Equation of Time curve
The Daily Pages
Tables of Increments and Corrections for Sun, planets, Aries, Moon (“the yellow pages”)
Conversion of Arc to Time
Altitude Corrections for Sun, Planets, Stars (includes Refraction and Dip)
Altitude Corrections for the Moon
Navigational Star Chart
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
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.
www.TheNauticalAlmanac.com
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.
www.TheNauticalAlmanac.com
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
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Celestial Navigation useful Formulas
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
fair winds...clear skies and following seas TheNauticalAlmanac.com
Formula Sheet added to NA.odt
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
January 01, 02, 03 UT (Fri., Sat., Sun.)
Aries Venus Mars Jupiter Saturn Fri GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10005.4 21942.3 S1836.9 25300.9 S0933.5 28553.1 N0351.3 21016.0 S2029.6 1 11507.9 23441.6 37.6 26802.1 34.0 30055.5 51.3 22518.2 29.6 2 13010.4 24941.0 38.3 28303.2 34.5 31557.9 51.3 24020.4 29.7 3 14512.8 26440.3 · · 38.9 29804.4 · · 35.0 33100.3 · · 51.3 25522.6 · · 29.7 4 16015.3 27939.6 39.6 31305.5 35.5 34602.7 51.3 27024.7 29.7 5 17517.8 29439.0 40.3 32806.7 36.0 105.1 51.3 28526.9 29.8
6 19020.2 30938.3 S1840.9 34307.8 S0936.5 1607.5 N0351.3 30029.1 S2029.8 7 20522.7 32437.6 41.6 35809.0 37.0 3110.0 51.3 31531.3 29.8 8 22025.2 33937.0 42.2 1310.1 37.5 4612.4 51.2 33033.4 29.9 9 23527.6 35436.3 · · 42.9 2811.3 · · 37.9 6114.8 · · 51.2 34535.6 · · 29.9 10 25030.1 935.7 43.6 4312.4 38.4 7617.2 51.2 037.8 30.0 11 26532.6 2435.0 44.2 5813.6 38.9 9119.6 51.2 1540.0 30.0
12 28035.0 3934.3 S1844.9 7314.7 S0939.4 10622.0 N0351.2 3042.1 S2030.0 13 29537.5 5433.7 45.5 8815.8 39.9 12124.4 51.2 4544.3 30.1 14 31039.9 6933.0 46.2 10317.0 40.4 13626.8 51.2 6046.5 30.1 15 32542.4 8432.3 · · 46.8 11818.1 · · 40.9 15129.2 · · 51.2 7548.7 · · 30.1 16 34044.9 9931.7 47.5 13319.3 41.4 16631.6 51.2 9050.9 30.2 17 35547.3 11431.0 48.2 14820.4 41.9 18134.1 51.2 10553.0 30.2
18 1049.8 12930.3 S1848.8 16321.6 S0942.4 19636.5 N0351.1 12055.2 S2030.2 19 2552.3 14429.7 49.5 17822.7 42.8 21138.9 51.1 13557.4 30.3 20 4054.7 15929.0 50.1 19323.9 43.3 22641.3 51.1 15059.6 30.3 21 5557.2 17428.3 · · 50.8 20825.0 · · 43.8 24143.7 · · 51.1 16601.7 · · 30.4 22 7059.7 18927.7 51.4 22326.2 44.3 25646.1 51.1 18103.9 30.4 23 8602.1 20427.0 52.1 23827.3 44.8 27148.5 51.1 19606.1 30.4
Mer.pass.:17:17 v-0.7 d-0.7 m-3.9 v1.1 d-0.5 m1.3 v2.4 d-0.0 m-2.0 v2.2 d-0.0 m0.5
Sat GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10104.6 21926.3 S1852.7 25328.5 S0945.3 28650.9 N0351.1 21108.3 S2030.5 1 11607.0 23425.7 53.4 26829.6 45.8 30153.4 51.1 22610.5 30.5 2 13109.5 24925.0 54.0 28330.8 46.3 31655.8 51.1 24112.6 30.5 3 14612.0 26424.3 · · 54.6 29831.9 · · 46.7 33158.2 · · 51.1 25614.8 · · 30.6 4 16114.4 27923.6 55.3 31333.1 47.2 34700.6 51.1 27117.0 30.6 5 17616.9 29423.0 55.9 32834.2 47.7 203.0 51.0 28619.2 30.6
6 19119.4 30922.3 S1856.6 34335.4 S0948.2 1705.4 N0351.0 30121.3 S2030.7 7 20621.8 32421.6 57.2 35836.5 48.7 3207.8 51.0 31623.5 30.7 8 22124.3 33920.9 57.9 1337.7 49.2 4710.3 51.0 33125.7 30.7 9 23626.8 35420.3 · · 58.5 2838.8 · · 49.7 6212.7 · · 51.0 34627.9 · · 30.8 10 25129.2 919.6 59.1 4340.0 50.2 7715.1 51.0 130.1 30.8 11 26631.7 2418.9 1859.8 5841.1 50.6 9217.5 51.0 1632.2 30.9
12 28134.2 3918.2 S1900.4 7342.3 S0951.1 10719.9 N0351.0 3134.4 S2030.9 13 29636.6 5417.6 01.1 8843.4 51.6 12222.3 51.0 4636.6 30.9 14 31139.1 6916.9 01.7 10344.6 52.1 13724.8 51.0 6138.8 31.0 15 32641.5 8416.2 · · 02.3 11845.7 · · 52.6 15227.2 · · 51.0 7641.0 · · 31.0 16 34144.0 9915.5 03.0 13346.9 53.1 16729.6 51.0 9143.1 31.0 17 35646.5 11414.9 03.6 14848.0 53.6 18232.0 51.0 10645.3 31.1
18 1148.9 12914.2 S1904.2 16349.2 S0954.0 19734.4 N0350.9 12147.5 S2031.1 19 2651.4 14413.5 04.9 17850.3 54.5 21236.9 50.9 13649.7 31.1 20 4153.9 15912.8 05.5 19351.4 55.0 22739.3 50.9 15151.8 31.2 21 5656.3 17412.1 · · 06.1 20852.6 · · 55.5 24241.7 · · 50.9 16654.0 · · 31.2 22 7158.8 18911.4 06.8 22353.7 56.0 25744.1 50.9 18156.2 31.2 23 8701.3 20410.8 07.4 23854.9 56.5 27246.5 50.9 19658.4 31.3
Mer.pass.:17:13 v-0.7 d-0.6 m-3.9 v1.1 d-0.5 m1.2 v2.4 d-0.0 m-2.0 v2.2 d-0.0 m0.5
Sun GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10203.7 21910.1 S1908.0 25356.0 S0956.9 28749.0 N0350.9 21200.6 S2031.3 1 11706.2 23409.4 08.6 26857.2 57.4 30251.4 50.9 22702.7 31.4 2 13208.7 24908.7 09.3 28358.3 57.9 31753.8 50.9 24204.9 31.4 3 14711.1 26408.0 · · 09.9 29859.5 · · 58.4 33256.2 · · 50.9 25707.1 · · 31.4 4 16213.6 27907.3 10.5 31400.6 58.9 34758.6 50.9 27209.3 31.5 5 17716.0 29406.7 11.1 32901.8 59.4 301.1 50.9 28711.5 31.5
6 19218.5 30906.0 S1911.8 34402.9 S0959.9 1803.5 N0350.9 30213.6 S2031.5 7 20721.0 32405.3 12.4 35904.1 1000.3 3305.9 50.9 31715.8 31.6 8 22223.4 33904.6 13.0 1405.3 00.8 4808.3 50.9 33218.0 31.6 9 23725.9 35403.9 · · 13.6 2906.4 · · 01.3 6310.8 · · 50.9 34720.2 · · 31.6 10 25228.4 903.2 14.2 4407.6 01.8 7813.2 50.9 222.4 31.7 11 26730.8 2402.5 14.9 5908.7 02.3 9315.6 50.9 1724.5 31.7
