 28 29 30 31
2021 Day of Week, Week Number, Day of Year, Remaining Days of Year
D ay
o f
M o
January February March April May June
Day Day Day Day Day Day Day Day Day Day Day Day
of of of of of of of of of of of of
Week Year Week Year Week Year Week Year Week Year Week Year 1 Fri 1 364 1 Mon 32 333 5 1 Mon 60 305 9 1 Thu 91 274 13 1 Sat 121 244 17 1 Tue 152 213 22
2 Sat 2 363 2 Tue 33 332 2 Tue 61 304 2 Fri 92 273 2 Sun 122 243 18 2 Wed 153 212
3 Sun 3 362 1 3 Wed 34 331 3 Wed 62 303 3 Sat 93 272 3 Mon 123 242 3 Thu 154 211
4 Mon 4 361 4 Thu 35 330 4 Thu 63 302 4 Sun 94 271 14 4 Tue 124 241 4 Fri 155 210
5 Tue 5 360 5 Fri 36 329 5 Fri 64 301 5 Mon 95 270 5 Wed 125 240 5 Sat 156 209
6 Wed 6 359 6 Sat 37 328 6 Sat 65 300 6 Tue 96 269 6 Thu 126 239 6 Sun 157 208 23
7 Thu 7 358 7 Sun 38 327 6 7 Sun 66 299 10 7 Wed 97 268 7 Fri 127 238 7 Mon 158 207
8 Fri 8 357 8 Mon 39 326 8 Mon 67 298 8 Thu 98 267 8 Sat 128 237 8 Tue 159 206
9 Sat 9 356 9 Tue 40 325 9 Tue 68 297 9 Fri 99 266 9 Sun 129 236 19 9 Wed 160 205
10 Sun 10 355 2 10 Wed 41 324 10 Wed 69 296 10 Sat 100 265 10 Mon 130 235 10 Thu 161 204
11 Mon 11 354 11 Thu 42 323 11 Thu 70 295 11 Sun 101 264 15 11 Tue 131 234 11 Fri 162 203
12 Tue 12 353 12 Fri 43 322 12 Fri 71 294 12 Mon 102 263 12 Wed 132 233 12 Sat 163 202
13 Wed 13 352 13 Sat 44 321 13 Sat 72 293 13 Tue 103 262 13 Thu 133 232 13 Sun 164 201 24
14 Thu 14 351 14 Sun 45 320 7 14 Sun 73 292 11 14 Wed 104 261 14 Fri 134 231 14 Mon 165 200
15 Fri 15 350 15 Mon 46 319 15 Mon 74 291 15 Thu 105 260 15 Sat 135 230 15 Tue 166 199
16 Sat 16 349 16 Tue 47 318 16 Tue 75 290 16 Fri 106 259 16 Sun 136 229 20 16 Wed 167 198
17 Sun 17 348 3 17 Wed 48 317 17 Wed 76 289 17 Sat 107 258 17 Mon 137 228 17 Thu 168 197
18 Mon 18 347 18 Thu 49 316 18 Thu 77 288 18 Sun 108 257 16 18 Tue 138 227 18 Fri 169 196
19 Tue 19 346 19 Fri 50 315 19 Fri 78 287 19 Mon 109 256 19 Wed 139 226 19 Sat 170 195
20 Wed 20 345 20 Sat 51 314 20 Sat 79 286 20 Tue 110 255 20 Thu 140 225 20 Sun 171 194 25
21 Thu 21 344 21 Sun 52 313 8 21 Sun 80 285 12 21 Wed 111 254 21 Fri 141 224 21 Mon 172 193
22 Fri 22 343 22 Mon 53 312 22 Mon 81 284 22 Thu 112 253 22 Sat 142 223 22 Tue 173 192
23 Sat 23 342 23 Tue 54 311 23 Tue 82 283 23 Fri 113 252 23 Sun 143 222 21 23 Wed 174 191
24 Sun 24 341 4 24 Wed 55 310 24 Wed 83 282 24 Sat 114 251 24 Mon 144 221 24 Thu 175 190
25 Mon 25 340 25 Thu 56 309 25 Thu 84 281 25 Sun 115 250 17 25 Tue 145 220 25 Fri 176 189
26 Tue 26 339 26 Fri 57 308 26 Fri 85 280 26 Mon 116 249 26 Wed 146 219 26 Sat 177 188
27 Wed 27 338 27 Sat 58 307 27 Sat 86 279 27 Tue 117 248 27 Thu 147 218 27 Sun 178 187 26
28 Thu 28 337 28 Sun 59 306 9 28 Sun 87 278 13 28 Wed 118 247 28 Fri 148 217 28 Mon 179 186
29 Fri 29 336 29 Mon 88 277 29 Thu 119 246 29 Sat 149 216 29 Tue 180 185
30 Sat 30 335 30 Tue 89 276 30 Fri 120 245 30 Sun 150 215 22 30 Wed 181 184
31 Sun 31 334 5 31 Wed 90 275 31 Mon 151 214
Day of Week, Week Number, Day of Year, Remaining Days of Year
D ay
o f
M o
July August September October November December
Day Day Day Day Day Day Day Day Day Day Day Day
of of of of of of of of of of of of
Week Year Week Year Week Year Week Year Week Year Week Year 1 Thu 182 183 26 1 Sun 213 152 31 1 Wed 244 121 35 1 Fri 274 91 39 1 Mon 305 60 44 1 Wed 335 30 48
2 Fri 183 182 2 Mon 214 151 2 Thu 245 120 2 Sat 275 90 2 Tue 306 59 2 Thu 336 29
3 Sat 184 181 3 Tue 215 150 3 Fri 246 119 3 Sun 276 89 40 3 Wed 307 58 3 Fri 337 28
4 Sun 185 180 27 4 Wed 216 149 4 Sat 247 118 4 Mon 277 88 4 Thu 308 57 4 Sat 338 27
5 Mon 186 179 5 Thu 217 148 5 Sun 248 117 36 5 Tue 278 87 5 Fri 309 56 5 Sun 339 26 49
6 Tue 187 178 6 Fri 218 147 6 Mon 249 116 6 Wed 279 86 6 Sat 310 55 6 Mon 340 25
7 Wed 188 177 7 Sat 219 146 7 Tue 250 115 7 Thu 280 85 7 Sun 311 54 45 7 Tue 341 24
8 Thu 189 176 8 Sun 220 145 32 8 Wed 251 114 8 Fri 281 84 8 Mon 312 53 8 Wed 342 23
9 Fri 190 175 9 Mon 221 144 9 Thu 252 113 9 Sat 282 83 9 Tue 313 52 9 Thu 343 22
10 Sat 191 174 10 Tue 222 143 10 Fri 253 112 10 Sun 283 82 41 10 Wed 314 51 10 Fri 344 21
11 Sun 192 173 28 11 Wed 223 142 11 Sat 254 111 11 Mon 284 81 11 Thu 315 50 11 Sat 345 20
12 Mon 193 172 12 Thu 224 141 12 Sun 255 110 37 12 Tue 285 80 12 Fri 316 49 12 Sun 346 19 50
13 Tue 194 171 13 Fri 225 140 13 Mon 256 109 13 Wed 286 79 13 Sat 317 48 13 Mon 347 18
14 Wed 195 170 14 Sat 226 139 14 Tue 257 108 14 Thu 287 78 14 Sun 318 47 46 14 Tue 348 17
15 Thu 196 169 15 Sun 227 138 33 15 Wed 258 107 15 Fri 288 77 15 Mon 319 46 15 Wed 349 16
16 Fri 197 168 16 Mon 228 137 16 Thu 259 106 16 Sat 289 76 16 Tue 320 45 16 Thu 350 15
17 Sat 198 167 17 Tue 229 136 17 Fri 260 105 17 Sun 290 75 42 17 Wed 321 44 17 Fri 351 14
18 Sun 199 166 29 18 Wed 230 135 18 Sat 261 104 18 Mon 291 74 18 Thu 322 43 18 Sat 352 13
19 Mon 200 165 19 Thu 231 134 19 Sun 262 103 38 19 Tue 292 73 19 Fri 323 42 19 Sun 353 12 51
20 Tue 201 164 20 Fri 232 133 20 Mon 263 102 20 Wed 293 72 20 Sat 324 41 20 Mon 354 11
21 Wed 202 163 21 Sat 233 132 21 Tue 264 101 21 Thu 294 71 21 Sun 325 40 47 21 Tue 355 10
22 Thu 203 162 22 Sun 234 131 34 22 Wed 265 100 22 Fri 295 70 22 Mon 326 39 22 Wed 356 9
23 Fri 204 161 23 Mon 235 130 23 Thu 266 99 23 Sat 296 69 23 Tue 327 38 23 Thu 357 8
24 Sat 205 160 24 Tue 236 129 24 Fri 267 98 24 Sun 297 68 43 24 Wed 328 37 24 Fri 358 7
25 Sun 206 159 30 25 Wed 237 128 25 Sat 268 97 25 Mon 298 67 25 Thu 329 36 25 Sat 359 6
26 Mon 207 158 26 Thu 238 127 26 Sun 269 96 39 26 Tue 299 66 26 Fri 330 35 26 Sun 360 5 52
27 Tue 208 157 27 Fri 239 126 27 Mon 270 95 27 Wed 300 65 27 Sat 331 34 27 Mon 361 4
28 Wed 209 156 28 Sat 240 125 28 Tue 271 94 28 Thu 301 64 28 Sun 332 33 48 28 Tue 362 3
29 Thu 210 155 29 Sun 241 124 35 29 Wed 272 93 29 Fri 302 63 29 Mon 333 32 29 Wed 363 2
30 Fri 211 154 30 Mon 242 123 30 Thu 273 92 30 Sat 303 62 30 Tue 334 31 30 Thu 364 1
31 Sat 212 153 31 Tue 243 122 31 Sun 304 61 44 31 Fri 365 0
Thirty days hath September, April, June, and November; February has twenty-eight alone, All the rest have thirty-one, Excepting leap-year, that's the time when February's days are twenty-nine.
Useful Information
CHU English: 613-745-1576 (CHU provides only Eastern time announcements) French: 613-745-9426
Time signals- by Radio
WWV (Fort Collins, Colorado) 2.5, 5, 10, 15, 20 MHz (male voice) WWVH ( Kauai, Hawaii) 2.5, 5, 10, 15 MHz (female voice) CHU (Ottawa, Canada) 3330, 7850, and 14,670 kHz (USB)
Bowditch 2017- The American Practical Navigator
https://TheNauticalAlmanac.com/2017_Bowditch-_American_Practical_Navigator.html
Organized in a convenient and useful manner. Download the Chapters, Parts or Tables you want or the entire work.
The Terrestrial Almanac Annual calendar and day planner for the entire year.
https://TheNauticalAlmanac.com/TerrestrialAlmanac.html
https://TheNauticalAlmanac.com/Pub. No. 249.html
Pub. No. 229 Download individual Volumes covering a range of Latitudes
https://TheNauticalAlmanac.com/Pub. No. 229.html
About Calculators
The Casio fx-300ES Plus is an inexpensive calculator at about 11 USD. It features natural input so you enter a formula just as it would be written on paper. Entering degrees, minutes and seconds is very simple. The Casio fx-300ES Plus has 9 memory locations and you can review many of the previous entries you make using a special key on the calculator.
Determine Hc using a calculator
The formula
Hc = asin[sin(Declination)*sin(Latitude) + cos(Latitude)*cos(Declination)*cos(LHA)]
As it would be entered into the Casio calculator Note- Sin-1 is the arc-sin key
Sin-1(Sin(Ap Latitude) x Sin(Declination) + Cos(Ap Latitude) x Cos(Declination) x Cos(LHA)
Declination is the declination of the Celestial body you're observing. When the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign before it.
Latitude is the Latitude where you are, think you are or where you would like to determine Hc for. Typically, you'll be using an Assumed position Latitude or Ap Latitude as it's called.
In Western Longitudes
LHA is the Local Hour Angle which is derived from subtracting your whole number value of Longitude (Assumed or otherwise) from the whole number value of GHA (Greenwich Hour Angle).
In Eastern Longitudes
LHA, in Eastern Longitudes, is determined by rounding up the GHA figure to the next highest whole degree figure then adding the DR. Longitude to GHA to obtain LHA. Only add the whole degree DR. Longitude figure to the rounded up whole degree GHA figure. If the resulting LHA figure is greater than 360° then subtract 360° from the figure to obtain the LHA.
Why would you want to determine Hc using a calculator?
It's faster than looking up in Pub. No. 249 and Pub. No. 229, highly accurate and you don't need a lot of printed out pages of Latitudes from Pub. No. 249 and Pub. No. 229. Pub. No. 249 Vol. 2 & 3 don't cover any declination greater than 29 degrees so you'd have to use Pub. No. 229 which is extremely large.
Celestial Navigation
Determine Z
Z = acos[(sin(Declination) – sin(Ap Latitude) x sin(Hc)) ÷ (cos(Ap Latitude) x cos(Hc))]
As it would be entered into the Casio calculator... Note- Cos-1 is the arc-cosine key
Cos-1((Sin(Declination) – Sin(AP Latitude) x Sin(Hc)) ÷ (Cos(AP Latitude) x Cos(Hc)
If the heavenly body's declination is Contrary name to the Ap Latitude enter a negative sign before it.
To obtain Zn see the rules below for Northern and Southern latitudes.
Determine Z independent of Hc
“L” is latitude and “d” is declination. When the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign before it.
As it would be entered into the Casio calculator... Note- tan-1 is the arc-tangent key
Z = tan-1 ((sin (LHA) ÷ (cos(AP latitude) x tan(declination) – (sin(AP latitude) x cos(LHA))
The sign convention used in the calculation of this azimuth formula is as follows: from Bowditch Chapter 22 CALCULATIONS AND CONVERSIONS, page 331
1) If latitude and declination are of contrary name, declination is treated as a negative quantity; 2) If the local hour angle is greater than 180°, it is treated as a negative quantity. If the azimuth angle as calculated is negative, add 180° to obtain the desired value.
To obtain Zn apply the following rules
In Northern Latitudes LHA greater than 180°....Zn=Z LHA less than 180°...........Zn=360° – Z
In Southern Latitudes LHA greater than 180°....Zn= 180° – Z LHA less than 180°...........Zn= 180° + Z
Determine Refraction 0.96 ÷ Tan of (Ha) Gives good results down to about 8° from the horizon but not less.