12 28233.3 3901.9 S1915.5 7409.9 S1002.7 10818.0 N0350.9 3226.7 S2031.7 13 29735.8 5401.2 16.1 8911.0 03.2 12320.5 50.8 4728.9 31.8 14 31238.2 6900.5 16.7 10412.2 03.7 13822.9 50.8 6231.1 31.8 15 32740.7 8359.8 · · 17.3 11913.3 · · 04.2 15325.3 · · 50.8 7733.3 · · 31.8 16 34243.1 9859.1 17.9 13414.5 04.7 16827.7 50.8 9235.4 31.9 17 35745.6 11358.4 18.6 14915.6 05.2 18330.2 50.8 10737.6 31.9
18 1248.1 12857.7 S1919.2 16416.8 S1005.6 19832.6 N0350.8 12239.8 S2031.9 19 2750.5 14357.0 19.8 17917.9 06.1 21335.0 50.8 13742.0 32.0 20 4253.0 15856.3 20.4 19419.1 06.6 22837.4 50.8 15244.2 32.0 21 5755.5 17355.6 · · 21.0 20920.2 · · 07.1 24339.9 · · 50.8 16746.4 · · 32.1 22 7257.9 18854.9 21.6 22421.4 07.6 25842.3 50.8 18248.5 32.1 23 8800.4 20354.2 22.2 23922.5 08.0 27344.7 50.8 19750.7 32.1
Mer.pass.:17:09 v-0.7 d-0.6 m-3.9 v1.1 d-0.5 m1.2 v2.4 d-0.0 m-2.0 v2.2 d-0.0 m0.5
Stars SHA Dec
Alpheratz 35741.7 2910.9 Ankaa 35314.1 -4213.4
Schedar 34938.4 5637.7 Diphda 34854.2 -1754.1
Achernar 33525.5 -5709.7 Hamal 32758.6 2332.3 Polaris 31640.7 8920.1 Acamar 31516.8 -4014.8 Menkar 31413.0 409.0 Mirfak 30837.4 4955.1
Aldebaran 29047.1 1632.3 Rigel 28110.1 -811.3
Capella 28031.4 4600.7 Bellatrix 27829.8 621.6 Elnath 27810.1 2837.0 Alnilam 27544.3 -111.8
Betelgeuse 27059.1 724.3 Canopus 26354.8 -5242.5
Sirius 25831.8 -1644.5 Adhara 25510.8 -2859.9 Procyon 24457.6 510.8 Pollux 24325.3 2759.0 Avior 23416.6 -5933.7 Suhail 22250.7 -4329.8
Miaplacidus 22138.3 -6946.9 Alphard 21754.1 -843.8 Regulus 20741.5 1153.2 Dubhe 19349.5 6139.5
Denebola 18231.9 1428.8 Gienah 17550.5 -1737.7 Acrux 17307.1 -6310.9
Gacrux 17158.8 -5711.9 Alioth 16619.3 5552.1 Spica 15829.5 -1114.6 Alkaid 15257.8 4913.8 Hadar 14845.5 -6026.6
Menkent 14805.6 -3626.6 Arcturus 14554.3 1905.9
Rigil Kent. 13949.5 -6053.6 Kochab 13721.0 7405.2
Zuben’ubi 13703.7 -1606.3 Alphecca 12609.8 2639.7 Antares 11224.4 -2627.8
Atria 10725.2 -6903.0 Sabik 10210.9 -1544.4
Shaula 9620.0 -3706.6 Rasalhague 9605.2 1233.1
Eltanin 9045.9 5129.3 Kaus Aust. 8341.9 -3422.4
Vega 8038.2 3848.1 Nunki 7556.6 -2616.4 Altair 6206.9 854.8
Peacock 5317.2 -5641.0 Deneb 4930.7 4520.5
Enif 3345.7 957.0 Al Na’ir 2742.0 -4653.1
Fomalhaut 1522.3 -2932.4 Scheat 1351.8 2810.3 Markab 1336.7 1517.6
Jan 01 Fri SHA Mer.pass Venus 11936.8 09:22 Mars 15255.5 07:07
Jupiter 18547.7 04:56 Saturn 11010.6 09:57
Jan 02 Sat SHA Mer.pass Venus 11821.7 09:23 Mars 15223.9 07:06
Jupiter 18546.4 04:52 Saturn 11003.7 09:54
Jan 03 Sun SHA Mer.pass Venus 11706.4 09:24 Mars 15152.3 07:04
Jupiter 18545.2 04:48 Saturn 10956.8 09:51
Horizontal parallax Venus: 0.1 Mars: 0.1
2
DUT1 = UT1-UTC = +0.0816 sec T = TT-UT1 = +68.1024 sec 2016 January 01 to Jan. 03 UT
h Sun Moon Fri GHA Dec GHA ν Dec d HP
0 17913.9 S2303.5 28303.3 15.2’ N0127.6 -9.4’ 54.4’ 1 19413.6 03.4 29737.4 15.2’ 0118.2 -9.4’ 54.4’ 2 20913.3 03.2 31211.6 15.2’ 0108.8 -9.4’ 54.4’ 3 22413.0 · · 03.0 32645.8 15.2’ 0059.5 -9.4’ 54.4’ 4 23912.7 02.8 34120.0 15.2’ 0050.1 -9.4’ 54.4’ 5 25412.4 02.6 35554.3 15.2’ 0040.7 -9.4’ 54.4’
6 26912.1 S2302.4 1028.5 15.2’ N0031.3 -9.4’ 54.4’ 7 28411.8 02.2 2502.8 15.3’ 0021.9 -9.4’ 54.4’ 8 29911.5 02.0 3937.0 15.3’ 0012.6 -9.4’ 54.4’ 9 31411.2 · · 01.8 5411.3 15.3’ N0003.2 -9.4’ 54.3’ 10 32910.9 01.6 6845.6 15.3’ S0006.2 -9.4’ 54.3’ 11 34410.6 01.4 8319.9 15.3’ 0015.5 -9.4’ 54.3’
12 35910.3 S2301.2 9754.2 15.3’ S0024.9 -9.4’ 54.3’ 13 1410.0 01.0 11228.5 15.3’ 0034.3 -9.4’ 54.3’ 14 2909.7 00.8 12702.8 15.3’ 0043.6 -9.3’ 54.3’ 15 4409.5 · · 00.6 14137.1 15.3’ 0052.9 -9.3’ 54.3’ 16 5909.2 00.4 15611.4 15.3’ 0102.3 -9.3’ 54.3’ 17 7408.9 00.2 17045.8 15.3’ 0111.6 -9.3’ 54.3’
18 8908.6 S2300.0 18520.1 15.3’ S0120.9 -9.3’ 54.3’ 19 10408.3 2259.8 19954.4 15.3’ 0130.3 -9.3’ 54.3’ 20 11908.0 59.6 21428.8 15.3’ 0139.6 -9.3’ 54.3’ 21 13407.7 · · 59.4 22903.1 15.3’ 0148.9 -9.3’ 54.3’ 22 14907.4 59.2 24337.5 15.3’ 0158.2 -9.3’ 54.3’ 23 16407.1 58.9 25811.8 15.3’ 0207.5 -9.3’ 54.3’
SD.=16.3 d=0.2 S.D.=14.8
Sat GHA Dec GHA ν Dec d HP
0 17906.8 S2258.7 27246.1 15.3’ S0216.7 -9.3’ 54.3’ 1 19406.5 58.5 28720.5 15.3’ 0226.0 -9.3’ 54.3’ 2 20906.2 58.3 30154.8 15.3’ 0235.2 -9.2’ 54.3’ 3 22405.9 · · 58.1 31629.1 15.3’ 0244.5 -9.2’ 54.2’ 4 23905.6 57.9 33103.4 15.3’ 0253.7 -9.2’ 54.2’ 5 25405.3 57.7 34537.8 15.3’ 0302.9 -9.2’ 54.2’
6 26905.0 S2257.5 012.1 15.3’ S0312.1 -9.2’ 54.2’ 7 28404.7 57.2 1446.4 15.3’ 0321.3 -9.2’ 54.2’ 8 29904.4 57.0 2920.7 15.3’ 0330.5 -9.2’ 54.2’ 9 31404.2 · · 56.8 4355.0 15.3’ 0339.7 -9.2’ 54.2’ 10 32903.9 56.6 5829.3 15.3’ 0348.8 -9.1’ 54.2’ 11 34403.6 56.4 7303.5 15.3’ 0357.9 -9.1’ 54.2’
12 35903.3 S2256.2 8737.8 15.3’ S0407.1 -9.1’ 54.2’ 13 1403.0 55.9 10212.0 15.2’ 0416.2 -9.1’ 54.2’ 14 2902.7 55.7 11646.3 15.2’ 0425.2 -9.1’ 54.2’ 15 4402.4 · · 55.5 13120.5 15.2’ 0434.3 -9.1’ 54.2’ 16 5902.1 55.3 14554.7 15.2’ 0443.3 -9.0’ 54.2’ 17 7401.8 55.0 16028.9 15.2’ 0452.4 -9.0’ 54.2’
18 8901.5 S2254.8 17503.1 15.2’ S0501.4 -9.0’ 54.2’ 19 10401.2 54.6 18937.3 15.2’ 0510.4 -9.0’ 54.2’ 20 11900.9 54.4 20411.4 15.1’ 0519.3 -9.0’ 54.2’ 21 13400.7 · · 54.1 21845.6 15.1’ 0528.3 -8.9’ 54.2’ 22 14900.4 53.9 23319.7 15.1’ 0537.2 -8.9’ 54.3’ 23 16400.1 53.7 24753.8 15.1’ 0546.1 -8.9’ 54.3’
SD.=16.3 d=0.2 S.D.=14.8
Sun GHA Dec GHA ν Dec d HP