Refraction (good overall formula from 90° to below 8° from the horizon)
As it would be entered into the Casio calculator...
1 ÷ Tan((Ha + (7.31 ÷ (Ha + 4.4))
Both refraction formulas use the standard pressure and temperature of;
1010 mb 10° C 29.83 in 53° F
Determine Dip using feet 0.97 x (Square Root of He (Height of Eye) in feet)
Determine Dip using meters 1.76 x (Square Root of He (Height of eye) in meters )
Rules to Calculate Latitude using the Sun- Noon-Sight
1- Latitude and declination Same name but latitude is greater than declination:
Latitude= (90º – Ho) + declination
2- Latitude and declination Same name but declination greater than latitude:
Latitude= Declination – (90º – Ho)
Latitude= (90o – Ho) – Declination
In Western longitudes
Combine the DR Longitude figure with only the minutes (of arc) of the total GHA figure. The Ap λ figure will be used when plotting the LOP on the UPS.
In Eastern longitudes
In Eastern longitudes the Ap λ is determined as follows;
DR longitude + (0°60' minus GHA minutes of arc)
Example- E 075° + (0°60' – 0° 02')= 75° 58' Ap longitude
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Formula Sheet added to NA.odt
Explanation of The Nautical Almanac Daily Pages
1 Date and Time based on GMT/UT
2 Mer. pass- meridian passage of Aries at the Prime Meridian- Greenwich- 0°. Time figure is GMT/UT.
3
Planet or Moon GHA v value and planet or Moon declination d value.
v- “The change in hour angle arising from v of the body at the time of the sight observation is accounted for with the v correction.” Source- Bowditch 2017, Chapter 19- Sight Reduction p. 313. The planet’s v is positive unless preceeded by a minus sign which is sometimes the case with Venus. The sign of the Moon’s v is positive.
d- “The change in declination of the body at the time of the sight observation is accounted for with the d correction.” Source- Bowditch 2017, Chapter 19- Sight Reduction p. 313. The sign of the Moon or planet’s d correction is determined by the declination trend- positive if successive declination values increase and negative if they decrease.
Corrections for both v and d are found in the Increments and Corrections pages of The Nautical Almanac.
To find the correction for either v or d enter the Increments and Corrections pages for the minutes in time of the observation and find the value in the v and d corr. columns Find the v, or d, value in the left side of one of the three columns. To the right of that value is the v, or d, correction. Be sure to add or subtract the values depending upon the sign of the value as mentioned above.
Example for v & d correction- June 10, 2020 GMT- 21:19:10 Body- Moon
GHA= 247° 20.4’ v = 12.1’ GHA increment 4° 34.4’ v- correction for 12.1’ + 0° 03.9’ GHA= 251° 58.7’
Dec= S 17° 43.8’ d= 8.9’ d- correction for 8.9’ – 0° 02.9’ dec= S 17° 40.9’
declination trend is decreasing so the sign of d correction is negative
4
m- is the magnitude or brightness of the planet.
A bright planet will have a minus sign beside the figure. A fainter planet will have no sign beside its magnitude figure.
5
Stars- SHA, Sidereal Hour Angle, and Declination. 59 stars are listed.
Typically, only 57 stars are used for navigational purposes in both Northern and Southern Hemispheres. Here you’ll also find Polaris and Scheat. In the Northern Hemisphere Polaris is often used for determination of latitude.
6 Mer. pass- planet meridian passage time at the Prime Meridian- Greenwich- 0°. Time figure is GMT/UT.
7
SHA- planet SHA.
Planet SHA is calculated by subtracting Aries GHA from planet GHA. If planet GHA figure is less than Aries GHA, add 360° to planet GHA and then subtract Aries GHA.
8
Horizontal parallax- for Venus and Mars.
Horizontal parallax is the angle subtended by half the Earth’s diameter as viewed from the planet in minutes of arc.
9 SD- Semi-diameter of the Sun in minutes of arc.
One half of the angular width of the Sun as observed on earth.
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10 d- the daily average change, per hour, in the Sun’s declination in minutes of arc.
11 SD- Semi-diameter of the Moon in minutes of arc.
Semi-diameter is one half of the angular width of the Moon, as observed on earth.
12
HP- the angle between two lines, one from the center of the Moon to the center of the Earth, the other from the center of the Moon to the edge of the Earth. This angle is about 56', but it changes slightly from day to day as the distance to the Moon changes along its elliptical path around the Earth. Source- starpath.com
13
Sun- Eqn. of Time- Basically the Equation of Time (EoT) is the difference between clock time and time seen on a sundial. This is comparing “clock time”, as a mechanical measurement of time, and the sundial being time determined by the position of the Sun at any given moment. The figures listed are for 00h and 12h. Using the EoT you can get fairly accurate determination of when Meridian Passage (Local Apparent Noon) occurs at your position. Unshaded EoT values are subtracted from 12:00 to get Meridian Passage. Shaded EoT values are added to 12:00 to get Meridian Passage. An Equation of Time chart (as a curve) is provided in each almanac on TheNauticalAlmanac.com
Example- Meridian Passage on May 30, 2020 equals 12:00 – EoT of 2 minutes 21 seconds
MP= 11:57:39 Local Apparent Noon
Example- Meridian Passage on August 25, 2020 equals 12:00 + EoT of 1 minute 59 seconds
MP= 12:01:59 Local Apparent Noon
14 Sun- Mer. Pass just to the right of the Eqn. of Time is the approximate GMT/UT when the Sun crosses The Prime Meridian (at Greenwich) for that specific date.
15
Moon- Mer. Pass- is the approximate GMT/UT when the Moon crosses The Prime Meridian (at Greenwich) or the 180° line of longitude.
Upper means the GMT/UT when the Moon crosses The Prime Meridian (Greenwich).
Lower means the GMT/UT when the Moon crosses the 180° line of longitude.
16
Moon- Age- this is the number of days past a new Moon. Typically, there are 29 days in a lunar month.
Moon- %- the amount of the Moon's illumination. 100% would be a full moon. 49% would be about ½ of the Moon is illuminated. A 3 day range percentage is provided but only one graphic for the phase.
17*
(morning) Twilight- Naut.- the approximate GMT/UT when morning Nautical Twilight begins.
Nautical twilight is the time when the center of the sun is 12° below the horizon and the horizon is visible enough to be used for marine sextant observations.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
17*
(morning) Twilight- Civil- the approximate GMT/UT of morning civil twilight starts when the geometric center of the sun is 6° below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
17*
see notes at bottom
Sunrise- the approximate GMT/UT when the Sun is 0° 50' (semi-diameter plus refraction) below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
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17*
see notes at bottom
Sunset- the approximate GMT/UT when the Sun is 0° 50' (semi-diameter plus refraction) below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
17*
see notes at bottom
(evening) Twilight- Civil- the approximate GMT/UT of evening civil twilight that ends when the geometric center of the sun is 6° below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
17*
(evening) Twilight- Naut.- the approximate GMT/UT of when evening Nautical Twilight ends.
Nautical twilight is the time when the center of the sun is 12° below the horizon and the horizon is no longer visible enough to be used for sextant observations.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time.
18*
see notes at bottom
Moonrise- the approximate GMT/UT when the Moon is about 0° 05' to 0° 10' below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time under the specific day.
18*
see notes at bottom
Moonset- the approximate GMT/UT when the Moon is about 0° 05' to 0° 10' below the horizon.
First locate your approximate Latitude in the Lat. column and then follow across horizontally to the right to find the time under the specific day.
* Note-
means the Sun or Moon remains continuously above the horizon on that day.
: can also mean twilight lasts all night: can also mean twilight lasts all night : can also mean twilight lasts all night
means the Sun or Moon remains continuously below the horizon on that day.
: means Moon does not rise or set on that day but may have risen or set the previous day or following day.: can also mean twilight lasts all night : can also mean twilight lasts all night
* Note- Time of Sunrise, Sunset, Moonrise, Moonset and twilight is based on GMT/UT of the event at 0° (Greenwich) and can be condsidered as approximate LMT (Local Mean Time) with a tolerance of +/- 30 minutes depending on where you are within a time zone.
Wednesday, February 24, 2021
2020 J anuary 01 to J an. 03
h Sun Moon Wed GHA Dec GHA ν Dec d HP
0 17913.7 S2303.5 11056.9 15.3’ S0958.5 10.7’ 54.3’ 1 19413.4 03.3 12531.3 15.4’ 0947.8 10.7’ 54.3’ 2 20913.1 03.1 14005.7 15.4’ 0937.1 10.7’ 54.3’ 3 22412.8 · · 03.0 15440.1 15.5’ 0926.3 10.8’ 54.3’ 4 23912.5 02.8 16914.6 15.5’ 0915.5 10.8’ 54.3’ 5 25412.2 02.6 18349.1 15.5’ 0904.7 10.8’ 54.2’ 6 26911.9 S2302.4 19823.6 15.6’ S0853.8 10.9’ 54.2’ 7 28411.6 02.2 21258.2 15.6’ 0842.9 10.9’ 54.2’ 8 29911.3 02.0 22732.8 15.6’ 0832.0 10.9’ 54.2’ 9 31411.0 · · 01.8 24207.5 15.7’ 0821.0 11.0’ 54.2’ 10 32910.7 01.6 25642.2 15.7’ 0810.0 11.0’ 54.2’ 11 34410.4 01.4 27116.9 15.7’ 0759.0 11.0’ 54.2’ 12 35910.1 S2301.2 28551.7 15.8’ S0748.0 11.1’ 54.2’ 13 1409.8 01.0 30026.4 15.8’ 0736.9 11.1’ 54.2’ 14 2909.5 00.8 31501.2 15.8’ 0725.8 11.1’ 54.2’ 15 4409.2 · · 00.6 32936.1 15.9’ 0714.7 11.1’ 54.2’ 16 5908.9 00.4 34410.9 15.9’ 0703.5 11.2’ 54.2’ 17 7408.6 00.2 35845.8 15.9’ 0652.3 11.2’ 54.2’ 18 8908.3 S2300.0 1320.7 15.9’ S0641.1 11.2’ 54.2’ 19 10408.0 2259.7 2755.7 16.0’ 0629.9 11.2’ 54.2’ 20 11907.7 59.5 4230.7 16.0’ 0618.7 11.3’ 54.2’ 21 13407.5 · · 59.3 5705.6 16.0’ 0607.4 11.3’ 54.2’ 22 14907.2 59.1 7140.6 16.0’ 0556.1 11.3’ 54.2’ 23 16406.9 58.9 8615.7 16.0’ 0544.8 11.3’ 54.2’
SD.=16.3 d=0.2 S.D.=14.8
Thu GHA Dec GHA ν Dec d HP
0 17906.6 S2258.7 10050.7 16.1’ S0533.4 11.3’ 54.2’ 1 19406.3 58.5 11525.8 16.1’ 0522.1 11.4’ 54.2’ 2 20906.0 58.3 13000.9 16.1’ 0510.7 11.4’ 54.2’ 3 22405.7 · · 58.1 14436.0 16.1’ 0459.3 11.4’ 54.2’ 4 23905.4 57.9 15911.1 16.1’ 0447.9 11.4’ 54.2’ 5 25405.1 57.6 17346.3 16.1’ 0436.5 11.4’ 54.2’ 6 26904.8 S2257.4 18821.4 16.2’ S0425.0 11.5’ 54.2’ 7 28404.5 57.2 20256.6 16.2’ 0413.5 11.5’ 54.2’ 8 29904.2 57.0 21731.7 16.2’ 0402.1 11.5’ 54.2’ 9 31403.9 · · 56.8 23206.9 16.2’ 0350.6 11.5’ 54.2’ 10 32903.6 56.6 24642.1 16.2’ 0339.0 11.5’ 54.2’ 11 34403.3 56.3 26117.3 16.2’ 0327.5 11.5’ 54.2’ 12 35903.0 S2256.1 27552.6 16.2’ S0316.0 11.5’ 54.2’ 13 1402.8 55.9 29027.8 16.2’ 0304.4 11.6’ 54.2’ 14 2902.5 55.7 30503.0 16.2’ 0252.8 11.6’ 54.2’ 15 4402.2 · · 55.5 31938.3 16.2’ 0241.3 11.6’ 54.2’ 16 5901.9 55.2 33413.5 16.2’ 0229.7 11.6’ 54.2’ 17 7401.6 55.0 34848.8 16.3’ 0218.1 11.6’ 54.2’ 18 8901.3 S2254.8 324.0 16.3’ S0206.5 11.6’ 54.2’ 19 10401.0 54.6 1759.3 16.3’ 0154.8 11.6’ 54.2’ 20 11900.7 54.3 3234.5 16.3’ 0143.2 11.6’ 54.2’ 21 13400.4 · · 54.1 4709.8 16.3’ 0131.6 11.6’ 54.2’ 22 14900.1 53.9 6145.0 16.3’ 0119.9 11.7’ 54.2’ 23 16359.8 53.7 7620.3 16.3’ 0108.2 11.7’ 54.3’
SD.=16.3 d=0.2 S.D.=14.8
Fri GHA Dec GHA ν Dec d HP
0 17859.5 S2253.4 9055.5 16.2’ S0056.6 11.7’ 54.3’ 1 19359.3 53.2 10530.8 16.2’ 0044.9 11.7’ 54.3’ 2 20859.0 53.0 12006.0 16.2’ 0033.2 11.7’ 54.3’ 3 22358.7 · · 52.7 13441.3 16.2’ 0021.5 11.7’ 54.3’ 4 23858.4 52.5 14916.5 16.2’ S0009.9 11.7’ 54.3’ 5 25358.1 52.3 16351.7 16.2’ N0001.8 11.7’ 54.3’ 6 26857.8 S2252.0 17826.9 16.2’ N0013.5 11.7’ 54.3’ 7 28357.5 51.8 19302.1 16.2’ 0025.2 11.7’ 54.3’ 8 29857.2 51.6 20737.3 16.2’ 0036.9 11.7’ 54.3’ 9 31356.9 · · 51.3 22212.5 16.2’ 0048.6 11.7’ 54.3’ 10 32856.6 51.1 23647.7 16.2’ 0100.3 11.7’ 54.3’ 11 34356.4 50.8 25122.8 16.1’ 0112.0 11.7’ 54.4’ 12 35856.1 S2250.6 26558.0 16.1’ N0123.7 11.7’ 54.4’ 13 1355.8 50.4 28033.1 16.1’ 0135.4 11.7’ 54.4’ 14 2855.5 50.1 29508.2 16.1’ 0147.1 11.7’ 54.4’ 15 4355.2 · · 49.9 30943.3 16.1’ 0158.8 11.7’ 54.4’ 16 5854.9 49.6 32418.4 16.1’ 0210.5 11.7’ 54.4’ 17 7354.6 49.4 33853.4 16.0’ 0222.2 11.7’ 54.4’ 18 8854.3 S2249.2 35328.4 16.0’ N0233.9 11.7’ 54.4’ 19 10354.0 48.9 803.5 16.0’ 0245.6 11.7’ 54.4’ 20 11853.8 48.7 2238.4 16.0’ 0257.3 11.7’ 54.5’ 21 13353.5 · · 48.4 3713.4 16.0’ 0309.0 11.7’ 54.5’ 22 14853.2 48.2 5148.4 15.9’ 0320.6 11.7’ 54.5’ 23 16352.9 47.9 6623.3 15.9’ 0332.3 11.7’ 54.5’
SD.=16.3 d=0.2 S.D.=14.8
Lat. Twilight Sunrise Sunset Twilight Naut. Civil Civil Naut.