0 17859.8 S2253.5 26227.9 15.1’ S0555.0 -8.9’ 54.3’ 1 19359.5 53.2 27701.9 15.1’ 0603.9 -8.9’ 54.3’ 2 20859.2 53.0 29136.0 15.0’ 0612.7 -8.8’ 54.3’ 3 22358.9 · · 52.8 30610.0 15.0’ 0621.5 -8.8’ 54.3’ 4 23858.6 52.5 32044.0 15.0’ 0630.3 -8.8’ 54.3’ 5 25358.3 52.3 33518.0 15.0’ 0639.1 -8.8’ 54.3’
6 26858.0 S2252.1 34951.9 14.9’ S0647.8 -8.7’ 54.3’ 7 28357.7 51.8 425.9 14.9’ 0656.5 -8.7’ 54.3’ 8 29857.5 51.6 1859.8 14.9’ 0705.2 -8.7’ 54.3’ 9 31357.2 · · 51.4 3333.6 14.9’ 0713.9 -8.6’ 54.3’ 10 32856.9 51.1 4807.5 14.8’ 0722.5 -8.6’ 54.3’ 11 34356.6 50.9 6241.3 14.8’ 0731.1 -8.6’ 54.3’
12 35856.3 S2250.7 7715.1 14.8’ S0739.7 -8.6’ 54.3’ 13 1356.0 50.4 9148.9 14.8’ 0748.3 -8.5’ 54.3’ 14 2855.7 50.2 10622.6 14.7’ 0756.8 -8.5’ 54.3’ 15 4355.4 · · 49.9 12056.3 14.7’ 0805.3 -8.5’ 54.3’ 16 5855.1 49.7 13530.0 14.7’ 0813.7 -8.4’ 54.4’ 17 7354.9 49.4 15003.7 14.6’ 0822.2 -8.4’ 54.4’
18 8854.6 S2249.2 16437.3 14.6’ S0830.6 -8.4’ 54.4’ 19 10354.3 49.0 17910.9 14.6’ 0838.9 -8.4’ 54.4’ 20 11854.0 48.7 19344.4 14.5’ 0847.3 -8.3’ 54.4’ 21 13353.7 · · 48.5 20817.9 14.5’ 0855.6 -8.3’ 54.4’ 22 14853.4 48.2 22251.4 14.5’ 0903.8 -8.2’ 54.4’ 23 16353.1 48.0 23724.9 14.4’ 0912.1 -8.2’ 54.4’
SD.=16.3 d=0.2 S.D.=14.8
Lat. Twilight
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 09:22 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 18:39 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 03:19 20:48 21:48 58 01:51 03:03 21:04 22:15
S 60 01:08 02:44 21:23 22:58
Lat. Moonrise Moonset
N 72 –:– 00:19 01:53 11:22 11:17 11:12
N 70 –:– 00:16 01:43 11:23 11:23 11:23 68 –:– 00:13 01:36 11:23 11:27 11:32 66 –:– 00:11 01:30 11:24 11:31 11:40 64 –:– 00:09 01:24 11:24 11:35 11:46 62 –:– 00:07 01:20 11:24 11:37 11:51 60 –:– 00:06 01:16 11:24 11:40 11:56
N 58 –:– 00:04 01:12 11:25 11:42 12:01 56 –:– 00:03 01:09 11:25 11:44 12:04 54 –:– 00:02 01:06 11:25 11:46 12:08 52 –:– 00:01 01:04 11:25 11:48 12:11 50 –:– 00:00 01:02 11:25 11:49 12:14 45 23:58 –:– 00:57 11:26 11:52 12:20
N 40 23:57 –:– 00:53 11:26 11:55 12:25 35 23:56 –:– 00:49 11:26 11:57 12:30 30 23:54 –:– 00:46 11:26 12:00 12:34 20 23:52 –:– 00:40 11:27 12:03 12:40
N 10 23:51 –:– 00:36 11:27 12:06 12:46 0 23:49 –:– 00:31 11:27 12:09 12:52
S 10 23:47 –:– 00:27 11:27 12:12 12:58 20 23:46 –:– 00:22 11:28 12:16 13:04 30 23:44 –:– 00:17 11:28 12:19 13:11 35 23:43 –:– 00:14 11:28 12:21 13:15 40 23:41 –:– 00:11 11:28 12:24 13:19 45 23:40 –:– 00:07 11:28 12:27 13:25
S 50 23:38 –:– 00:02 11:29 12:30 13:31 52 23:37 –:– 00:00 11:29 12:31 13:34 54 23:37 23:58 –:– 11:29 12:33 13:37 56 23:36 23:55 –:– 11:29 12:35 13:41 58 23:35 23:53 –:– 11:29 12:37 13:45
S 60 23:34 23:49 –:– 11:29 12:39 13:49
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 57-38%
01 03:04 03:19 12:03 05:17 17:38 02 03:33 03:47 12:04 05:59 18:20 03 04:01 04:15 12:04 06:42 19:03
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 10302.9 21853.6 S1922.8 25423.7 S1008.5 28847.2 N0350.8 21252.9 S2032.2 1 11805.3 23352.9 23.4 26924.8 09.0 30349.6 50.8 22755.1 32.2 2 13307.8 24852.2 24.0 28426.0 09.5 31852.0 50.8 24257.3 32.2 3 14810.3 26351.5 · · 24.6 29927.1 · · 10.0 33354.4 · · 50.8 25759.4 · · 32.3 4 16312.7 27850.8 25.2 31428.3 10.5 34856.9 50.8 27301.6 32.3 5 17815.2 29350.1 25.8 32929.4 10.9 359.3 50.8 28803.8 32.3
6 19317.6 30849.4 S1926.4 34430.6 S1011.4 1901.7 N0350.8 30306.0 S2032.4 7 20820.1 32348.7 27.0 35931.7 11.9 3404.2 50.8 31808.2 32.4 8 22322.6 33848.0 27.6 1432.9 12.4 4906.6 50.8 33310.3 32.4 9 23825.0 35347.3 · · 28.2 2934.0 · · 12.9 6409.0 · · 50.8 34812.5 · · 32.5 10 25327.5 846.6 28.8 4435.2 13.3 7911.5 50.8 314.7 32.5 11 26830.0 2345.9 29.4 5936.3 13.8 9413.9 50.8 1816.9 32.5
12 28332.4 3845.2 S1930.0 7437.5 S1014.3 10916.3 N0350.8 3319.1 S2032.6 13 29834.9 5344.5 30.6 8938.6 14.8 12418.7 50.8 4821.3 32.6 14 31337.4 6843.8 31.2 10439.8 15.2 13921.2 50.8 6323.4 32.6 15 32839.8 8343.1 · · 31.8 11941.0 · · 15.7 15423.6 · · 50.8 7825.6 · · 32.7 16 34342.3 9842.4 32.4 13442.1 16.2 16926.0 50.8 9327.8 32.7 17 35844.8 11341.7 33.0 14943.3 16.7 18428.5 50.8 10830.0 32.7
18 1347.2 12841.0 S1933.6 16444.4 S1017.2 19930.9 N0350.8 12332.2 S2032.8 19 2849.7 14340.3 34.2 17945.6 17.6 21433.3 50.8 13834.4 32.8 20 4352.1 15839.6 34.8 19446.7 18.1 22935.8 50.8 15336.5 32.9 21 5854.6 17338.9 · · 35.4 20947.9 · · 18.6 24438.2 · · 50.8 16838.7 · · 32.9 22 7357.1 18838.2 36.0 22449.0 19.1 25940.7 50.8 18340.9 32.9 23 8859.5 20337.4 36.6 23950.2 19.6 27443.1 50.8 19843.1 33.0
Mer.pass.:17:05 v-0.7 d-0.6 m-3.9 v1.2 d-0.5 m1.2 v2.4 d-0.0 m-2.0 v2.2 d-0.0 m0.5
Tue GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10402.0 21836.7 S1937.1 25451.3 S1020.0 28945.5 N0350.8 21345.3 S2033.0 1 11904.5 23336.0 37.7 26952.5 20.5 30448.0 50.8 22847.4 33.0 2 13406.9 24835.3 38.3 28453.6 21.0 31950.4 50.8 24349.6 33.1 3 14909.4 26334.6 · · 38.9 29954.8 · · 21.5 33452.8 · · 50.8 25851.8 · · 33.1 4 16411.9 27833.9 39.5 31455.9 21.9 34955.3 50.8 27354.0 33.1 5 17914.3 29333.2 40.1 32957.1 22.4 457.7 50.8 28856.2 33.2
6 19416.8 30832.5 S1940.6 34458.3 S1022.9 2000.1 N0350.8 30358.4 S2033.2 7 20919.2 32331.8 41.2 35959.4 23.4 3502.6 50.8 31900.5 33.2 8 22421.7 33831.1 41.8 1500.6 23.8 5005.0 50.8 33402.7 33.3 9 23924.2 35330.4 · · 42.4 3001.7 · · 24.3 6507.5 · · 50.8 34904.9 · · 33.3 10 25426.6 829.7 43.0 4502.9 24.8 8009.9 50.8 407.1 33.3 11 26929.1 2328.9 43.5 6004.0 25.3 9512.3 50.8 1909.3 33.4