N 72 08:23 10:41 13:27 15:45
N 70 08:05 09:49 14:19 16:03 68 07:50 09:16 14:52 16:18 66 07:37 08:53 10:27 13:41 15:15 16:31 64 07:26 08:34 09:49 14:19 15:34 16:41 62 07:17 08:18 09:23 14:45 15:49 16:51 60 07:09 08:05 09:02 15:06 16:02 16:59
N 58 07:02 07:54 08:45 15:23 16:14 17:06 56 06:56 07:44 08:31 15:37 16:24 17:12 54 06:50 07:35 08:19 15:49 16:32 17:18 52 06:44 07:28 08:08 16:00 16:40 17:24 50 06:39 07:20 07:58 16:09 16:47 17:29 45 06:28 07:05 07:38 16:29 17:03 17:40
N 40 06:18 06:52 07:22 16:46 17:16 17:50 35 06:08 06:40 07:08 17:00 17:28 17:59 30 06:00 06:30 06:56 17:12 17:38 18:08 20 05:44 06:11 06:35 17:32 17:56 18:24
N 10 05:28 05:54 06:17 17:50 18:13 18:40 0 05:11 05:38 06:00 18:08 18:30 18:56
S 10 04:53 05:20 05:43 18:25 18:48 19:15 20 04:31 05:00 05:24 18:43 19:08 19:37 30 04:02 04:35 05:03 19:05 19:32 20:05 35 03:44 04:20 04:50 19:17 19:47 20:23 40 03:21 04:03 04:35 19:32 20:05 20:46 45 02:52 03:41 04:18 19:50 20:27 21:15
S 50 02:08 03:12 03:56 20:11 20:55 21:59 52 01:42 02:57 03:45 20:22 21:10 22:24 54 01:02 02:40 03:33 20:34 21:27 23:03 56 02:19 03:20 20:47 21:48 58 01:51 03:03 21:04 22:15
S 60 01:08 02:44 21:23 22:58
Lat. Moonrise Moonset Wed Thu Fri Wed Thu Fri
N 72 12:37 12:18 12:00 21:58 23:43 –:–
N 70 12:26 12:13 12:02 22:06 23:44 –:– 68 12:17 12:10 12:03 22:14 23:45 –:– 66 12:09 12:07 12:04 22:20 23:46 –:– 64 12:02 12:04 12:05 22:25 23:47 –:– 62 11:57 12:02 12:06 22:29 23:48 –:– 60 11:52 12:00 12:07 22:33 23:49 –:–
N 58 11:48 11:58 12:08 22:36 23:49 –:– 56 11:44 11:56 12:08 22:39 23:50 –:– 54 11:40 11:55 12:09 22:42 23:50 –:– 52 11:37 11:54 12:10 22:44 23:51 –:– 50 11:34 11:52 12:10 22:46 23:51 –:– 45 11:28 11:50 12:11 22:51 23:52 –:–
N 40 11:23 11:48 12:12 22:55 23:52 –:– 35 11:18 11:46 12:13 22:58 23:53 –:– 30 11:14 11:44 12:14 23:01 23:54 –:– 20 11:07 11:41 12:15 23:06 23:54 –:–
N 10 11:01 11:39 12:16 23:11 23:55 –:– 0 10:55 11:36 12:17 23:15 23:56 –:–
S 10 10:49 11:34 12:18 23:19 23:57 –:– 20 10:43 11:31 12:19 23:24 23:57 –:– 30 10:36 11:28 12:20 23:29 23:58 –:– 35 10:32 11:26 12:21 23:31 23:59 –:– 40 10:27 11:25 12:22 23:35 23:59 –:– 45 10:21 11:22 12:23 23:38 –:– 00:00
S 50 10:15 11:20 12:24 23:43 –:– 00:00 52 10:12 11:18 12:25 23:45 –:– 00:01 54 10:08 11:17 12:25 23:47 –:– 00:01 56 10:05 11:15 12:26 23:49 –:– 00:01 58 10:01 11:14 12:27 23:52 –:– 00:02
S 60 09:56 11:12 12:28 23:55 –:– 00:02
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age 00h 12h Pass Upper Lower 6-8
mm:ss mm:ss hh:mm hh:mm hh:mm 34-53%
01 03:05 03:20 12:03 17:05 04:44 02 03:34 03:48 12:04 17:46 05:26 03 04:02 04:16 12:04 18:27 06:06
3
1
117
18
Equation_of_Time_Curve.odt
Ti m
e in
m in
u te
-20
-16
-12
-8
-4
0
4
8
12
16
20
January February March April May June July August September October November December
2021 Moon Phases
New Moon First Quarter Full Moon Last Quarter
-- -- -- January 06
02:24
Add or subtract your time diference from Greenwich to determine local time and date of Moon phase.
Moon Phases.odt
January 01, 02, 03 UT (Fri., Sat., Sun.)
Aries Venus Mars Jupiter Saturn Fri GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10051.9 20114.8 S2226.0 7547.3 N1120.7 15540.7 S2000.7 15654.3 S2010.5 1 11554.3 21613.9 26.4 9048.8 21.1 17042.6 00.6 17156.4 10.4 2 13056.8 23113.0 26.7 10550.3 21.6 18544.5 00.5 18658.6 10.4 3 14559.3 24612.0 · · 27.0 12051.7 · · 22.0 20046.3 · · 00.4 20200.8 · · 10.3 4 16101.7 26111.1 27.3 13553.2 22.4 21548.2 00.2 21702.9 10.2 5 17604.2 27610.2 27.6 15054.6 22.9 23050.1 00.1 23205.1 10.2
6 19106.7 29109.3 S2228.0 16556.1 N1123.3 24552.0 S2000.0 24707.3 S2010.1 7 20609.1 30608.4 28.3 18057.5 23.7 26053.8 1959.8 26209.4 10.1 8 22111.6 32107.5 28.6 19559.0 24.2 27555.7 59.7 27711.6 10.0 9 23614.1 33606.6 · · 28.9 21100.4 · · 24.6 29057.6 · · 59.6 29213.8 · · 09.9 10 25116.5 35105.7 29.2 22601.9 25.0 30559.4 59.5 30716.0 09.9 11 26619.0 604.8 29.6 24103.3 25.5 32101.3 59.3 32218.1 09.8
12 28121.4 2103.9 S2229.9 25604.8 N1125.9 33603.2 S1959.2 33720.3 S2009.7 13 29623.9 3603.0 30.2 27106.2 26.3 35105.1 59.1 35222.5 09.7 14 31126.4 5102.1 30.5 28607.7 26.8 606.9 58.9 724.6 09.6 15 32628.8 6601.1 · · 30.8 30109.1 · · 27.2 2108.8 · · 58.8 2226.8 · · 09.6 16 34131.3 8100.2 31.1 31610.6 27.7 3610.7 58.7 3729.0 09.5 17 35633.8 9559.3 31.4 33112.0 28.1 5112.5 58.6 5231.1 09.4
18 1136.2 11058.4 S2231.7 34613.5 N1128.5 6614.4 S1958.4 6733.3 S2009.4 19 2638.7 12557.5 32.0 114.9 29.0 8116.3 58.3 8235.5 09.3 20 4141.2 14056.6 32.3 1616.3 29.4 9618.2 58.2 9737.6 09.3 21 5643.6 15555.7 · · 32.6 3117.8 · · 29.8 11120.0 · · 58.0 11239.8 · · 09.2 22 7146.1 17054.8 32.9 4619.2 30.3 12621.9 57.9 12742.0 09.1 23 8648.6 18553.9 33.2 6120.7 30.7 14123.8 57.8 14244.1 09.1
Mer.pass.:17:14 v-0.9 d-0.3 m-3.8 v1.5 d0.4 m-0.2 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Sat GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10151.0 20052.9 S2233.5 7622.1 N1131.1 15625.6 S1957.6 15746.3 S2009.0 1 11653.5 21552.0 33.8 9123.6 31.6 17127.5 57.5 17248.5 09.0 2 13155.9 23051.1 34.1 10625.0 32.0 18629.4 57.4 18750.6 08.9 3 14658.4 24550.2 · · 34.4 12126.4 · · 32.5 20131.3 · · 57.3 20252.8 · · 08.8 4 16200.9 26049.3 34.7 13627.9 32.9 21633.1 57.1 21755.0 08.8 5 17703.3 27548.4 35.0 15129.3 33.3 23135.0 57.0 23257.1 08.7
6 19205.8 29047.5 S2235.3 16630.8 N1133.8 24636.9 S1956.9 24759.3 S2008.6 7 20708.3 30546.6 35.6 18132.2 34.2 26138.7 56.7 26301.5 08.6 8 22210.7 32045.6 35.9 19633.6 34.6 27640.6 56.6 27803.6 08.5 9 23713.2 33544.7 · · 36.2 21135.1 · · 35.1 29142.5 · · 56.5 29305.8 · · 08.5 10 25215.7 35043.8 36.5 22636.5 35.5 30644.4 56.4 30808.0 08.4 11 26718.1 542.9 36.8 24138.0 35.9 32146.2 56.2 32310.1 08.3
12 28220.6 2042.0 S2237.1 25639.4 N1136.4 33648.1 S1956.1 33812.3 S2008.3 13 29723.1 3541.1 37.3 27140.8 36.8 35150.0 56.0 35314.5 08.2 14 31225.5 5040.1 37.6 28642.3 37.3 651.8 55.8 816.6 08.2 15 32728.0 6539.2 · · 37.9 30143.7 · · 37.7 2153.7 · · 55.7 2318.8 · · 08.1 16 34230.4 8038.3 38.2 31645.1 38.1 3655.6 55.6 3821.0 08.0 17 35732.9 9537.4 38.5 33146.6 38.6 5157.5 55.4 5323.1 08.0
18 1235.4 11036.5 S2238.7 34648.0 N1139.0 6659.3 S1955.3 6825.3 S2007.9 19 2737.8 12535.6 39.0 149.4 39.4 8201.2 55.2 8327.5 07.8 20 4240.3 14034.6 39.3 1650.9 39.9 9703.1 55.1 9829.6 07.8 21 5742.8 15533.7 · · 39.6 3152.3 · · 40.3 11204.9 · · 54.9 11331.8 · · 07.7 22 7245.2 17032.8 39.8 4653.7 40.8 12706.8 54.8 12834.0 07.7 23 8747.7 18531.9 40.1 6155.2 41.2 14208.7 54.7 14336.1 07.6
Mer.pass.:17:10 v-0.9 d-0.3 m-3.8 v1.4 d0.4 m-0.2 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Sun GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10250.2 20031.0 S2240.4 7656.6 N1141.6 15710.5 S1954.5 15838.3 S2007.5 1 11752.6 21530.1 40.7 9158.0 42.1 17212.4 54.4 17340.4 07.5 2 13255.1 23029.1 40.9 10659.4 42.5 18714.3 54.3 18842.6 07.4 3 14757.5 24528.2 · · 41.2 12200.9 · · 43.0 20216.2 · · 54.1 20344.8 · · 07.4 4 16300.0 26027.3 41.5 13702.3 43.4 21718.0 54.0 21846.9 07.3 5 17802.5 27526.4 41.7 15203.7 43.8 23219.9 53.9 23349.1 07.2
6 19304.9 29025.5 S2242.0 16705.2 N1144.3 24721.8 S1953.7 24851.3 S2007.2 7 20807.4 30524.5 42.3 18206.6 44.7 26223.6 53.6 26353.4 07.1 8 22309.9 32023.6 42.5 19708.0 45.1 27725.5 53.5 27855.6 07.0 9 23812.3 33522.7 · · 42.8 21209.4 · · 45.6 29227.4 · · 53.4 29357.8 · · 07.0 10 25314.8 35021.8 43.0 22710.9 46.0 30729.2 53.2 30859.9 06.9 11 26817.3 520.9 43.3 24212.3 46.5 32231.1 53.1 32402.1 06.9
12 28319.7 2019.9 S2243.6 25713.7 N1146.9 33733.0 S1953.0 33904.3 S2006.8 13 29822.2 3519.0 43.8 27215.1 47.3 35234.9 52.8 35406.4 06.7 14 31324.7 5018.1 44.1 28716.6 47.8 736.7 52.7 908.6 06.7 15 32827.1 6517.2 · · 44.3 30218.0 · · 48.2 2238.6 · · 52.6 2410.8 · · 06.6 16 34329.6 8016.2 44.6 31719.4 48.7 3740.5 52.4 3912.9 06.5 17 35832.0 9515.3 44.8 33220.8 49.1 5242.3 52.3 5415.1 06.5
18 1334.5 11014.4 S2245.1 34722.2 N1149.5 6744.2 S1952.2 6917.3 S2006.4 19 2837.0 12513.5 45.3 223.7 50.0 8246.1 52.0 8419.4 06.4 20 4339.4 14012.6 45.6 1725.1 50.4 9747.9 51.9 9921.6 06.3 21 5841.9 15511.6 · · 45.8 3226.5 · · 50.9 11249.8 · · 51.8 11423.8 · · 06.2 22 7344.4 17010.7 46.1 4727.9 51.3 12751.7 51.6 12925.9 06.2 23 8846.8 18509.8 46.3 6229.3 51.7 14253.5 51.5 14428.1 06.1
Mer.pass.:17:06 v-0.9 d-0.3 m-3.8 v1.4 d0.4 m-0.2 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Stars SHA Dec