12 28431.6 3828.2 S1944.1 7505.2 S1025.7 11014.8 N0350.8 3411.5 S2033.4 13 29934.0 5327.5 44.7 9006.3 26.2 12517.2 50.8 4913.6 33.4 14 31436.5 6826.8 45.3 10507.5 26.7 14019.7 50.8 6415.8 33.5 15 32939.0 8326.1 · · 45.8 12008.6 · · 27.2 15522.1 · · 50.8 7918.0 · · 33.5 16 34441.4 9825.4 46.4 13509.8 27.6 17024.5 50.8 9420.2 33.5 17 35943.9 11324.7 47.0 15011.0 28.1 18527.0 50.8 10922.4 33.6
18 1446.4 12823.9 S1947.5 16512.1 S1028.6 20029.4 N0350.8 12424.6 S2033.6 19 2948.8 14323.2 48.1 18013.3 29.1 21531.9 50.8 13926.8 33.6 20 4451.3 15822.5 48.7 19514.4 29.5 23034.3 50.8 15428.9 33.7 21 5953.7 17321.8 · · 49.2 21015.6 · · 30.0 24536.7 · · 50.8 16931.1 · · 33.7 22 7456.2 18821.1 49.8 22516.7 30.5 26039.2 50.8 18433.3 33.7 23 8958.7 20320.4 50.4 24017.9 31.0 27541.6 50.8 19935.5 33.8
Mer.pass.:17:01 v-0.7 d-0.6 m-3.9 v1.2 d-0.5 m1.2 v2.4 d0.0 m-2.0 v2.2 d-0.0 m0.5
Wed GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10501.1 21819.6 S1950.9 25519.0 S1031.4 29044.1 N0350.8 21437.7 S2033.8 1 12003.6 23318.9 51.5 27020.2 31.9 30546.5 50.8 22939.9 33.8 2 13506.1 24818.2 52.1 28521.4 32.4 32049.0 50.8 24442.0 33.9 3 15008.5 26317.5 · · 52.6 30022.5 · · 32.9 33551.4 · · 50.9 25944.2 · · 33.9 4 16511.0 27816.8 53.2 31523.7 33.3 35053.8 50.9 27446.4 33.9 5 18013.5 29316.1 53.8 33024.8 33.8 556.3 50.9 28948.6 34.0
6 19515.9 30815.3 S1954.3 34526.0 S1034.3 2058.7 N0350.9 30450.8 S2034.0 7 21018.4 32314.6 54.9 027.1 34.8 3601.2 50.9 31953.0 34.0 8 22520.9 33813.9 55.4 1528.3 35.2 5103.6 50.9 33455.2 34.1 9 24023.3 35313.2 · · 56.0 3029.4 · · 35.7 6606.1 · · 50.9 34957.3 · · 34.1 10 25525.8 812.4 56.5 4530.6 36.2 8108.5 50.9 459.5 34.1 11 27028.2 2311.7 57.1 6031.8 36.6 9611.0 50.9 2001.7 34.2
12 28530.7 3811.0 S1957.7 7532.9 S1037.1 11113.4 N0350.9 3503.9 S2034.2 13 30033.2 5310.3 58.2 9034.1 37.6 12615.9 50.9 5006.1 34.2 14 31535.6 6809.5 58.8 10535.2 38.1 14118.3 50.9 6508.3 34.3 15 33038.1 8308.8 · · 59.3 12036.4 · · 38.5 15620.8 · · 50.9 8010.5 · · 34.3 16 34540.6 9808.1 1959.9 13537.5 39.0 17123.2 50.9 9512.6 34.3 17 043.0 11307.4 2000.4 15038.7 39.5 18625.6 50.9 11014.8 34.4
18 1545.5 12806.6 S2001.0 16539.9 S1039.9 20128.1 N0350.9 12517.0 S2034.4 19 3048.0 14305.9 01.5 18041.0 40.4 21630.5 50.9 14019.2 34.4 20 4550.4 15805.2 02.1 19542.2 40.9 23133.0 50.9 15521.4 34.5 21 6052.9 17304.5 · · 02.6 21043.3 · · 41.4 24635.4 · · 50.9 17023.6 · · 34.5 22 7555.4 18803.7 03.1 22544.5 41.8 26137.9 51.0 18525.8 34.5 23 9057.8 20303.0 03.7 24045.6 42.3 27640.3 51.0 20027.9 34.6
Mer.pass.:16:57 v-0.7 d-0.6 m-3.9 v1.2 d-0.5 m1.2 v2.4 d0.0 m-2.0 v2.2 d-0.0 m0.5
Stars SHA Dec
Alpheratz 35741.7 2910.8 Ankaa 35314.1 -4213.4
Schedar 34938.4 5637.7 Diphda 34854.2 -1754.1
Achernar 33525.5 -5709.7 Hamal 32758.6 2332.3 Polaris 31641.8 8920.1 Acamar 31516.8 -4014.8 Menkar 31413.0 409.0 Mirfak 30837.5 4955.1
Aldebaran 29047.1 1632.3 Rigel 28110.1 -811.3
Capella 28031.4 4600.7 Bellatrix 27829.8 621.6 Elnath 27810.1 2837.0 Alnilam 27544.3 -111.8
Betelgeuse 27059.1 724.3 Canopus 26354.8 -5242.5
Sirius 25831.8 -1644.5 Adhara 25510.8 -2859.9 Procyon 24457.6 510.8 Pollux 24325.3 2759.0 Avior 23416.6 -5933.7 Suhail 22250.7 -4329.9
Miaplacidus 22138.3 -6946.9 Alphard 21754.1 -843.8 Regulus 20741.5 1153.1 Dubhe 19349.4 6139.5
Denebola 18231.8 1428.8 Gienah 17550.4 -1737.8 Acrux 17307.1 -6310.9
Gacrux 17158.8 -5711.9 Alioth 16619.3 5552.1 Spica 15829.5 -1114.6 Alkaid 15257.8 4913.8 Hadar 14845.5 -6026.6
Menkent 14805.6 -3626.6 Arcturus 14554.3 1905.9
Rigil Kent. 13949.5 -6053.6 Kochab 13720.9 7405.2
Zuben’ubi 13703.7 -1606.3 Alphecca 12609.8 2639.7 Antares 11224.4 -2627.8
Atria 10725.1 -6903.0 Sabik 10210.9 -1544.4
Shaula 9620.0 -3706.6 Rasalhague 9605.2 1233.1
Eltanin 9045.9 5129.3 Kaus Aust. 8341.9 -3422.4
Vega 8038.2 3848.1 Nunki 7556.6 -2616.4 Altair 6206.9 854.8
Peacock 5317.2 -5640.9 Deneb 4930.7 4520.5
Enif 3345.7 957.0 Al Na’ir 2742.0 -4653.1
Fomalhaut 1522.3 -2932.4 Scheat 1351.8 2810.3 Markab 1336.7 1517.6
Jan 04 Mon SHA Mer.pass Venus 11550.7 09:25 Mars 15120.8 07:02
Jupiter 18544.3 04:44 Saturn 10950.0 09:47
Jan 05 Tue SHA Mer.pass Venus 11434.7 09:26 Mars 15049.3 07:00
Jupiter 18543.5 04:40 Saturn 10943.3 09:44
Jan 06 Wed SHA Mer.pass Venus 11318.5 09:27 Mars 15017.9 06:58
Jupiter 18542.9 04:36 Saturn 10936.5 09:40
Horizontal parallax Venus: 0.1 Mars: 0.1
4
DUT1 = UT1-UTC = +0.0762 sec T = TT-UT1 = +68.1078 sec 2016 January 04 to Jan. 06 UT
h Sun Moon Mon GHA Dec GHA ν Dec d HP
0 17852.8 S2247.7 25158.3 14.4’ S0920.3 -8.2’ 54.4’ 1 19352.6 47.5 26631.7 14.4’ 0928.4 -8.1’ 54.4’ 2 20852.3 47.2 28105.0 14.3’ 0936.6 -8.1’ 54.5’ 3 22352.0 · · 47.0 29538.3 14.3’ 0944.6 -8.1’ 54.5’ 4 23851.7 46.7 31011.6 14.2’ 0952.7 -8.0’ 54.5’ 5 25351.4 46.5 32444.8 14.2’ 1000.7 -8.0’ 54.5’
6 26851.1 S2246.2 33918.0 14.2’ S1008.7 -8.0’ 54.5’ 7 28350.8 46.0 35351.2 14.1’ 1016.6 -7.9’ 54.5’ 8 29850.5 45.7 824.3 14.1’ 1024.5 -7.9’ 54.5’ 9 31350.3 · · 45.5 2257.3 14.1’ 1032.4 -7.8’ 54.5’ 10 32850.0 45.2 3730.4 14.0’ 1040.2 -7.8’ 54.6’ 11 34349.7 45.0 5203.4 14.0’ 1048.0 -7.8’ 54.6’