Alpheratz 35738.2 2912.4 Ankaa 35310.5 -4211.9
Schedar 34934.6 5639.3 Diphda 34850.6 -1752.5
Achernar 33522.6 -5708.2 Hamal 32754.7 2333.7 Polaris 31513.2 8921.3 Acamar 31514.1 -4013.6 Menkar 31409.4 410.2 Mirfak 30832.5 4956.2
Aldebaran 29043.0 1633.0 Rigel 28106.7 -810.8
Capella 28026.2 4601.1 Bellatrix 27826.0 622.0 Elnath 27805.6 2837.4 Alnilam 27540.7 -111.4
Betelgeuse 27055.3 724.6 Canopus 26353.3 -5242.5
Sirius 25828.7 -1644.8 Adhara 25508.0 -2900.1 Procyon 24453.9 510.2 Pollux 24320.9 2758.4 Avior 23415.4 -5934.5 Suhail 22248.3 -4330.9
Miaplacidus 22138.0 -6948.0 Alphard 21750.7 -844.9 Regulus 20737.7 1151.8 Dubhe 19344.8 6138.1
Denebola 18228.2 1427.3 Gienah 17546.9 -1739.3 Acrux 17303.5 -6312.5
Gacrux 17155.1 -5713.5 Alioth 16616.0 5550.6 Spica 15825.8 -1116.1 Alkaid 15254.8 4912.4 Hadar 14840.7 -6028.0
Menkent 14801.6 -3628.1 Arcturus 14551.1 1904.4
Rigil Kent. 13945.0 -6054.9 Kochab 13720.6 7403.9
Zuben’ubi 13659.8 -1607.6 Alphecca 12606.8 2638.6 Antares 11220.1 -2628.5
Atria 10717.8 -6903.6 Sabik 10206.8 -1544.9
Shaula 9615.2 -3707.0 Rasalhague 9601.9 1232.7
Eltanin 9044.2 5129.1 Kaus Aust. 8337.3 -3422.4
Vega 8035.9 3848.2 Nunki 7552.2 -2616.2 Altair 6203.5 855.4
Peacock 5311.5 -5640.2 Deneb 4928.4 4521.4
Enif 3342.2 958.2 Al Na’ir 2737.4 -4651.8
Fomalhaut 1518.3 -2930.9 Scheat 1348.5 2811.8 Markab 1333.3 1519.1
Jan 01 Fri SHA Mer.pass Venus 10022.9 10:36 Mars 33455.5 18:55
Jupiter 5448.8 13:36 Saturn 5602.4 13:30
Jan 02 Sat SHA Mer.pass Venus 9901.9 10:37 Mars 33431.1 18:53
Jupiter 5434.6 13:33 Saturn 5555.3 13:27
Jan 03 Sun SHA Mer.pass Venus 9740.8 10:39 Mars 33406.4 18:50
Jupiter 5420.4 13:30 Saturn 5548.1 13:24
Horizontal parallax Venus: 0.1 Mars: 0.2
2
DUT1 = UT1-UTC = -0.1753 sec T = TT-UT1 = +69.3593 sec 2021 January 01 to Jan. 03 UT
h Sun Moon Fri GHA Dec GHA ν Dec d HP
0 17908.5 S2300.0 33457.7 8.5’ N2301.4 -5.5’ 56.7’ 1 19408.2 2259.7 34925.2 8.5’ 2255.8 -5.6’ 56.8’ 2 20907.9 59.5 352.7 8.5’ 2250.1 -5.8’ 56.8’ 3 22407.6 · · 59.3 1820.2 8.5’ 2244.3 -5.9’ 56.8’ 4 23907.3 59.1 3247.7 8.6’ 2238.3 -6.0’ 56.8’ 5 25407.0 58.9 4715.3 8.6’ 2232.3 -6.1’ 56.8’
6 26906.7 S2258.7 6142.9 8.6’ N2226.0 -6.3’ 56.9’ 7 28406.4 58.5 7610.6 8.7’ 2219.7 -6.4’ 56.9’ 8 29906.1 58.3 9038.2 8.7’ 2213.2 -6.5’ 56.9’ 9 31405.8 · · 58.1 10505.9 8.7’ 2206.6 -6.7’ 56.9’ 10 32905.5 57.9 11933.7 8.7’ 2159.9 -6.8’ 56.9’ 11 34405.3 57.6 13401.4 8.8’ 2153.1 -6.9’ 57.0’
12 35905.0 S2257.4 14829.2 8.8’ N2146.1 -7.0’ 57.0’ 13 1404.7 57.2 16257.1 8.9’ 2139.0 -7.2’ 57.0’ 14 2904.4 57.0 17724.9 8.9’ 2131.8 -7.3’ 57.0’ 15 4404.1 · · 56.8 19152.8 8.9’ 2124.4 -7.4’ 57.0’ 16 5903.8 56.6 20620.8 9.0’ 2117.0 -7.5’ 57.1’ 17 7403.5 56.3 22048.8 9.0’ 2109.4 -7.7’ 57.1’
18 8903.2 S2256.1 23516.8 9.0’ N2101.7 -7.8’ 57.1’ 19 10402.9 55.9 24944.8 9.1’ 2053.8 -7.9’ 57.1’ 20 11902.6 55.7 26412.9 9.1’ 2045.9 -8.0’ 57.1’ 21 13402.3 · · 55.5 27841.1 9.2’ 2037.8 -8.1’ 57.2’ 22 14902.0 55.2 29309.2 9.2’ 2029.6 -8.2’ 57.2’ 23 16401.7 55.0 30737.5 9.2’ 2021.3 -8.4’ 57.2’
SD.=16.3 d=0.2 S.D.=15.5
Sat GHA Dec GHA ν Dec d HP
0 17901.5 S2254.8 32205.7 9.3’ N2012.9 -8.5’ 57.2’ 1 19401.2 54.6 33634.0 9.3’ 2004.4 -8.6’ 57.2’ 2 20900.9 54.3 35102.4 9.4’ 1955.7 -8.7’ 57.2’ 3 22400.6 · · 54.1 530.7 9.4’ 1947.0 -8.8’ 57.3’ 4 23900.3 53.9 1959.2 9.4’ 1938.1 -8.9’ 57.3’ 5 25400.0 53.6 3427.6 9.5’ 1929.1 -9.0’ 57.3’
6 26859.7 S2253.4 4856.1 9.5’ N1920.0 -9.2’ 57.3’ 7 28359.4 53.2 6324.7 9.6’ 1910.8 -9.3’ 57.3’ 8 29859.1 53.0 7753.3 9.6’ 1901.5 -9.4’ 57.4’ 9 31358.8 · · 52.7 9221.9 9.7’ 1852.0 -9.5’ 57.4’ 10 32858.6 52.5 10650.6 9.7’ 1842.5 -9.6’ 57.4’ 11 34358.3 52.3 12119.4 9.8’ 1832.9 -9.7’ 57.4’
12 35858.0 S2252.0 13548.1 9.8’ N1823.1 -9.8’ 57.4’ 13 1357.7 51.8 15016.9 9.8’ 1813.2 -9.9’ 57.5’ 14 2857.4 51.6 16445.8 9.9’ 1803.3 -10.0’ 57.5’ 15 4357.1 · · 51.3 17914.7 9.9’ 1753.2 -10.1’ 57.5’ 16 5856.8 51.1 19343.7 10.0’ 1743.1 -10.2’ 57.5’ 17 7356.5 50.8 20812.7 10.0’ 1732.8 -10.3’ 57.5’
18 8856.2 S2250.6 22241.7 10.1’ N1722.4 -10.4’ 57.6’ 19 10356.0 50.4 23710.8 10.1’ 1712.0 -10.5’ 57.6’ 20 11855.7 50.1 25139.9 10.1’ 1701.4 -10.6’ 57.6’ 21 13355.4 · · 49.9 26609.1 10.2’ 1650.8 -10.7’ 57.6’ 22 14855.1 49.6 28038.3 10.2’ 1640.0 -10.8’ 57.6’ 23 16354.8 49.4 29507.6 10.3’ 1629.2 -10.9’ 57.7’
SD.=16.3 d=0.2 S.D.=15.7
Sun GHA Dec GHA ν Dec d HP
0 17854.5 S2249.2 30936.9 10.3’ N1618.2 -11.0’ 57.7’ 1 19354.2 48.9 32406.2 10.4’ 1607.2 -11.1’ 57.7’ 2 20853.9 48.7 33835.6 10.4’ 1556.1 -11.2’ 57.7’ 3 22353.7 · · 48.4 35305.0 10.5’ 1544.9 -11.3’ 57.7’ 4 23853.4 48.2 734.5 10.5’ 1533.6 -11.3’ 57.7’ 5 25353.1 47.9 2204.0 10.5’ 1522.2 -11.4’ 57.8’
6 26852.8 S2247.7 3633.6 10.6’ N1510.7 -11.5’ 57.8’ 7 28352.5 47.4 5103.2 10.6’ 1459.2 -11.6’ 57.8’ 8 29852.2 47.2 6532.8 10.7’ 1447.5 -11.7’ 57.8’ 9 31351.9 · · 46.9 8002.5 10.7’ 1435.8 -11.8’ 57.8’ 10 32851.7 46.7 9432.2 10.7’ 1424.0 -11.9’ 57.9’ 11 34351.4 46.4 10902.0 10.8’ 1412.1 -11.9’ 57.9’
12 35851.1 S2246.2 12331.8 10.8’ N1400.1 -12.0’ 57.9’ 13 1350.8 45.9 13801.6 10.9’ 1348.0 -12.1’ 57.9’ 14 2850.5 45.7 15231.5 10.9’ 1335.9 -12.2’ 57.9’ 15 4350.2 · · 45.4 16701.4 10.9’ 1323.7 -12.2’ 57.9’ 16 5849.9 45.2 18131.4 11.0’ 1311.4 -12.3’ 58.0’ 17 7349.7 44.9 19601.4 11.0’ 1259.0 -12.4’ 58.0’
18 8849.4 S2244.6 21031.4 11.0’ N1246.6 -12.5’ 58.0’ 19 10349.1 44.4 22501.4 11.1’ 1234.1 -12.5’ 58.0’ 20 11848.8 44.1 23931.5 11.1’ 1221.5 -12.6’ 58.0’ 21 13348.5 · · 43.9 25401.7 11.1’ 1208.9 -12.7’ 58.1’ 22 14848.2 43.6 26831.8 11.2’ 1156.1 -12.8’ 58.1’ 23 16348.0 43.3 28302.0 11.2’ 1143.4 -12.8’ 58.1’
SD.=16.3 d=0.2 S.D.=15.8
Lat. Twilight
N 72 08:23 10:39 13:30 15:46
N 70 08:04 09:48 14:21 16:05 68 07:49 09:16 14:53 16:20 66 07:37 08:52 10:25 13:43 15:17 16:32 64 07:26 08:33 09:48 14:20 15:35 16:42 62 07:17 08:18 09:22 14:47 15:50 16:52 60 07:09 08:05 09:02 15:07 16:03 17:00
N 58 07:02 07:54 08:45 15:24 16:15 17:07 56 06:55 07:44 08:31 15:38 16:24 17:13 54 06:50 07:35 08:19 15:50 16:33 17:19 52 06:44 07:27 08:08 16:01 16:41 17:24 50 06:39 07:20 07:58 16:10 16:48 17:29 45 06:28 07:05 07:38 16:30 17:04 17:41
N 40 06:18 06:52 07:22 16:46 17:17 17:51 35 06:09 06:40 07:08 17:00 17:28 18:00 30 06:00 06:30 06:56 17:12 17:38 18:08 20 05:44 06:12 06:36 17:33 17:57 18:24
N 10 05:28 05:55 06:17 17:51 18:14 18:40 0 05:12 05:38 06:00 18:08 18:30 18:56
S 10 04:53 05:20 05:43 18:25 18:48 19:15 20 04:31 05:00 05:25 18:43 19:08 19:37 30 04:03 04:36 05:03 19:05 19:32 20:05 35 03:45 04:21 04:51 19:18 19:47 20:23 40 03:22 04:03 04:36 19:32 20:05 20:46 45 02:52 03:41 04:18 19:50 20:26 21:15
S 50 02:09 03:13 03:57 20:11 20:55 21:58 52 01:43 02:58 03:46 20:22 21:10 22:24 54 01:04 02:41 03:34 20:34 21:27 23:02 56 –:– 02:20 03:20 20:47 21:47 –:– 58 –:– 01:52 03:04 21:03 22:15 –:–
S 60 –:– 01:10 02:45 21:22 22:56 –:–
Lat. Moonrise Moonset
Fri Sat Sun Fri Sat Sun
N 72 15:55 19:10 14:31 13:02
N 70 17:10 19:34 13:14 12:36 68 15:16 17:47 19:52 13:17 12:35 12:16 66 16:14 18:13 20:06 12:18 12:08 12:01 64 16:48 18:33 20:18 11:44 11:47 11:47 62 17:12 18:50 20:28 11:19 11:30 11:36 60 17:32 19:03 20:36 10:59 11:16 11:27
N 58 17:48 19:15 20:43 10:42 11:03 11:18 56 18:01 19:24 20:50 10:28 10:53 11:11 54 18:13 19:33 20:56 10:16 10:43 11:04 52 18:23 19:41 21:01 10:05 10:35 10:59 50 18:32 19:48 21:06 09:56 10:27 10:53 45 18:52 20:03 21:16 09:36 10:11 10:41
N 40 19:07 20:15 21:24 09:19 09:58 10:32 35 19:21 20:26 21:31 09:05 09:46 10:23 30 19:32 20:35 21:38 08:53 09:36 10:16 20 19:52 20:50 21:48 08:32 09:19 10:03
N 10 20:09 21:04 21:58 08:14 09:04 09:51 0 20:25 21:17 22:07 07:57 08:50 09:41
S 10 20:40 21:29 22:15 07:40 08:35 09:30 20 20:57 21:43 22:25 07:21 08:20 09:18 30 21:17 21:58 22:35 07:00 08:02 09:05 35 21:28 22:07 22:42 06:47 07:52 08:57 40 21:41 22:17 22:48 06:33 07:40 08:48 45 21:56 22:29 22:57 06:15 07:25 08:38
S 50 22:14 22:43 23:06 05:54 07:08 08:25 52 22:23 22:49 23:11 05:44 07:00 08:19 54 22:33 22:57 23:15 05:32 06:50 08:12 56 22:44 23:05 23:21 05:19 06:40 08:05 58 22:56 23:14 23:27 05:03 06:28 07:56
S 60 23:11 23:24 23:33 04:45 06:14 07:47
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age
00h 12h Pass Upper Lower 18-20 mm:ss mm:ss hh:mm hh:mm hh:mm 94-80%
01 03:26 03:40 12:04 01:44 14:11 02 03:54 04:08 12:04 02:37 15:03 03 04:22 04:36 12:05 03:29 15:54
3
January 04, 05, 06 UT (Mon., Tue., Wed.)
Aries Venus Mars Jupiter Saturn Mon GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10349.3 20008.9 S2246.6 7730.8 N1152.2 15755.4 S1951.4 15930.3 S2006.1 1 11851.8 21507.9 46.8 9232.2 52.6 17257.3 51.3 17432.4 06.0 2 13354.2 23007.0 47.0 10733.6 53.1 18759.2 51.1 18934.6 05.9 3 14856.7 24506.1 · · 47.3 12235.0 · · 53.5 20301.0 · · 51.0 20436.7 · · 05.9 4 16359.2 26005.2 47.5 13736.4 53.9 21802.9 50.9 21938.9 05.8 5 17901.6 27504.2 47.7 15237.8 54.4 23304.8 50.7 23441.1 05.7
6 19404.1 29003.3 S2248.0 16739.3 N1154.8 24806.6 S1950.6 24943.2 S2005.7 7 20906.5 30502.4 48.2 18240.7 55.2 26308.5 50.5 26445.4 05.6 8 22409.0 32001.5 48.5 19742.1 55.7 27810.4 50.3 27947.6 05.6 9 23911.5 33500.5 · · 48.7 21243.5 · · 56.1 29312.2 · · 50.2 29449.7 · · 05.5 10 25413.9 34959.6 48.9 22744.9 56.6 30814.1 50.1 30951.9 05.4 11 26916.4 458.7 49.1 24246.3 57.0 32316.0 49.9 32454.1 05.4
12 28418.9 1957.8 S2249.4 25747.7 N1157.5 33817.8 S1949.8 33956.2 S2005.3 13 29921.3 3456.8 49.6 27249.1 57.9 35319.7 49.7 35458.4 05.2 14 31423.8 4955.9 49.8 28750.6 58.3 821.6 49.5 1000.6 05.2 15 32926.3 6455.0 · · 50.1 30252.0 · · 58.8 2323.4 · · 49.4 2502.7 · · 05.1 16 34428.7 7954.0 50.3 31753.4 59.2 3825.3 49.3 4004.9 05.1 17 35931.2 9453.1 50.5 33254.8 1159.7 5327.2 49.1 5507.0 05.0
18 1433.6 10952.2 S2250.7 34756.2 N1200.1 6829.1 S1949.0 7009.2 S2004.9 19 2936.1 12451.3 50.9 257.6 00.5 8330.9 48.9 8511.4 04.9 20 4438.6 13950.3 51.2 1759.0 01.0 9832.8 48.7 10013.5 04.8 21 5941.0 15449.4 · · 51.4 3300.4 · · 01.4 11334.7 · · 48.6 11515.7 · · 04.7 22 7443.5 16948.5 51.6 4801.8 01.9 12836.5 48.5 13017.9 04.7 23 8946.0 18447.5 51.8 6303.2 02.3 14338.4 48.3 14520.0 04.6
Mer.pass.:17:02 v-0.9 d-0.2 m-3.8 v1.4 d0.4 m-0.1 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Tue GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10448.4 19946.6 S2252.0 7804.6 N1202.7 15840.3 S1948.2 16022.2 S2004.6 1 11950.9 21445.7 52.2 9306.0 03.2 17342.1 48.1 17524.4 04.5 2 13453.4 22944.8 52.5 10807.4 03.6 18844.0 48.0 19026.5 04.4 3 14955.8 24443.8 · · 52.7 12308.9 · · 04.1 20345.9 · · 47.8 20528.7 · · 04.4 4 16458.3 25942.9 52.9 13810.3 04.5 21847.7 47.7 22030.9 04.3 5 18000.8 27442.0 53.1 15311.7 04.9 23349.6 47.6 23533.0 04.2
6 19503.2 28941.0 S2253.3 16813.1 N1205.4 24851.5 S1947.4 25035.2 S2004.2 7 21005.7 30440.1 53.5 18314.5 05.8 26353.3 47.3 26537.3 04.1 8 22508.1 31939.2 53.7 19815.9 06.3 27855.2 47.2 28039.5 04.1 9 24010.6 33438.2 · · 53.9 21317.3 · · 06.7 29357.1 · · 47.0 29541.7 · · 04.0 10 25513.1 34937.3 54.1 22818.7 07.1 30858.9 46.9 31043.8 03.9 11 27015.5 436.4 54.3 24320.1 07.6 32400.8 46.8 32546.0 03.9
12 28518.0 1935.5 S2254.5 25821.5 N1208.0 33902.7 S1946.6 34048.2 S2003.8 13 30020.5 3434.5 54.7 27322.9 08.5 35404.5 46.5 35550.3 03.7 14 31522.9 4933.6 54.9 28824.3 08.9 906.4 46.4 1052.5 03.7 15 33025.4 6432.7 · · 55.1 30325.7 · · 09.4 2408.3 · · 46.2 2554.7 · · 03.6 16 34527.9 7931.7 55.3 31827.1 09.8 3910.1 46.1 4056.8 03.6 17 030.3 9430.8 55.5 33328.5 10.2 5412.0 46.0 5559.0 03.5
18 1532.8 10929.9 S2255.7 34829.9 N1210.7 6913.9 S1945.8 7101.1 S2003.4 19 3035.3 12428.9 55.9 331.2 11.1 8415.7 45.7 8603.3 03.4 20 4537.7 13928.0 56.1 1832.6 11.6 9917.6 45.6 10105.5 03.3 21 6040.2 15427.1 · · 56.2 3334.0 · · 12.0 11419.5 · · 45.4 11607.6 · · 03.2 22 7542.6 16926.1 56.4 4835.4 12.4 12921.3 45.3 13109.8 03.2 23 9045.1 18425.2 56.6 6336.8 12.9 14423.2 45.2 14612.0 03.1
Mer.pass.:16:58 v-0.9 d-0.2 m-3.8 v1.4 d0.4 m-0.1 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Wed GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10547.6 19924.3 S2256.8 7838.2 N1213.3 15925.1 S1945.0 16114.1 S2003.1 1 12050.0 21423.3 57.0 9339.6 13.8 17426.9 44.9 17616.3 03.0 2 13552.5 22922.4 57.2 10841.0 14.2 18928.8 44.8 19118.4 02.9 3 15055.0 24421.5 · · 57.4 12342.4 · · 14.7 20430.7 · · 44.6 20620.6 · · 02.9 4 16557.4 25920.5 57.5 13843.8 15.1 21932.5 44.5 22122.8 02.8 5 18059.9 27419.6 57.7 15345.2 15.5 23434.4 44.4 23624.9 02.7
6 19602.4 28918.7 S2257.9 16846.6 N1216.0 24936.3 S1944.2 25127.1 S2002.7 7 21104.8 30417.7 58.1 18348.0 16.4 26438.1 44.1 26629.3 02.6 8 22607.3 31916.8 58.2 19849.4 16.9 27940.0 43.9 28131.4 02.6 9 24109.7 33415.9 · · 58.4 21350.7 · · 17.3 29441.9 · · 43.8 29633.6 · · 02.5 10 25612.2 34914.9 58.6 22852.1 17.8 30943.7 43.7 31135.7 02.4 11 27114.7 414.0 58.8 24353.5 18.2 32445.6 43.5 32637.9 02.4
12 28617.1 1913.0 S2258.9 25854.9 N1218.6 33947.5 S1943.4 34140.1 S2002.3 13 30119.6 3412.1 59.1 27356.3 19.1 35449.3 43.3 35642.2 02.2 14 31622.1 4911.2 59.3 28857.7 19.5 951.2 43.1 1144.4 02.2 15 33124.5 6410.2 · · 59.4 30359.1 · · 20.0 2453.1 · · 43.0 2646.6 · · 02.1 16 34627.0 7909.3 59.6 31900.5 20.4 3954.9 42.9 4148.7 02.0 17 129.5 9408.4 59.8 33401.8 20.9 5456.8 42.7 5650.9 02.0
18 1631.9 10907.4 S2259.9 34903.2 N1221.3 6958.7 S1942.6 7153.1 S2001.9 19 3134.4 12406.5 2300.1 404.6 21.7 8500.5 42.5 8655.2 01.9 20 4636.9 13905.6 00.3 1906.0 22.2 10002.4 42.3 10157.4 01.8 21 6139.3 15404.6 · · 00.4 3407.4 · · 22.6 11504.3 · · 42.2 11659.5 · · 01.7 22 7641.8 16903.7 00.6 4908.8 23.1 13006.1 42.1 13201.7 01.7 23 9144.2 18402.7 00.7 6410.1 23.5 14508.0 41.9 14703.9 01.6
Mer.pass.:16:54 v-0.9 d-0.2 m-3.8 v1.4 d0.4 m-0.1 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Stars SHA Dec
Alpheratz 35738.2 2912.4 Ankaa 35310.5 -4211.9
Schedar 34934.7 5639.3 Diphda 34850.6 -1752.5
Achernar 33522.6 -5708.2 Hamal 32754.7 2333.7 Polaris 31514.5 8921.4 Acamar 31514.1 -4013.6 Menkar 31409.4 410.2 Mirfak 30832.5 4956.2
Aldebaran 29043.1 1633.0 Rigel 28106.7 -810.8
Capella 28026.2 4601.1 Bellatrix 27826.0 622.0 Elnath 27805.6 2837.4 Alnilam 27540.7 -111.4
Betelgeuse 27055.3 724.6 Canopus 26353.3 -5242.5
Sirius 25828.7 -1644.8 Adhara 25508.0 -2900.1 Procyon 24453.9 510.2 Pollux 24320.9 2758.4 Avior 23415.3 -5934.5 Suhail 22248.2 -4330.9
Miaplacidus 22137.9 -6948.0 Alphard 21750.7 -844.9 Regulus 20737.7 1151.8 Dubhe 19344.8 6138.1
Denebola 18228.2 1427.3 Gienah 17546.8 -1739.3 Acrux 17303.5 -6312.5
Gacrux 17155.1 -5713.5 Alioth 16615.9 5550.6 Spica 15825.8 -1116.1 Alkaid 15254.8 4912.3 Hadar 14840.7 -6028.1
Menkent 14801.5 -3628.1 Arcturus 14551.0 1904.4
Rigil Kent. 13945.0 -6054.9 Kochab 13720.5 7403.9
Zuben’ubi 13659.8 -1607.6 Alphecca 12606.8 2638.6 Antares 11220.1 -2628.5
Atria 10717.7 -6903.6 Sabik 10206.8 -1544.9
Shaula 9615.2 -3707.0 Rasalhague 9601.9 1232.7
Eltanin 9044.2 5129.1 Kaus Aust. 8337.2 -3422.4
Vega 8035.8 3848.2 Nunki 7552.2 -2616.2 Altair 6203.5 855.4
Peacock 5311.5 -5640.2 Deneb 4928.4 4521.4
Enif 3342.2 958.2 Al Na’ir 2737.4 -4651.8
Fomalhaut 1518.3 -2930.9 Scheat 1348.5 2811.8 Markab 1333.3 1519.1
Jan 04 Mon SHA Mer.pass Venus 9619.6 10:40 Mars 33341.5 18:48
Jupiter 5406.1 13:27 Saturn 5541.0 13:20
Jan 05 Tue SHA Mer.pass Venus 9458.2 10:42 Mars 33316.2 18:46