12 35849.4 S2244.7 6636.3 13.9’ S1055.7 -7.7’ 54.6’ 13 1349.1 44.4 8109.2 13.9’ 1103.4 -7.7’ 54.6’ 14 2848.8 44.2 9542.1 13.8’ 1111.0 -7.6’ 54.6’ 15 4348.6 · · 43.9 11014.9 13.8’ 1118.6 -7.6’ 54.6’ 16 5848.3 43.7 12447.7 13.7’ 1126.2 -7.5’ 54.6’ 17 7348.0 43.4 13920.4 13.7’ 1133.7 -7.5’ 54.7’
18 8847.7 S2243.1 15353.1 13.7’ S1141.2 -7.4’ 54.7’ 19 10347.4 42.9 16825.7 13.6’ 1148.6 -7.4’ 54.7’ 20 11847.1 42.6 18258.3 13.6’ 1156.0 -7.4’ 54.7’ 21 13346.8 · · 42.3 19730.8 13.5’ 1203.3 -7.3’ 54.7’ 22 14846.6 42.1 21203.3 13.5’ 1210.6 -7.3’ 54.7’ 23 16346.3 41.8 22635.8 13.4’ 1217.8 -7.2’ 54.8’
SD.=16.3 d=0.2 S.D.=14.9
Tue GHA Dec GHA ν Dec d HP
0 17846.0 S2241.5 24108.2 13.4’ S1225.0 -7.2’ 54.8’ 1 19345.7 41.3 25540.5 13.3’ 1232.1 -7.1’ 54.8’ 2 20845.4 41.0 27012.8 13.3’ 1239.2 -7.1’ 54.8’ 3 22345.1 · · 40.7 28445.1 13.2’ 1246.2 -7.0’ 54.8’ 4 23844.9 40.5 29917.3 13.2’ 1253.2 -7.0’ 54.8’ 5 25344.6 40.2 31349.4 13.1’ 1300.2 -6.9’ 54.9’
6 26844.3 S2239.9 32821.5 13.1’ S1307.0 -6.8’ 54.9’ 7 28344.0 39.7 34253.6 13.0’ 1313.8 -6.8’ 54.9’ 8 29843.7 39.4 35725.6 13.0’ 1320.6 -6.7’ 54.9’ 9 31343.5 · · 39.1 1157.5 12.9’ 1327.3 -6.7’ 54.9’ 10 32843.2 38.8 2629.4 12.9’ 1334.0 -6.6’ 55.0’ 11 34342.9 38.6 4101.2 12.8’ 1340.6 -6.6’ 55.0’
12 35842.6 S2238.3 5533.0 12.8’ S1347.1 -6.5’ 55.0’ 13 1342.3 38.0 7004.8 12.7’ 1353.6 -6.5’ 55.0’ 14 2842.0 37.7 8436.4 12.7’ 1400.0 -6.4’ 55.0’ 15 4341.8 · · 37.5 9908.1 12.6’ 1406.4 -6.3’ 55.1’ 16 5841.5 37.2 11339.6 12.5’ 1412.7 -6.3’ 55.1’ 17 7341.2 36.9 12811.2 12.5’ 1418.9 -6.2’ 55.1’
18 8840.9 S2236.6 14242.6 12.4’ S1425.1 -6.1’ 55.1’ 19 10340.6 36.3 15714.0 12.4’ 1431.2 -6.1’ 55.1’ 20 11840.4 36.1 17145.4 12.3’ 1437.3 -6.0’ 55.2’ 21 13340.1 · · 35.8 18616.7 12.3’ 1443.3 -6.0’ 55.2’ 22 14839.8 35.5 20047.9 12.2’ 1449.2 -5.9’ 55.2’ 23 16339.5 35.2 21519.1 12.2’ 1455.1 -5.8’ 55.2’
SD.=16.3 d=0.3 S.D.=15.0
Wed GHA Dec GHA ν Dec d HP
0 17839.2 S2234.9 22950.2 12.1’ S1500.9 -5.8’ 55.2’ 1 19339.0 34.6 24421.3 12.0’ 1506.6 -5.7’ 55.3’ 2 20838.7 34.3 25852.3 12.0’ 1512.2 -5.6’ 55.3’ 3 22338.4 · · 34.1 27323.3 11.9’ 1517.8 -5.6’ 55.3’ 4 23838.1 33.8 28754.2 11.9’ 1523.4 -5.5’ 55.3’ 5 25337.9 33.5 30225.0 11.8’ 1528.8 -5.4’ 55.4’
6 26837.6 S2233.2 31655.8 11.8’ S1534.2 -5.4’ 55.4’ 7 28337.3 32.9 33126.5 11.7’ 1539.6 -5.3’ 55.4’ 8 29837.0 32.6 34557.2 11.6’ 1544.8 -5.2’ 55.4’ 9 31336.7 · · 32.3 027.8 11.6’ 1550.0 -5.1’ 55.5’ 10 32836.5 32.0 1458.4 11.5’ 1555.1 -5.1’ 55.5’ 11 34336.2 31.7 2928.9 11.5’ 1600.1 -5.0’ 55.5’
12 35835.9 S2231.4 4359.3 11.4’ S1605.1 -4.9’ 55.5’ 13 1335.6 31.1 5829.7 11.4’ 1610.0 -4.8’ 55.6’ 14 2835.4 30.8 7300.1 11.3’ 1614.8 -4.8’ 55.6’ 15 4335.1 · · 30.5 8730.3 11.2’ 1619.5 -4.7’ 55.6’ 16 5834.8 30.2 10200.5 11.2’ 1624.2 -4.6’ 55.6’ 17 7334.5 30.0 11630.7 11.1’ 1628.7 -4.5’ 55.6’
18 8834.3 S2229.7 13100.8 11.1’ S1633.2 -4.5’ 55.7’ 19 10334.0 29.4 14530.8 11.0’ 1637.7 -4.4’ 55.7’ 20 11833.7 29.1 16000.8 11.0’ 1642.0 -4.3’ 55.7’ 21 13333.4 · · 28.7 17430.8 10.9’ 1646.3 -4.2’ 55.8’ 22 14833.2 28.4 18900.6 10.8’ 1650.5 -4.1’ 55.8’ 23 16332.9 28.1 20330.5 10.8’ 1654.6 -4.1’ 55.8’
SD.=16.3 d=0.3 S.D.=15.1
Lat. Twilight
N 72 08:20 10:31 13:39 15:51
N 70 08:02 09:44 14:27 16:09 68 07:47 09:13 11:33 12:38 14:58 16:23 66 07:35 08:50 10:21 13:50 15:21 16:35 64 07:25 08:32 09:45 14:25 15:39 16:46 62 07:16 08:17 09:20 14:51 15:54 16:55 60 07:08 08:04 09:00 15:11 16:06 17:02
N 58 07:01 07:53 08:44 15:27 16:17 17:09 56 06:55 07:44 08:30 15:41 16:27 17:16 54 06:49 07:35 08:18 15:53 16:36 17:21 52 06:44 07:27 08:07 16:03 16:43 17:27 50 06:39 07:20 07:58 16:13 16:51 17:32 45 06:28 07:05 07:38 16:32 17:06 17:43
N 40 06:18 06:52 07:22 16:48 17:19 17:53 35 06:09 06:41 07:08 17:02 17:30 18:01 30 06:01 06:30 06:57 17:14 17:40 18:10 20 05:45 06:12 06:36 17:34 17:58 18:25
N 10 05:29 05:56 06:18 17:52 18:15 18:41 0 05:13 05:39 06:01 18:09 18:31 18:57
S 10 04:55 05:22 05:44 18:26 18:49 19:16 20 04:33 05:02 05:26 18:44 19:08 19:37 30 04:05 04:38 05:05 19:05 19:32 20:05 35 03:47 04:23 04:52 19:18 19:47 20:23 40 03:24 04:05 04:38 19:32 20:05 20:45 45 02:55 03:44 04:21 19:49 20:26 21:14
S 50 02:13 03:15 03:59 20:11 20:54 21:57 52 01:48 03:01 03:49 20:21 21:08 22:21 54 01:11 02:44 03:37 20:33 21:25 22:57 56 02:24 03:24 20:46 21:45 58 01:57 03:08 21:02 22:12
S 60 01:17 02:49 21:21 22:50
Lat. Moonrise Moonset
N 72 03:28 05:08 06:55 11:06 11:00 10:51
N 70 03:12 04:43 06:15 11:24 11:27 11:32 68 02:59 04:23 05:48 11:38 11:47 12:00 66 02:49 04:08 05:27 11:50 12:03 12:22 64 02:40 03:56 05:10 11:59 12:16 12:39 62 02:32 03:45 04:57 12:08 12:27 12:53 60 02:26 03:36 04:45 12:15 12:37 13:05
N 58 02:20 03:28 04:35 12:21 12:45 13:15 56 02:15 03:21 04:27 12:27 12:53 13:24 54 02:11 03:15 04:19 12:32 12:59 13:32 52 02:07 03:10 04:12 12:36 13:05 13:39 50 02:03 03:05 04:06 12:41 13:11 13:46 45 01:55 02:54 03:53 12:50 13:22 14:00
N 40 01:48 02:45 03:42 12:57 13:32 14:11 35 01:43 02:37 03:32 13:04 13:40 14:21 30 01:38 02:30 03:24 13:09 13:48 14:30 20 01:29 02:19 03:10 13:19 14:00 14:45
N 10 01:22 02:09 02:58 13:28 14:11 14:58 0 01:15 02:00 02:46 13:36 14:22 15:10
S 10 01:08 01:50 02:35 13:44 14:32 15:22 20 01:00 01:40 02:23 13:53 14:43 15:35 30 00:52 01:29 02:09 14:03 14:56 15:50 35 00:47 01:23 02:01 14:09 15:04 15:59 40 00:42 01:15 01:52 14:15 15:12 16:09 45 00:36 01:07 01:42 14:23 15:22 16:21