Jupiter 5351.8 13:24 Saturn 5533.8 13:17
Jan 06 Wed SHA Mer.pass Venus 9336.7 10:43 Mars 33250.7 18:44
Jupiter 5337.5 13:21 Saturn 5526.5 13:13
Horizontal parallax Venus: 0.1 Mars: 0.2
4
DUT1 = UT1-UTC = -0.1743 sec T = TT-UT1 = +69.3583 sec 2021 January 04 to Jan. 06 UT
h Sun Moon Mon GHA Dec GHA ν Dec d HP
0 17847.7 S2243.1 29732.3 11.2’ N1130.5 -12.9’ 58.1’ 1 19347.4 42.8 31202.5 11.3’ 1117.6 -13.0’ 58.1’ 2 20847.1 42.6 32632.8 11.3’ 1104.6 -13.0’ 58.1’ 3 22346.8 · · 42.3 34103.2 11.3’ 1051.5 -13.1’ 58.2’ 4 23846.5 42.0 35533.5 11.4’ 1038.4 -13.1’ 58.2’ 5 25346.3 41.8 1003.9 11.4’ 1025.2 -13.2’ 58.2’
6 26846.0 S2241.5 2434.3 11.4’ N1012.0 -13.3’ 58.2’ 7 28345.7 41.2 3904.8 11.5’ 0958.7 -13.3’ 58.2’ 8 29845.4 41.0 5335.2 11.5’ 0945.4 -13.4’ 58.2’ 9 31345.1 · · 40.7 6805.7 11.5’ 0932.0 -13.4’ 58.3’ 10 32844.9 40.4 8236.2 11.5’ 0918.5 -13.5’ 58.3’ 11 34344.6 40.1 9706.8 11.6’ 0905.0 -13.5’ 58.3’
12 35844.3 S2239.9 11137.3 11.6’ N0851.4 -13.6’ 58.3’ 13 1344.0 39.6 12607.9 11.6’ 0837.8 -13.7’ 58.3’ 14 2843.7 39.3 14038.5 11.6’ 0824.1 -13.7’ 58.4’ 15 4343.4 · · 39.0 15509.2 11.6’ 0810.4 -13.8’ 58.4’ 16 5843.2 38.8 16939.8 11.7’ 0756.6 -13.8’ 58.4’ 17 7342.9 38.5 18410.5 11.7’ 0742.8 -13.8’ 58.4’
18 8842.6 S2238.2 19841.2 11.7’ N0728.9 -13.9’ 58.4’ 19 10342.3 37.9 21311.9 11.7’ 0715.0 -13.9’ 58.4’ 20 11842.0 37.7 22742.6 11.7’ 0701.0 -14.0’ 58.5’ 21 13341.8 · · 37.4 24213.3 11.7’ 0647.0 -14.0’ 58.5’ 22 14841.5 37.1 25644.1 11.8’ 0633.0 -14.1’ 58.5’ 23 16341.2 36.8 27114.9 11.8’ 0618.9 -14.1’ 58.5’
SD.=16.3 d=0.3 S.D.=15.9
Tue GHA Dec GHA ν Dec d HP
0 17840.9 S2236.5 28545.6 11.8’ N0604.8 -14.1’ 58.5’ 1 19340.7 36.3 30016.4 11.8’ 0550.6 -14.2’ 58.5’ 2 20840.4 36.0 31447.2 11.8’ 0536.4 -14.2’ 58.6’ 3 22340.1 · · 35.7 32918.0 11.8’ 0522.2 -14.3’ 58.6’ 4 23839.8 35.4 34348.8 11.8’ 0507.9 -14.3’ 58.6’ 5 25339.5 35.1 35819.7 11.8’ 0453.6 -14.3’ 58.6’
6 26839.3 S2234.8 1250.5 11.8’ N0439.3 -14.3’ 58.6’ 7 28339.0 34.6 2721.3 11.8’ 0424.9 -14.4’ 58.6’ 8 29838.7 34.3 4152.2 11.8’ 0410.5 -14.4’ 58.6’ 9 31338.4 · · 34.0 5623.0 11.8’ 0356.1 -14.4’ 58.7’ 10 32838.1 33.7 7053.9 11.8’ 0341.6 -14.5’ 58.7’ 11 34337.9 33.4 8524.7 11.8’ 0327.2 -14.5’ 58.7’
12 35837.6 S2233.1 9955.6 11.8’ N0312.7 -14.5’ 58.7’ 13 1337.3 32.8 11426.4 11.8’ 0258.1 -14.5’ 58.7’ 14 2837.0 32.5 12857.2 11.8’ 0243.6 -14.6’ 58.7’ 15 4336.8 · · 32.2 14328.1 11.8’ 0229.0 -14.6’ 58.8’ 16 5836.5 31.9 15758.9 11.8’ 0214.4 -14.6’ 58.8’ 17 7336.2 31.7 17229.7 11.8’ 0159.8 -14.6’ 58.8’
18 8835.9 S2231.4 18700.6 11.8’ N0145.2 -14.6’ 58.8’ 19 10335.7 31.1 20131.4 11.8’ 0130.6 -14.6’ 58.8’ 20 11835.4 30.8 21602.2 11.8’ 0115.9 -14.7’ 58.8’ 21 13335.1 · · 30.5 23033.0 11.8’ 0101.2 -14.7’ 58.9’ 22 14834.8 30.2 24503.8 11.8’ 0046.6 -14.7’ 58.9’ 23 16334.6 29.9 25934.5 11.8’ 0031.9 -14.7’ 58.9’
SD.=16.3 d=0.3 S.D.=16.0
Wed GHA Dec GHA ν Dec d HP
0 17834.3 S2229.6 27405.3 11.8’ N0017.2 -14.7’ 58.9’ 1 19334.0 29.3 28836.1 11.7’ N0002.4 -14.7’ 58.9’ 2 20833.7 29.0 30306.8 11.7’ S0012.3 -14.7’ 58.9’ 3 22333.5 · · 28.7 31737.5 11.7’ 0027.0 -14.7’ 58.9’ 4 23833.2 28.4 33208.2 11.7’ 0041.7 -14.7’ 59.0’ 5 25332.9 28.1 34638.9 11.7’ 0056.5 -14.7’ 59.0’
6 26832.6 S2227.8 109.5 11.6’ S0111.2 -14.7’ 59.0’ 7 28332.4 27.5 1540.2 11.6’ 0125.9 -14.7’ 59.0’ 8 29832.1 27.1 3010.8 11.6’ 0140.7 -14.7’ 59.0’ 9 31331.8 · · 26.8 4441.4 11.6’ 0155.4 -14.7’ 59.0’ 10 32831.5 26.5 5911.9 11.6’ 0210.1 -14.7’ 59.0’ 11 34331.3 26.2 7342.5 11.5’ 0224.9 -14.7’ 59.1’
12 35831.0 S2225.9 8813.0 11.5’ S0239.6 -14.7’ 59.1’ 13 1330.7 25.6 10243.5 11.5’ 0254.3 -14.7’ 59.1’ 14 2830.5 25.3 11714.0 11.4’ 0309.0 -14.7’ 59.1’ 15 4330.2 · · 25.0 13144.4 11.4’ 0323.7 -14.7’ 59.1’ 16 5829.9 24.7 14614.8 11.4’ 0338.4 -14.7’ 59.1’ 17 7329.6 24.4 16045.1 11.3’ 0353.1 -14.7’ 59.1’
18 8829.4 S2224.0 17515.5 11.3’ S0407.8 -14.7’ 59.2’ 19 10329.1 23.7 18945.8 11.3’ 0422.4 -14.6’ 59.2’ 20 11828.8 23.4 20416.0 11.2’ 0437.0 -14.6’ 59.2’ 21 13328.6 · · 23.1 21846.3 11.2’ 0451.6 -14.6’ 59.2’ 22 14828.3 22.8 23316.4 11.2’ 0506.2 -14.6’ 59.2’ 23 16328.0 22.5 24746.6 11.1’ 0520.8 -14.6’ 59.2’
SD.=16.3 d=0.3 S.D.=16.1
Lat. Twilight
N 72 08:19 10:29 13:43 15:52
N 70 08:01 09:42 14:29 16:10 68 07:47 09:12 11:27 12:44 15:00 16:25 66 07:35 08:49 10:19 13:52 15:22 16:37 64 07:25 08:31 09:44 14:27 15:40 16:47 62 07:16 08:16 09:19 14:52 15:55 16:56 60 07:08 08:04 08:59 15:12 16:08 17:03
N 58 07:01 07:53 08:43 15:28 16:18 17:10 56 06:55 07:43 08:30 15:42 16:28 17:17 54 06:49 07:35 08:18 15:54 16:37 17:22 52 06:44 07:27 08:07 16:04 16:44 17:28 50 06:39 07:20 07:58 16:13 16:51 17:32 45 06:28 07:05 07:38 16:33 17:07 17:43
N 40 06:18 06:52 07:22 16:49 17:19 17:53 35 06:09 06:41 07:09 17:03 17:31 18:02 30 06:01 06:31 06:57 17:14 17:41 18:10 20 05:45 06:12 06:36 17:35 17:59 18:26
N 10 05:30 05:56 06:19 17:52 18:15 18:41 0 05:13 05:39 06:02 18:09 18:32 18:58
S 10 04:55 05:22 05:45 18:26 18:49 19:16 20 04:33 05:02 05:27 18:44 19:09 19:38 30 04:05 04:38 05:05 19:05 19:32 20:05 35 03:47 04:24 04:53 19:18 19:47 20:23 40 03:25 04:06 04:39 19:32 20:04 20:45 45 02:56 03:45 04:21 19:49 20:26 21:14
S 50 02:14 03:16 04:00 20:11 20:54 21:56 52 01:49 03:02 03:50 20:21 21:08 22:20 54 01:13 02:46 03:38 20:32 21:24 22:55 56 –:– 02:25 03:25 20:46 21:45 –:– 58 –:– 01:59 03:09 21:01 22:11 –:–
S 60 –:– 01:20 02:50 21:20 22:48 –:–
Lat. Moonrise Moonset
N 72 21:30 23:40 ·· ·· 12:26 11:58 11:33
N 70 21:40 23:41 ·· ·· 12:13 11:54 11:36 68 21:48 23:41 ·· ·· 12:03 11:51 11:39 66 21:54 23:41 ·· ·· 11:54 11:48 11:42 64 22:00 23:41 ·· ·· 11:47 11:45 11:44 62 22:05 23:42 ·· ·· 11:40 11:43 11:46 60 22:09 23:42 ·· ·· 11:35 11:41 11:47
N 58 22:13 23:42 ·· ·· 11:30 11:40 11:49 56 22:16 23:42 ·· ·· 11:26 11:38 11:50 54 22:19 23:42 ·· ·· 11:22 11:37 11:51 52 22:21 23:42 ·· ·· 11:18 11:36 11:52 50 22:24 23:42 ·· ·· 11:15 11:34 11:53 45 22:29 23:42 ·· ·· 11:08 11:32 11:56
N 40 22:33 23:43 ·· ·· 11:02 11:30 11:57 35 22:37 23:43 ·· ·· 10:56 11:28 11:59 30 22:40 23:43 ·· ·· 10:52 11:26 12:00 20 22:46 23:43 ·· ·· 10:44 11:23 12:03
N 10 22:51 23:43 ·· ·· 10:37 11:21 12:05 0 22:55 23:44 ·· ·· 10:30 11:18 12:07
S 10 23:00 23:44 ·· ·· 10:23 11:16 12:09 20 23:05 23:44 ·· ·· 10:16 11:13 12:11 30 23:11 23:45 ·· ·· 10:08 11:10 12:13 35 23:14 23:45 ·· ·· 10:03 11:08 12:15 40 23:17 23:45 ·· ·· 09:57 11:06 12:16 45 23:22 23:45 ·· ·· 09:51 11:04 12:18
S 50 23:27 23:46 ·· ·· 09:43 11:01 12:20 52 23:29 23:46 ·· ·· 09:39 11:00 12:21 54 23:31 23:46 ·· ·· 09:35 10:58 12:22 56 23:34 23:46 23:59 09:31 10:57 12:23 58 23:37 23:46 23:56 09:26 10:55 12:25
S 60 23:41 23:47 23:53 09:20 10:53 12:26
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age
00h 12h Pass Upper Lower 21-23 mm:ss mm:ss hh:mm hh:mm hh:mm 71-49%
04 04:49 05:03 12:05 04:18 16:43 05 05:16 05:30 12:05 05:07 17:31 06 05:43 05:56 12:06 05:55 18:20
5
January 07, 08, 09 UT (Thu., Fri., Sat.)
Aries Venus Mars Jupiter Saturn Thu GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10646.7 19901.8 S2300.9 7911.5 N1224.0 16009.9 S1941.8 16206.0 S2001.5 1 12149.2 21400.9 01.0 9412.9 24.4 17511.7 41.7 17708.2 01.5 2 13651.6 22859.9 01.2 10914.3 24.8 19013.6 41.5 19210.3 01.4 3 15154.1 24359.0 · · 01.3 12415.7 · · 25.3 20515.5 · · 41.4 20712.5 · · 01.4 4 16656.6 25858.1 01.5 13917.0 25.7 22017.3 41.3 22214.7 01.3 5 18159.0 27357.1 01.6 15418.4 26.2 23519.2 41.1 23716.8 01.2
6 19701.5 28856.2 S2301.8 16919.8 N1226.6 25021.1 S1941.0 25219.0 S2001.2 7 21204.0 30355.2 01.9 18421.2 27.1 26522.9 40.9 26721.2 01.1 8 22706.4 31854.3 02.1 19922.6 27.5 28024.8 40.7 28223.3 01.0 9 24208.9 33353.4 · · 02.2 21423.9 · · 27.9 29526.7 · · 40.6 29725.5 · · 01.0 10 25711.4 34852.4 02.4 22925.3 28.4 31028.5 40.4 31227.6 00.9 11 27213.8 351.5 02.5 24426.7 28.8 32530.4 40.3 32729.8 00.8
12 28716.3 1850.5 S2302.7 25928.1 N1229.3 34032.2 S1940.2 34232.0 S2000.8 13 30218.7 3349.6 02.8 27429.4 29.7 35534.1 40.0 35734.1 00.7 14 31721.2 4848.7 02.9 28930.8 30.2 1036.0 39.9 1236.3 00.7 15 33223.7 6347.7 · · 03.1 30432.2 · · 30.6 2537.8 · · 39.8 2738.5 · · 00.6 16 34726.1 7846.8 03.2 31933.6 31.1 4039.7 39.6 4240.6 00.5 17 228.6 9345.8 03.4 33434.9 31.5 5541.6 39.5 5742.8 00.5
18 1731.1 10844.9 S2303.5 34936.3 N1231.9 7043.4 S1939.4 7244.9 S2000.4 19 3233.5 12344.0 03.6 437.7 32.4 8545.3 39.2 8747.1 00.3 20 4736.0 13843.0 03.8 1939.1 32.8 10047.2 39.1 10249.3 00.3 21 6238.5 15342.1 · · 03.9 3440.4 · · 33.3 11549.0 · · 39.0 11751.4 · · 00.2 22 7740.9 16841.1 04.0 4941.8 33.7 13050.9 38.8 13253.6 00.1 23 9243.4 18340.2 04.1 6443.2 34.2 14552.8 38.7 14755.7 00.1
Mer.pass.:16:50 v-0.9 d-0.2 m-3.8 v1.4 d0.4 m-0.1 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Fri GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10745.8 19839.3 S2304.3 7944.5 N1234.6 16054.6 S1938.6 16257.9 S2000.0 1 12248.3 21338.3 04.4 9445.9 35.0 17556.5 38.4 17800.1 2000.0 2 13750.8 22837.4 04.5 10947.3 35.5 19058.4 38.3 19302.2 1959.9 3 15253.2 24336.4 · · 04.6 12448.7 · · 35.9 20600.2 · · 38.1 20804.4 · · 59.8 4 16755.7 25835.5 04.8 13950.0 36.4 22102.1 38.0 22306.6 59.8 5 18258.2 27334.6 04.9 15451.4 36.8 23604.0 37.9 23808.7 59.7
6 19800.6 28833.6 S2305.0 16952.8 N1237.3 25105.8 S1937.7 25310.9 S1959.6 7 21303.1 30332.7 05.1 18454.1 37.7 26607.7 37.6 26813.0 59.6 8 22805.6 31831.7 05.2 19955.5 38.2 28109.5 37.5 28315.2 59.5 9 24308.0 33330.8 · · 05.4 21456.9 · · 38.6 29611.4 · · 37.3 29817.4 · · 59.4 10 25810.5 34829.9 05.5 22958.2 39.0 31113.3 37.2 31319.5 59.4 11 27313.0 328.9 05.6 24459.6 39.5 32615.1 37.1 32821.7 59.3
12 28815.4 1828.0 S2305.7 26001.0 N1239.9 34117.0 S1936.9 34323.8 S1959.3 13 30317.9 3327.0 05.8 27502.3 40.4 35618.9 36.8 35826.0 59.2 14 31820.3 4826.1 05.9 29003.7 40.8 1120.7 36.6 1328.2 59.1 15 33322.8 6325.1 · · 06.0 30505.0 · · 41.3 2622.6 · · 36.5 2830.3 · · 59.1 16 34825.3 7824.2 06.1 32006.4 41.7 4124.5 36.4 4332.5 59.0 17 327.7 9323.3 06.2 33507.8 42.2 5626.3 36.2 5834.6 58.9
18 1830.2 10822.3 S2306.3 35009.1 N1242.6 7128.2 S1936.1 7336.8 S1958.9 19 3332.7 12321.4 06.4 510.5 43.0 8630.1 36.0 8839.0 58.8 20 4835.1 13820.4 06.5 2011.9 43.5 10131.9 35.8 10341.1 58.7 21 6337.6 15319.5 · · 06.6 3513.2 · · 43.9 11633.8 · · 35.7 11843.3 · · 58.7 22 7840.1 16818.5 06.7 5014.6 44.4 13135.6 35.6 13345.5 58.6 23 9342.5 18317.6 06.8 6515.9 44.8 14637.5 35.4 14847.6 58.6
Mer.pass.:16:46 v-0.9 d-0.1 m-3.8 v1.4 d0.4 m-0.1 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Sat GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10845.0 19816.7 S2306.9 8017.3 N1245.3 16139.4 S1935.3 16349.8 S1958.5 1 12347.5 21315.7 07.0 9518.6 45.7 17641.2 35.1 17851.9 58.4 2 13849.9 22814.8 07.1 11020.0 46.2 19143.1 35.0 19354.1 58.4 3 15352.4 24313.8 · · 07.2 12521.4 · · 46.6 20645.0 · · 34.9 20856.3 · · 58.3 4 16854.8 25812.9 07.3 14022.7 47.1 22146.8 34.7 22358.4 58.2 5 18357.3 27311.9 07.4 15524.1 47.5 23648.7 34.6 23900.6 58.2
6 19859.8 28811.0 S2307.5 17025.4 N1247.9 25150.6 S1934.5 25402.7 S1958.1 7 21402.2 30310.0 07.6 18526.8 48.4 26652.4 34.3 26904.9 58.0 8 22904.7 31809.1 07.7 20028.1 48.8 28154.3 34.2 28407.1 58.0 9 24407.2 33308.2 · · 07.8 21529.5 · · 49.3 29656.1 · · 34.0 29909.2 · · 57.9 10 25909.6 34807.2 07.8 23030.9 49.7 31158.0 33.9 31411.4 57.8 11 27412.1 306.3 07.9 24532.2 50.2 32659.9 33.8 32913.5 57.8
12 28914.6 1805.3 S2308.0 26033.6 N1250.6 34201.7 S1933.6 34415.7 S1957.7 13 30417.0 3304.4 08.1 27534.9 51.1 35703.6 33.5 35917.9 57.7 14 31919.5 4803.4 08.2 29036.3 51.5 1205.5 33.4 1420.0 57.6 15 33422.0 6302.5 · · 08.3 30537.6 · · 51.9 2707.3 · · 33.2 2922.2 · · 57.5 16 34924.4 7801.6 08.3 32039.0 52.4 4209.2 33.1 4424.3 57.5 17 426.9 9300.6 08.4 33540.3 52.8 5711.1 32.9 5926.5 57.4
18 1929.3 10759.7 S2308.5 35041.7 N1253.3 7212.9 S1932.8 7428.7 S1957.3 19 3431.8 12258.7 08.6 543.0 53.7 8714.8 32.7 8930.8 57.3 20 4934.3 13757.8 08.6 2044.4 54.2 10216.6 32.5 10433.0 57.2 21 6436.7 15256.8 · · 08.7 3545.7 · · 54.6 11718.5 · · 32.4 11935.1 · · 57.1 22 7939.2 16755.9 08.8 5047.1 55.1 13220.4 32.3 13437.3 57.1 23 9441.7 18254.9 08.8 6548.4 55.5 14722.2 32.1 14939.5 57.0
Mer.pass.:16:42 v-0.9 d-0.1 m-3.8 v1.4 d0.4 m-0.0 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Stars SHA Dec
Alpheratz 35738.2 2912.4 Ankaa 35310.5 -4211.9
Schedar 34934.7 5639.3 Diphda 34850.6 -1752.5
Achernar 33522.7 -5708.2 Hamal 32754.7 2333.7 Polaris 31515.7 8921.4 Acamar 31514.1 -4013.6 Menkar 31409.4 410.2 Mirfak 30832.5 4956.2
Aldebaran 29043.1 1633.0 Rigel 28106.7 -810.8
Capella 28026.2 4601.1 Bellatrix 27826.1 622.0 Elnath 27805.6 2837.4 Alnilam 27540.7 -111.4
Betelgeuse 27055.3 724.6 Canopus 26353.3 -5242.5
Sirius 25828.7 -1644.8 Adhara 25508.0 -2900.1 Procyon 24453.9 510.2 Pollux 24320.9 2758.4 Avior 23415.3 -5934.5 Suhail 22248.2 -4330.9
Miaplacidus 22137.9 -6948.0 Alphard 21750.7 -845.0 Regulus 20737.7 1151.8 Dubhe 19344.8 6138.1
Denebola 18228.2 1427.3 Gienah 17546.8 -1739.3 Acrux 17303.4 -6312.5
Gacrux 17155.0 -5713.5 Alioth 16615.9 5550.6 Spica 15825.7 -1116.1 Alkaid 15254.8 4912.3 Hadar 14840.7 -6028.1
Menkent 14801.5 -3628.1 Arcturus 14551.0 1904.4
Rigil Kent. 13944.9 -6054.9 Kochab 13720.5 7403.9
Zuben’ubi 13659.8 -1607.6 Alphecca 12606.8 2638.6 Antares 11220.1 -2628.5
Atria 10717.7 -6903.6 Sabik 10206.8 -1544.9
Shaula 9615.2 -3707.0 Rasalhague 9601.9 1232.7
Eltanin 9044.2 5129.1 Kaus Aust. 8337.2 -3422.4
Vega 8035.8 3848.2 Nunki 7552.2 -2616.2 Altair 6203.4 855.4
Peacock 5311.5 -5640.2 Deneb 4928.4 4521.4
Enif 3342.2 958.2 Al Na’ir 2737.4 -4651.8
Fomalhaut 1518.3 -2930.9 Scheat 1348.5 2811.8 Markab 1333.3 1519.0
Jan 07 Thu SHA Mer.pass Venus 9215.1 10:45 Mars 33224.8 18:42
Jupiter 5323.2 13:18 Saturn 5519.3 13:10
Jan 08 Fri SHA Mer.pass Venus 9053.4 10:46 Mars 33158.7 18:39
Jupiter 5308.8 13:15 Saturn 5512.1 13:06
Jan 09 Sat SHA Mer.pass Venus 8931.7 10:48 Mars 33132.3 18:37
Jupiter 5254.4 13:12 Saturn 5504.8 13:03
Horizontal parallax Venus: 0.1 Mars: 0.2
6
DUT1 = UT1-UTC = -0.1748 sec T = TT-UT1 = +69.3588 sec 2021 January 07 to Jan. 09 UT
h Sun Moon Thu GHA Dec GHA ν Dec d HP
0 17827.7 S2222.1 26216.7 11.1’ S0535.4 -14.5’ 59.2’ 1 19327.5 21.8 27646.8 11.0’ 0549.9 -14.5’ 59.2’ 2 20827.2 21.5 29116.8 11.0’ 0604.4 -14.5’ 59.3’ 3 22326.9 · · 21.2 30546.8 11.0’ 0618.9 -14.5’ 59.3’ 4 23826.7 20.9 32016.7 10.9’ 0633.3 -14.4’ 59.3’ 5 25326.4 20.5 33446.6 10.9’ 0647.8 -14.4’ 59.3’
6 26826.1 S2220.2 34916.4 10.8’ S0702.2 -14.4’ 59.3’ 7 28325.9 19.9 346.2 10.8’ 0716.5 -14.3’ 59.3’ 8 29825.6 19.6 1816.0 10.7’ 0730.8 -14.3’ 59.3’ 9 31325.3 · · 19.3 3245.7 10.7’ 0745.1 -14.3’ 59.3’ 10 32825.1 18.9 4715.3 10.6’ 0759.4 -14.2’ 59.3’ 11 34324.8 18.6 6144.9 10.6’ 0813.6 -14.2’ 59.4’
12 35824.5 S2218.3 7614.5 10.5’ S0827.8 -14.2’ 59.4’ 13 1324.3 17.9 9044.0 10.5’ 0841.9 -14.1’ 59.4’ 14 2824.0 17.6 10513.4 10.4’ 0856.0 -14.1’ 59.4’ 15 4323.7 · · 17.3 11942.8 10.3’ 0910.1 -14.0’ 59.4’ 16 5823.5 17.0 13412.1 10.3’ 0924.1 -14.0’ 59.4’ 17 7323.2 16.6 14841.3 10.2’ 0938.1 -13.9’ 59.4’
18 8822.9 S2216.3 16310.6 10.2’ S0952.0 -13.9’ 59.4’ 19 10322.7 16.0 17739.7 10.1’ 1005.9 -13.8’ 59.4’ 20 11822.4 15.6 19208.8 10.1’ 1019.7 -13.8’ 59.5’ 21 13322.1 · · 15.3 20637.8 10.0’ 1033.4 -13.7’ 59.5’ 22 14821.9 15.0 22106.8 9.9’ 1047.2 -13.7’ 59.5’ 23 16321.6 14.6 23535.7 9.9’ 1100.8 -13.6’ 59.5’
SD.=16.3 d=0.3 S.D.=16.2
Fri GHA Dec GHA ν Dec d HP
0 17821.3 S2214.3 25004.5 9.8’ S1114.4 -13.6’ 59.5’ 1 19321.1 13.9 26433.3 9.7’ 1128.0 -13.5’ 59.5’ 2 20820.8 13.6 27902.0 9.7’ 1141.4 -13.5’ 59.5’ 3 22320.5 · · 13.3 29330.6 9.6’ 1154.9 -13.4’ 59.5’ 4 23820.3 12.9 30759.2 9.5’ 1208.2 -13.3’ 59.5’ 5 25320.0 12.6 32227.7 9.5’ 1221.5 -13.3’ 59.5’
6 26819.7 S2212.3 33656.1 9.4’ S1234.7 -13.2’ 59.5’ 7 28319.5 11.9 35124.5 9.3’ 1247.9 -13.1’ 59.5’ 8 29819.2 11.6 552.8 9.3’ 1301.0 -13.1’ 59.6’ 9 31319.0 · · 11.2 2021.0 9.2’ 1314.0 -13.0’ 59.6’ 10 32818.7 10.9 3449.2 9.1’ 1327.0 -12.9’ 59.6’ 11 34318.4 10.5 4917.2 9.0’ 1339.8 -12.8’ 59.6’
12 35818.2 S2210.2 6345.2 9.0’ S1352.6 -12.8’ 59.6’ 13 1317.9 09.8 7813.2 8.9’ 1405.3 -12.7’ 59.6’ 14 2817.6 09.5 9241.0 8.8’ 1418.0 -12.6’ 59.6’ 15 4317.4 · · 09.1 10708.8 8.7’ 1430.6 -12.5’ 59.6’ 16 5817.1 08.8 12136.5 8.7’ 1443.0 -12.4’ 59.6’ 17 7316.9 08.5 13604.2 8.6’ 1455.4 -12.4’ 59.6’