S 50 00:28 00:56 01:29 14:32 15:34 16:35 52 00:25 00:52 01:23 14:37 15:39 16:41 54 00:21 00:46 01:16 14:41 15:46 16:49 56 00:17 00:41 01:09 14:47 15:52 16:57 58 00:12 00:34 01:01 14:53 16:00 17:06
S 60 00:07 00:27 00:52 14:59 16:09 17:17
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 29-14%
04 04:29 04:42 12:05 07:25 19:48 05 04:56 05:10 12:05 08:11 20:34 06 05:23 05:36 12:06 08:58 21:23
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 10600.3 21802.3 S2004.2 25546.8 S1042.8 29142.8 N0351.0 21530.1 S2034.6 1 12102.7 23301.6 04.8 27048.0 43.2 30645.2 51.0 23032.3 34.6 2 13605.2 24800.8 05.3 28549.1 43.7 32147.7 51.0 24534.5 34.7 3 15107.7 26300.1 · · 05.9 30050.3 · · 44.2 33650.1 · · 51.0 26036.7 · · 34.7 4 16610.1 27759.4 06.4 31551.4 44.7 35152.6 51.0 27538.9 34.7 5 18112.6 29258.6 06.9 33052.6 45.1 655.1 51.0 29041.1 34.8
6 19615.1 30757.9 S2007.5 34553.7 S1045.6 2157.5 N0351.0 30543.3 S2034.8 7 21117.5 32257.2 08.0 054.9 46.1 3700.0 51.0 32045.4 34.8 8 22620.0 33756.4 08.5 1556.1 46.5 5202.4 51.0 33547.6 34.9 9 24122.5 35255.7 · · 09.1 3057.2 · · 47.0 6704.9 · · 51.0 35049.8 · · 34.9 10 25624.9 755.0 09.6 4558.4 47.5 8207.3 51.0 552.0 34.9 11 27127.4 2254.2 10.1 6059.5 47.9 9709.8 51.1 2054.2 35.0
12 28629.8 3753.5 S2010.7 7600.7 S1048.4 11212.2 N0351.1 3556.4 S2035.0 13 30132.3 5252.8 11.2 9101.9 48.9 12714.7 51.1 5058.6 35.0 14 31634.8 6752.0 11.7 10603.0 49.3 14217.1 51.1 6600.8 35.1 15 33137.2 8251.3 · · 12.3 12104.2 · · 49.8 15719.6 · · 51.1 8102.9 · · 35.1 16 34639.7 9750.6 12.8 13605.3 50.3 17222.0 51.1 9605.1 35.1 17 142.2 11249.8 13.3 15106.5 50.7 18724.5 51.1 11107.3 35.2
18 1644.6 12749.1 S2013.8 16607.7 S1051.2 20227.0 N0351.1 12609.5 S2035.2 19 3147.1 14248.3 14.4 18108.8 51.7 21729.4 51.1 14111.7 35.2 20 4649.6 15747.6 14.9 19610.0 52.1 23231.9 51.1 15613.9 35.3 21 6152.0 17246.9 · · 15.4 21111.1 · · 52.6 24734.3 · · 51.1 17116.1 · · 35.3 22 7654.5 18746.1 15.9 22612.3 53.1 26236.8 51.2 18618.3 35.3 23 9157.0 20245.4 16.5 24113.4 53.5 27739.2 51.2 20120.4 35.4
Mer.pass.:16:53 v-0.7 d-0.5 m-3.9 v1.2 d-0.5 m1.2 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Fri GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10659.4 21744.6 S2017.0 25614.6 S1054.0 29241.7 N0351.2 21622.6 S2035.4 1 12201.9 23243.9 17.5 27115.8 54.5 30744.2 51.2 23124.8 35.4 2 13704.3 24743.2 18.0 28616.9 54.9 32246.6 51.2 24627.0 35.5 3 15206.8 26242.4 · · 18.5 30118.1 · · 55.4 33749.1 · · 51.2 26129.2 · · 35.5 4 16709.3 27741.7 19.1 31619.2 55.9 35251.5 51.2 27631.4 35.5 5 18211.7 29240.9 19.6 33120.4 56.3 754.0 51.2 29133.6 35.6
6 19714.2 30740.2 S2020.1 34621.6 S1056.8 2256.5 N0351.2 30635.8 S2035.6 7 21216.7 32239.5 20.6 122.7 57.3 3758.9 51.2 32138.0 35.6 8 22719.1 33738.7 21.1 1623.9 57.7 5301.4 51.3 33640.1 35.7 9 24221.6 35238.0 · · 21.6 3125.0 · · 58.2 6803.8 · · 51.3 35142.3 · · 35.7 10 25724.1 737.2 22.1 4626.2 58.7 8306.3 51.3 644.5 35.7 11 27226.5 2236.5 22.7 6127.4 59.1 9808.8 51.3 2146.7 35.8
12 28729.0 3735.7 S2023.2 7628.5 S1059.6 11311.2 N0351.3 3648.9 S2035.8 13 30231.5 5235.0 23.7 9129.7 1100.1 12813.7 51.3 5151.1 35.8 14 31733.9 6734.2 24.2 10630.9 00.5 14316.1 51.3 6653.3 35.9 15 33236.4 8233.5 · · 24.7 12132.0 · · 01.0 15818.6 · · 51.3 8155.5 · · 35.9 16 34738.8 9732.8 25.2 13633.2 01.5 17321.1 51.3 9657.7 35.9 17 241.3 11232.0 25.7 15134.3 01.9 18823.5 51.4 11159.8 36.0
18 1743.8 12731.3 S2026.2 16635.5 S1102.4 20326.0 N0351.4 12702.0 S2036.0 19 3246.2 14230.5 26.7 18136.7 02.8 21828.5 51.4 14204.2 36.0 20 4748.7 15729.8 27.2 19637.8 03.3 23330.9 51.4 15706.4 36.1 21 6251.2 17229.0 · · 27.7 21139.0 · · 03.8 24833.4 · · 51.4 17208.6 · · 36.1 22 7753.6 18728.3 28.2 22640.1 04.2 26335.9 51.4 18710.8 36.1 23 9256.1 20227.5 28.7 24141.3 04.7 27838.3 51.4 20213.0 36.2
Mer.pass.:16:49 v-0.7 d-0.5 m-3.9 v1.2 d-0.5 m1.2 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Sat GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10758.6 21726.8 S2029.2 25642.5 S1105.2 29340.8 N0351.5 21715.2 S2036.2 1 12301.0 23226.0 29.7 27143.6 05.6 30843.2 51.5 23217.4 36.2 2 13803.5 24725.3 30.2 28644.8 06.1 32345.7 51.5 24719.6 36.3 3 15306.0 26224.5 · · 30.7 30146.0 · · 06.6 33848.2 · · 51.5 26221.7 · · 36.3 4 16808.4 27723.8 31.2 31647.1 07.0 35350.6 51.5 27723.9 36.3 5 18310.9 29223.0 31.7 33148.3 07.5 853.1 51.5 29226.1 36.4
6 19813.3 30722.3 S2032.2 34649.4 S1107.9 2355.6 N0351.5 30728.3 S2036.4 7 21315.8 32221.5 32.7 150.6 08.4 3858.1 51.5 32230.5 36.4 8 22818.3 33720.7 33.2 1651.8 08.9 5400.5 51.6 33732.7 36.4 9 24320.7 35220.0 · · 33.6 3152.9 · · 09.3 6903.0 · · 51.6 35234.9 · · 36.5 10 25823.2 719.2 34.1 4654.1 09.8 8405.5 51.6 737.1 36.5 11 27325.7 2218.5 34.6 6155.3 10.2 9907.9 51.6 2239.3 36.5
12 28828.1 3717.7 S2035.1 7656.4 S1110.7 11410.4 N0351.6 3741.5 S2036.6 13 30330.6 5217.0 35.6 9157.6 11.2 12912.9 51.6 5243.7 36.6 14 31833.1 6716.2 36.1 10658.7 11.6 14415.3 51.7 6745.9 36.6 15 33335.5 8215.5 · · 36.6 12159.9 · · 12.1 15917.8 · · 51.7 8248.0 · · 36.7 16 34838.0 9714.7 37.0 13701.1 12.5 17420.3 51.7 9750.2 36.7 17 340.5 11213.9 37.5 15202.2 13.0 18922.7 51.7 11252.4 36.7
18 1842.9 12713.2 S2038.0 16703.4 S1113.5 20425.2 N0351.7 12754.6 S2036.8 19 3345.4 14212.4 38.5 18204.6 13.9 21927.7 51.7 14256.8 36.8 20 4847.8 15711.7 39.0 19705.7 14.4 23430.2 51.7 15759.0 36.8 21 6350.3 17210.9 · · 39.4 21206.9 · · 14.8 24932.6 · · 51.8 17301.2 · · 36.9 22 7852.8 18710.1 39.9 22708.1 15.3 26435.1 51.8 18803.4 36.9 23 9355.2 20209.4 40.4 24209.2 15.8 27937.6 51.8 20305.6 36.9
Mer.pass.:16:45 v-0.8 d-0.5 m-3.9 v1.2 d-0.5 m1.2 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Stars SHA Dec
Alpheratz 35741.7 2910.8 Ankaa 35314.1 -4213.4
Schedar 34938.4 5637.7 Diphda 34854.2 -1754.1
Achernar 33525.5 -5709.7 Hamal 32758.6 2332.3 Polaris 31642.8 8920.1 Acamar 31516.9 -4014.8 Menkar 31413.1 409.0 Mirfak 30837.5 4955.1
Aldebaran 29047.1 1632.3 Rigel 28110.1 -811.3
Capella 28031.4 4600.7 Bellatrix 27829.8 621.6 Elnath 27810.1 2837.0 Alnilam 27544.3 -111.8
Betelgeuse 27059.1 724.3 Canopus 26354.8 -5242.5
Sirius 25831.8 -1644.6 Adhara 25510.8 -2859.9 Procyon 24457.6 510.8 Pollux 24325.3 2759.0 Avior 23416.6 -5933.7 Suhail 22250.7 -4329.9
Miaplacidus 22138.3 -6946.9 Alphard 21754.1 -843.8 Regulus 20741.4 1153.1 Dubhe 19349.4 6139.5
Denebola 18231.8 1428.8 Gienah 17550.4 -1737.8 Acrux 17307.1 -6311.0
Gacrux 17158.7 -5711.9 Alioth 16619.3 5552.1 Spica 15829.4 -1114.6 Alkaid 15257.7 4913.8 Hadar 14845.4 -6026.6
Menkent 14805.6 -3626.6 Arcturus 14554.3 1905.9
Rigil Kent. 13949.5 -6053.6 Kochab 13720.9 7405.2
Zuben’ubi 13703.6 -1606.3 Alphecca 12609.8 2639.7 Antares 11224.4 -2627.8
Atria 10725.1 -6903.0 Sabik 10210.8 -1544.4
Shaula 9619.9 -3706.6 Rasalhague 9605.2 1233.1
Eltanin 9045.9 5129.3 Kaus Aust. 8341.9 -3422.4
Vega 8038.2 3848.1 Nunki 7556.6 -2616.4 Altair 6206.9 854.8
Peacock 5317.2 -5640.9 Deneb 4930.7 4520.5
Enif 3345.7 957.0 Al Na’ir 2742.0 -4653.1
Fomalhaut 1522.3 -2932.4 Scheat 1351.8 2810.3 Markab 1336.7 1517.6
Jan 07 Thu SHA Mer.pass Venus 11202.0 09:28 Mars 14946.5 06:56
Jupiter 18542.5 04:32 Saturn 10929.9 09:37
Jan 08 Fri SHA Mer.pass Venus 11045.2 09:29 Mars 14915.2 06:54
Jupiter 18542.3 04:28 Saturn 10923.2 09:33
Jan 09 Sat SHA Mer.pass Venus 10928.2 09:31 Mars 14843.9 06:53
Jupiter 18542.2 04:25 Saturn 10916.6 09:30
Horizontal parallax Venus: 0.1 Mars: 0.1
6
DUT1 = UT1-UTC = +0.0709 sec T = TT-UT1 = +68.1131 sec 2016 January 07 to Jan. 09 UT
h Sun Moon Thu GHA Dec GHA ν Dec d HP
0 17832.6 S2227.8 21800.2 10.7’ S1658.6 -4.0’ 55.8’ 1 19332.3 27.5 23229.9 10.7’ 1702.5 -3.9’ 55.9’ 2 20832.1 27.2 24659.6 10.6’ 1706.4 -3.8’ 55.9’ 3 22331.8 · · 26.9 26129.2 10.6’ 1710.1 -3.7’ 55.9’ 4 23831.5 26.6 27558.7 10.5’ 1713.8 -3.6’ 55.9’ 5 25331.2 26.3 29028.2 10.5’ 1717.4 -3.6’ 56.0’
6 26831.0 S2226.0 30457.6 10.4’ S1721.0 -3.5’ 56.0’ 7 28330.7 25.7 31927.0 10.3’ 1724.4 -3.4’ 56.0’ 8 29830.4 25.4 33356.3 10.3’ 1727.7 -3.3’ 56.0’ 9 31330.1 · · 25.1 34825.6 10.2’ 1731.0 -3.2’ 56.1’ 10 32829.9 24.8 254.8 10.2’ 1734.1 -3.1’ 56.1’ 11 34329.6 24.4 1723.9 10.1’ 1737.2 -3.0’ 56.1’
12 35829.3 S2224.1 3153.0 10.1’ S1740.2 -2.9’ 56.1’ 13 1329.1 23.8 4622.1 10.0’ 1743.1 -2.9’ 56.2’ 14 2828.8 23.5 6051.1 10.0’ 1745.9 -2.8’ 56.2’ 15 4328.5 · · 23.2 7520.0 9.9’ 1748.6 -2.7’ 56.2’ 16 5828.2 22.9 8948.9 9.9’ 1751.2 -2.6’ 56.3’ 17 7328.0 22.6 10417.7 9.8’ 1753.8 -2.5’ 56.3’
18 8827.7 S2222.2 11846.5 9.8’ S1756.2 -2.4’ 56.3’ 19 10327.4 21.9 13315.3 9.7’ 1758.5 -2.3’ 56.3’ 20 11827.2 21.6 14744.0 9.7’ 1800.8 -2.2’ 56.4’ 21 13326.9 · · 21.3 16212.6 9.6’ 1802.9 -2.1’ 56.4’ 22 14826.6 21.0 17641.2 9.6’ 1805.0 -2.0’ 56.4’ 23 16326.4 20.6 19109.7 9.5’ 1807.0 -1.9’ 56.4’
SD.=16.3 d=0.3 S.D.=15.3
Fri GHA Dec GHA ν Dec d HP
0 17826.1 S2220.3 20538.2 9.5’ S1808.8 -1.8’ 56.5’ 1 19325.8 20.0 22006.7 9.4’ 1810.6 -1.7’ 56.5’ 2 20825.5 19.7 23435.1 9.4’ 1812.2 -1.6’ 56.5’ 3 22325.3 · · 19.3 24903.4 9.3’ 1813.8 -1.5’ 56.6’ 4 23825.0 19.0 26331.8 9.3’ 1815.3 -1.4’ 56.6’ 5 25324.7 18.7 27800.0 9.2’ 1816.7 -1.3’ 56.6’
6 26824.5 S2218.4 29228.2 9.2’ S1817.9 -1.2’ 56.6’ 7 28324.2 18.0 30656.4 9.2’ 1819.1 -1.1’ 56.7’ 8 29823.9 17.7 32124.5 9.1’ 1820.2 -1.0’ 56.7’ 9 31323.7 · · 17.4 33552.6 9.1’ 1821.1 -0.9’ 56.7’ 10 32823.4 17.1 35020.7 9.0’ 1822.0 -0.8’ 56.7’ 11 34323.1 16.7 448.7 9.0’ 1822.8 -0.7’ 56.8’
12 35822.9 S2216.4 1916.7 8.9’ S1823.5 -0.6’ 56.8’ 13 1322.6 16.1 3344.6 8.9’ 1824.0 -0.5’ 56.8’ 14 2822.3 15.7 4812.5 8.9’ 1824.5 -0.4’ 56.9’ 15 4322.1 · · 15.4 6240.3 8.8’ 1824.8 -0.3’ 56.9’ 16 5821.8 15.1 7708.2 8.8’ 1825.1 -0.2’ 56.9’ 17 7321.5 14.7 9135.9 8.8’ 1825.2 -0.1’ 56.9’
18 8821.3 S2214.4 10603.7 8.7’ S1825.3 0.0’ 57.0’ 19 10321.0 14.1 12031.4 8.7’ 1825.2 0.1’ 57.0’ 20 11820.7 13.7 13459.1 8.7’ 1825.0 0.2’ 57.0’ 21 13320.5 · · 13.4 14926.7 8.6’ 1824.8 0.3’ 57.1’ 22 14820.2 13.0 16354.3 8.6’ 1824.4 0.4’ 57.1’ 23 16319.9 12.7 17821.9 8.6’ 1823.9 0.5’ 57.1’
SD.=16.3 d=0.3 S.D.=15.5
Sat GHA Dec GHA ν Dec d HP
0 17819.7 S2212.4 19249.4 8.5’ S1823.3 0.6’ 57.1’ 1 19319.4 12.0 20716.9 8.5’ 1822.6 0.7’ 57.2’ 2 20819.2 11.7 22144.4 8.5’ 1821.8 0.9’ 57.2’ 3 22318.9 · · 11.3 23611.9 8.4’ 1820.9 1.0’ 57.2’ 4 23818.6 11.0 25039.3 8.4’ 1819.9 1.1’ 57.2’ 5 25318.4 10.6 26506.7 8.4’ 1818.8 1.2’ 57.3’
6 26818.1 S2210.3 27934.1 8.4’ S1817.5 1.3’ 57.3’ 7 28317.8 10.0 29401.4 8.3’ 1816.2 1.4’ 57.3’ 8 29817.6 09.6 30828.7 8.3’ 1814.8 1.5’ 57.4’ 9 31317.3 · · 09.3 32256.0 8.3’ 1813.2 1.6’ 57.4’ 10 32817.0 08.9 33723.3 8.3’ 1811.5 1.7’ 57.4’ 11 34316.8 08.6 35150.6 8.2’ 1809.8 1.8’ 57.4’