18 8816.6 S2208.1 15031.7 8.5’ S1507.7 -12.3’ 59.6’ 19 10316.3 07.8 16459.2 8.4’ 1520.0 -12.2’ 59.6’ 20 11816.1 07.4 17926.6 8.4’ 1532.1 -12.1’ 59.6’ 21 13315.8 · · 07.0 19354.0 8.3’ 1544.2 -12.0’ 59.6’ 22 14815.6 06.7 20821.2 8.2’ 1556.1 -11.9’ 59.6’ 23 16315.3 06.3 22248.4 8.1’ 1608.0 -11.8’ 59.6’
SD.=16.3 d=0.3 S.D.=16.2
Sat GHA Dec GHA ν Dec d HP
0 17815.0 S2206.0 23715.5 8.1’ S1619.7 -11.7’ 59.6’ 1 19314.8 05.6 25142.5 8.0’ 1631.4 -11.6’ 59.7’ 2 20814.5 05.3 26609.5 7.9’ 1643.0 -11.5’ 59.7’ 3 22314.3 · · 04.9 28036.3 7.8’ 1654.5 -11.4’ 59.7’ 4 23814.0 04.6 29503.1 7.7’ 1705.8 -11.3’ 59.7’ 5 25313.7 04.2 30929.8 7.7’ 1717.1 -11.2’ 59.7’
6 26813.5 S2203.8 32356.4 7.6’ S1728.3 -11.1’ 59.7’ 7 28313.2 03.5 33823.0 7.5’ 1739.4 -11.0’ 59.7’ 8 29813.0 03.1 35249.5 7.4’ 1750.3 -10.9’ 59.7’ 9 31312.7 · · 02.8 715.9 7.4’ 1801.2 -10.8’ 59.7’ 10 32812.5 02.4 2142.2 7.3’ 1811.9 -10.7’ 59.7’ 11 34312.2 02.0 3608.4 7.2’ 1822.5 -10.6’ 59.7’
12 35811.9 S2201.7 5034.6 7.1’ S1833.0 -10.5’ 59.7’ 13 1311.7 01.3 6500.6 7.0’ 1843.4 -10.3’ 59.7’ 14 2811.4 00.9 7926.6 7.0’ 1853.7 -10.2’ 59.7’ 15 4311.2 · · 00.6 9352.6 6.9’ 1903.9 -10.1’ 59.7’ 16 5810.9 2200.2 10818.4 6.8’ 1913.9 -10.0’ 59.7’ 17 7310.7 2159.8 12244.2 6.7’ 1923.8 -9.9’ 59.7’
18 8810.4 S2159.5 13709.9 6.7’ S1933.6 -9.7’ 59.7’ 19 10310.1 59.1 15135.5 6.6’ 1943.3 -9.6’ 59.7’ 20 11809.9 58.7 16601.0 6.5’ 1952.9 -9.5’ 59.7’ 21 13309.6 · · 58.4 18026.5 6.4’ 2002.3 -9.4’ 59.7’ 22 14809.4 58.0 19451.9 6.4’ 2011.6 -9.2’ 59.7’ 23 16309.1 57.6 20917.2 6.3’ 2020.7 -9.1’ 59.7’
SD.=16.3 d=0.4 S.D.=16.3
Lat. Twilight
N 72 08:14 10:18 13:56 16:00
N 70 07:57 09:36 14:39 16:17 68 07:44 09:07 11:08 13:06 15:07 16:31 66 07:32 08:45 10:12 14:02 15:29 16:42 64 07:22 08:28 09:39 14:35 15:46 16:52 62 07:14 08:14 09:16 14:59 16:00 17:00 60 07:06 08:02 08:57 15:17 16:12 17:08
N 58 07:00 07:51 08:41 15:33 16:23 17:14 56 06:54 07:42 08:28 15:46 16:32 17:20 54 06:48 07:33 08:16 15:58 16:40 17:26 52 06:43 07:26 08:06 16:08 16:48 17:31 50 06:38 07:19 07:57 16:17 16:55 17:36 45 06:27 07:04 07:37 16:36 17:10 17:46
N 40 06:18 06:52 07:22 16:52 17:22 17:56 35 06:09 06:41 07:09 17:05 17:33 18:04 30 06:01 06:31 06:57 17:17 17:43 18:12 20 05:46 06:13 06:37 17:37 18:00 18:28
N 10 05:31 05:57 06:20 17:54 18:17 18:43 0 05:15 05:41 06:03 18:10 18:33 18:59
S 10 04:57 05:24 05:47 18:27 18:50 19:17 20 04:35 05:04 05:29 18:45 19:09 19:38 30 04:08 04:41 05:08 19:05 19:33 20:05 35 03:50 04:26 04:56 19:18 19:47 20:23 40 03:29 04:09 04:42 19:32 20:04 20:44 45 03:00 03:48 04:25 19:48 20:25 21:12
S 50 02:20 03:21 04:04 20:09 20:52 21:53 52 01:56 03:07 03:54 20:19 21:06 22:16 54 01:23 02:51 03:42 20:30 21:22 22:48 56 –:– 02:31 03:29 20:43 21:41 –:– 58 –:– 02:06 03:14 20:58 22:06 –:–
S 60 –:– 01:31 02:56 21:16 22:40 –:–
Lat. Moonrise Moonset
Thu Fri Sat Thu Fri Sat
N 72 01:53 04:18 11:05 10:27
N 70 01:43 03:55 06:31 11:17 10:53 10:10 68 01:36 03:37 05:51 11:27 11:13 10:51 66 01:30 03:23 05:23 11:35 11:28 11:20 64 01:24 03:11 05:03 11:43 11:42 11:42 62 01:20 03:01 04:46 11:49 11:53 11:59 60 01:16 02:53 04:32 11:54 12:02 12:14
N 58 01:12 02:45 04:20 11:59 12:11 12:27 56 01:09 02:39 04:10 12:03 12:18 12:38 54 01:07 02:33 04:01 12:07 12:25 12:47 52 01:04 02:28 03:53 12:10 12:31 12:56 50 01:02 02:23 03:46 12:13 12:36 13:04 45 00:57 02:13 03:31 12:20 12:48 13:20
N 40 00:53 02:05 03:18 12:26 12:58 13:34 35 00:50 01:58 03:08 12:31 13:06 13:46 30 00:47 01:52 02:59 12:35 13:13 13:56 20 00:41 01:41 02:43 12:43 13:26 14:13
N 10 00:37 01:32 02:29 12:50 13:38 14:29 0 00:33 01:23 02:17 12:56 13:48 14:43
S 10 00:28 01:15 02:04 13:03 13:59 14:58 20 00:24 01:06 01:51 13:10 14:10 15:13 30 00:19 00:55 01:35 13:17 14:23 15:31 35 00:16 00:50 01:27 13:22 14:31 15:42 40 00:13 00:43 01:17 13:27 14:40 15:54 45 00:09 00:35 01:05 13:33 14:50 16:08
S 50 00:05 00:26 00:51 13:40 15:02 16:25 52 00:03 00:22 00:45 13:44 15:08 16:34 54 00:01 00:18 00:38 13:47 15:15 16:43 56 ·· ·· 00:12 00:30 13:51 15:22 16:53 58 ·· ·· 00:07 00:21 13:56 15:30 17:05
S 60 ·· ·· 00:00 00:11 14:01 15:39 17:19
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age
00h 12h Pass Upper Lower 24-26 mm:ss mm:ss hh:mm hh:mm hh:mm 38-17%
07 06:09 06:22 12:06 06:44 19:10 08 06:35 06:47 12:07 07:36 20:02 09 07:00 07:12 12:07 08:30 20:58
7
January 10, 11, 12 UT (Sun., Mon., Tue.)
Aries Venus Mars Jupiter Saturn Sun GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10944.1 19754.0 S2308.9 8049.8 N1256.0 16224.1 S1932.0 16441.6 S1956.9 1 12446.6 21253.0 09.0 9551.1 56.4 17726.0 31.8 17943.8 56.9 2 13949.1 22752.1 09.0 11052.5 56.9 19227.8 31.7 19445.9 56.8 3 15451.5 24251.2 · · 09.1 12553.8 · · 57.3 20729.7 · · 31.6 20948.1 · · 56.8 4 16954.0 25750.2 09.2 14055.1 57.7 22231.5 31.4 22450.3 56.7 5 18456.4 27249.3 09.2 15556.5 58.2 23733.4 31.3 23952.4 56.6
6 19958.9 28748.3 S2309.3 17057.8 N1258.6 25235.3 S1931.2 25454.6 S1956.6 7 21501.4 30247.4 09.4 18559.2 59.1 26737.1 31.0 26956.7 56.5 8 23003.8 31746.4 09.4 20100.5 1259.5 28239.0 30.9 28458.9 56.4 9 24506.3 33245.5 · · 09.5 21601.9 1300.0 29740.9 · · 30.7 30001.1 · · 56.4 10 26008.8 34744.5 09.5 23103.2 00.4 31242.7 30.6 31503.2 56.3 11 27511.2 243.6 09.6 24604.6 00.9 32744.6 30.5 33005.4 56.2
12 29013.7 1742.6 S2309.6 26105.9 N1301.3 34246.4 S1930.3 34507.5 S1956.2 13 30516.2 3241.7 09.7 27607.2 01.8 35748.3 30.2 009.7 56.1 14 32018.6 4740.8 09.7 29108.6 02.2 1250.2 30.0 1511.9 56.0 15 33521.1 6239.8 · · 09.8 30609.9 · · 02.6 2752.0 · · 29.9 3014.0 · · 56.0 16 35023.6 7738.9 09.8 32111.3 03.1 4253.9 29.8 4516.2 55.9 17 526.0 9237.9 09.9 33612.6 03.5 5755.8 29.6 6018.3 55.9
18 2028.5 10737.0 S2309.9 35113.9 N1304.0 7257.6 S1929.5 7520.5 S1955.8 19 3530.9 12236.0 10.0 615.3 04.4 8759.5 29.4 9022.7 55.7 20 5033.4 13735.1 10.0 2116.6 04.9 10301.3 29.2 10524.8 55.7 21 6535.9 15234.1 · · 10.0 3618.0 · · 05.3 11803.2 · · 29.1 12027.0 · · 55.6 22 8038.3 16733.2 10.1 5119.3 05.8 13305.1 28.9 13529.1 55.5 23 9540.8 18232.2 10.1 6620.6 06.2 14806.9 28.8 15031.3 55.5
Mer.pass.:16:38 v-0.9 d-0.1 m-3.8 v1.3 d0.4 m-0.0 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Mon GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 11043.3 19731.3 S2310.2 8122.0 N1306.7 16308.8 S1928.7 16533.5 S1955.4 1 12545.7 21230.3 10.2 9623.3 07.1 17810.7 28.5 18035.6 55.3 2 14048.2 22729.4 10.2 11124.6 07.6 19312.5 28.4 19537.8 55.3 3 15550.7 24228.4 · · 10.3 12626.0 · · 08.0 20814.4 · · 28.2 21039.9 · · 55.2 4 17053.1 25727.5 10.3 14127.3 08.5 22316.2 28.1 22542.1 55.1 5 18555.6 27226.6 10.3 15628.6 08.9 23818.1 28.0 24044.3 55.1
6 20058.1 28725.6 S2310.4 17130.0 N1309.3 25320.0 S1927.8 25546.4 S1955.0 7 21600.5 30224.7 10.4 18631.3 09.8 26821.8 27.7 27048.6 54.9 8 23103.0 31723.7 10.4 20132.6 10.2 28323.7 27.5 28550.7 54.9 9 24605.4 33222.8 · · 10.5 21634.0 · · 10.7 29825.6 · · 27.4 30052.9 · · 54.8 10 26107.9 34721.8 10.5 23135.3 11.1 31327.4 27.3 31555.1 54.8 11 27610.4 220.9 10.5 24636.6 11.6 32829.3 27.1 33057.2 54.7
12 29112.8 1719.9 S2310.5 26138.0 N1312.0 34331.1 S1927.0 34559.4 S1954.6 13 30615.3 3219.0 10.6 27639.3 12.5 35833.0 26.8 101.5 54.6 14 32117.8 4718.0 10.6 29140.6 12.9 1334.9 26.7 1603.7 54.5 15 33620.2 6217.1 · · 10.6 30642.0 · · 13.4 2836.7 · · 26.6 3105.8 · · 54.4 16 35122.7 7716.1 10.6 32143.3 13.8 4338.6 26.4 4608.0 54.4 17 625.2 9215.2 10.6 33644.6 14.3 5840.5 26.3 6110.2 54.3
18 2127.6 10714.2 S2310.6 35145.9 N1314.7 7342.3 S1926.2 7612.3 S1954.2 19 3630.1 12213.3 10.7 647.3 15.1 8844.2 26.0 9114.5 54.2 20 5132.6 13712.3 10.7 2148.6 15.6 10346.0 25.9 10616.6 54.1 21 6635.0 15211.4 · · 10.7 3649.9 · · 16.0 11847.9 · · 25.7 12118.8 · · 54.0 22 8137.5 16710.5 10.7 5151.2 16.5 13349.8 25.6 13621.0 54.0 23 9639.9 18209.5 10.7 6652.6 16.9 14851.6 25.5 15123.1 53.9
Mer.pass.:16:34 v-0.9 d-0.0 m-3.8 v1.3 d0.4 m0.0 v1.9 d0.1 m-1.8 v2.2 d0.1 m0.6
Tue GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 11142.4 19708.6 S2310.7 8153.9 N1317.4 16353.5 S1925.3 16625.3 S1953.8 1 12644.9 21207.6 10.7 9655.2 17.8 17855.3 25.2 18127.4 53.8 2 14147.3 22706.7 10.7 11156.5 18.3 19357.2 25.0 19629.6 53.7 3 15649.8 24205.7 · · 10.7 12657.9 · · 18.7 20859.1 · · 24.9 21131.8 · · 53.6 4 17152.3 25704.8 10.7 14159.2 19.2 22400.9 24.8 22633.9 53.6 5 18654.7 27203.8 10.7 15700.5 19.6 23902.8 24.6 24136.1 53.5
6 20157.2 28702.9 S2310.7 17201.8 N1320.1 25404.7 S1924.5 25638.2 S1953.5 7 21659.7 30201.9 10.7 18703.2 20.5 26906.5 24.3 27140.4 53.4 8 23202.1 31701.0 10.7 20204.5 21.0 28408.4 24.2 28642.5 53.3 9 24704.6 33200.0 · · 10.7 21705.8 · · 21.4 29910.2 · · 24.1 30144.7 · · 53.3 10 26207.1 34659.1 10.7 23207.1 21.9 31412.1 23.9 31646.9 53.2 11 27709.5 158.1 10.7 24708.4 22.3 32914.0 23.8 33149.0 53.1
12 29212.0 1657.2 S2310.7 26209.8 N1322.7 34415.8 S1923.6 34651.2 S1953.1 13 30714.4 3156.2 10.7 27711.1 23.2 35917.7 23.5 153.3 53.0 14 32216.9 4655.3 10.7 29212.4 23.6 1419.5 23.4 1655.5 52.9 15 33719.4 6154.4 · · 10.7 30713.7 · · 24.1 2921.4 · · 23.2 3157.7 · · 52.9 16 35221.8 7653.4 10.7 32215.0 24.5 4423.3 23.1 4659.8 52.8 17 724.3 9152.5 10.7 33716.4 25.0 5925.1 22.9 6202.0 52.7
18 2226.8 10651.5 S2310.7 35217.7 N1325.4 7427.0 S1922.8 7704.1 S1952.7 19 3729.2 12150.6 10.6 719.0 25.9 8928.8 22.6 9206.3 52.6 20 5231.7 13649.6 10.6 2220.3 26.3 10430.7 22.5 10708.5 52.5 21 6734.2 15148.7 · · 10.6 3721.6 · · 26.8 11932.6 · · 22.4 12210.6 · · 52.5 22 8236.6 16647.7 10.6 5222