12 35816.5 S2208.2 617.8 8.2’ S1807.9 1.9’ 57.5’ 13 1316.3 07.9 2045.0 8.2’ 1805.9 2.0’ 57.5’ 14 2816.0 07.5 3512.2 8.2’ 1803.8 2.1’ 57.5’ 15 4315.7 · · 07.2 4939.4 8.2’ 1801.6 2.3’ 57.5’ 16 5815.5 06.8 6406.6 8.2’ 1759.3 2.4’ 57.6’ 17 7315.2 06.5 7833.7 8.1’ 1756.9 2.5’ 57.6’
18 8815.0 S2206.1 9300.8 8.1’ S1754.3 2.6’ 57.6’ 19 10314.7 05.7 10728.0 8.1’ 1751.7 2.7’ 57.6’ 20 11814.4 05.4 12155.0 8.1’ 1749.0 2.8’ 57.7’ 21 13314.2 · · 05.0 13622.1 8.1’ 1746.1 2.9’ 57.7’ 22 14813.9 04.7 15049.2 8.1’ 1743.1 3.0’ 57.7’ 23 16313.7 04.3 16516.3 8.1’ 1740.1 3.1’ 57.7’
SD.=16.3 d=0.3 S.D.=15.7
Lat. Twilight
N 72 08:16 10:21 13:53 15:58
N 70 07:58 09:37 14:36 16:15 68 07:45 09:08 11:12 13:01 15:05 16:29 66 07:33 08:47 10:14 14:00 15:27 16:41 64 07:23 08:29 09:41 14:33 15:44 16:50 62 07:14 08:15 09:16 14:57 15:59 16:59 60 07:07 08:02 08:57 15:16 16:11 17:06
N 58 07:00 07:52 08:42 15:32 16:22 17:13 56 06:54 07:42 08:28 15:45 16:31 17:19 54 06:48 07:34 08:16 15:57 16:39 17:25 52 06:43 07:26 08:06 16:07 16:47 17:30 50 06:38 07:19 07:57 16:16 16:54 17:35 45 06:28 07:04 07:38 16:36 17:09 17:46
N 40 06:18 06:52 07:22 16:51 17:21 17:55 35 06:09 06:41 07:09 17:05 17:32 18:04 30 06:01 06:31 06:57 17:16 17:42 18:12 20 05:46 06:13 06:37 17:36 18:00 18:27
N 10 05:31 05:57 06:19 17:54 18:16 18:42 0 05:14 05:40 06:03 18:10 18:33 18:59
S 10 04:56 05:23 05:46 18:27 18:50 19:16 20 04:35 05:04 05:28 18:45 19:09 19:38 30 04:07 04:40 05:07 19:06 19:33 20:05 35 03:50 04:26 04:55 19:18 19:47 20:23 40 03:28 04:08 04:41 19:32 20:04 20:45 45 02:59 03:47 04:24 19:49 20:25 21:13
S 50 02:18 03:20 04:03 20:10 20:53 21:54 52 01:54 03:06 03:53 20:20 21:06 22:17 54 01:21 02:49 03:41 20:31 21:22 22:50 56 02:30 03:28 20:44 21:42 58 02:04 03:13 20:59 22:07
S 60 01:28 02:54 21:17 22:42
Lat. Moonrise Moonset
N 72 08:58 10:32
N 70 07:45 09:03 09:52 11:45 12:16 13:19 68 07:08 08:18 09:09 12:23 13:01 14:02 66 06:42 07:48 08:40 12:49 13:31 14:30 64 06:22 07:26 08:18 13:10 13:53 14:52 62 06:06 07:08 08:01 13:26 14:11 15:09 60 05:52 06:53 07:46 13:40 14:26 15:24
N 58 05:40 06:41 07:34 13:52 14:39 15:36 56 05:30 06:30 07:23 14:02 14:50 15:47 54 05:21 06:20 07:13 14:11 14:59 15:56 52 05:13 06:12 07:05 14:19 15:08 16:05 50 05:06 06:04 06:57 14:27 15:15 16:12 45 04:51 05:48 06:41 14:42 15:32 16:28
N 40 04:38 05:34 06:28 14:55 15:45 16:41 35 04:28 05:23 06:17 15:06 15:57 16:52 30 04:19 05:13 06:07 15:16 16:07 17:02 20 04:03 04:56 05:50 15:32 16:24 17:19
N 10 03:49 04:41 05:35 15:47 16:39 17:33 0 03:36 04:27 05:21 16:00 16:53 17:47
S 10 03:23 04:14 05:07 16:14 17:07 18:00 20 03:09 03:59 04:52 16:28 17:22 18:15 30 02:53 03:42 04:35 16:45 17:39 18:31 35 02:44 03:32 04:25 16:54 17:49 18:41 40 02:34 03:21 04:14 17:05 18:00 18:52 45 02:22 03:08 04:01 17:18 18:13 19:05
S 50 02:07 02:52 03:45 17:34 18:29 19:20 52 02:00 02:44 03:37 17:41 18:37 19:27 54 01:52 02:36 03:29 17:49 18:46 19:36 56 01:44 02:27 03:19 17:59 18:55 19:45 58 01:34 02:16 03:08 18:09 19:06 19:55
S 60 01:23 02:04 02:56 18:21 19:18 20:07
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age
00h 12h Pass Upper Lower 27-29 mm:ss mm:ss hh:mm hh:mm hh:mm 7-1%
07 05:50 06:03 12:06 09:48 22:14 08 06:16 06:29 12:06 10:40 23:07 09 06:41 06:54 12:07 11:34 –:–
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 10857.7 21708.6 S2040.9 25710.4 S1116.2 29440.0 N0351.8 21807.8 S2037.0 1 12400.2 23207.9 41.3 27211.5 16.7 30942.5 51.8 23310.0 37.0 2 13902.6 24707.1 41.8 28712.7 17.1 32445.0 51.8 24812.2 37.0 3 15405.1 26206.3 · · 42.3 30213.9 · · 17.6 33947.5 · · 51.9 26314.3 · · 37.1 4 16907.6 27705.6 42.8 31715.0 18.1 35449.9 51.9 27816.5 37.1 5 18410.0 29204.8 43.2 33216.2 18.5 952.4 51.9 29318.7 37.1
6 19912.5 30704.1 S2043.7 34717.4 S1119.0 2454.9 N0351.9 30820.9 S2037.2 7 21415.0 32203.3 44.2 218.5 19.4 3957.4 51.9 32323.1 37.2 8 22917.4 33702.5 44.6 1719.7 19.9 5459.8 51.9 33825.3 37.2 9 24419.9 35201.8 · · 45.1 3220.9 · · 20.3 7002.3 · · 52.0 35327.5 · · 37.2 10 25922.3 701.0 45.6 4722.0 20.8 8504.8 52.0 829.7 37.3 11 27424.8 2200.2 46.0 6223.2 21.3 10007.3 52.0 2331.9 37.3
12 28927.3 3659.5 S2046.5 7724.4 S1121.7 11509.7 N0352.0 3834.1 S2037.3 13 30429.7 5158.7 46.9 9225.5 22.2 13012.2 52.0 5336.3 37.4 14 31932.2 6657.9 47.4 10726.7 22.6 14514.7 52.1 6838.5 37.4 15 33434.7 8157.2 · · 47.9 12227.9 · · 23.1 16017.2 · · 52.1 8340.7 · · 37.4 16 34937.1 9656.4 48.3 13729.0 23.5 17519.7 52.1 9842.9 37.5 17 439.6 11155.6 48.8 15230.2 24.0 19022.1 52.1 11345.1 37.5
18 1942.1 12654.9 S2049.2 16731.4 S1124.5 20524.6 N0352.1 12847.2 S2037.5 19 3444.5 14154.1 49.7 18232.5 24.9 22027.1 52.1 14349.4 37.6 20 4947.0 15653.3 50.2 19733.7 25.4 23529.6 52.2 15851.6 37.6 21 6449.4 17152.6 · · 50.6 21234.9 · · 25.8 25032.0 · · 52.2 17353.8 · · 37.6 22 7951.9 18651.8 51.1 22736.0 26.3 26534.5 52.2 18856.0 37.7 23 9454.4 20151.0 51.5 24237.2 26.7 28037.0 52.2 20358.2 37.7
Mer.pass.:16:41 v-0.8 d-0.5 m-3.9 v1.2 d-0.5 m1.2 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Mon GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 10956.8 21650.2 S2052.0 25738.4 S1127.2 29539.5 N0352.2 21900.4 S2037.7 1 12459.3 23149.5 52.4 27239.5 27.6 31042.0 52.3 23402.6 37.7 2 14001.8 24648.7 52.9 28740.7 28.1 32544.5 52.3 24904.8 37.8 3 15504.2 26147.9 · · 53.3 30241.9 · · 28.6 34046.9 · · 52.3 26407.0 · · 37.8 4 17006.7 27647.2 53.8 31743.0 29.0 35549.4 52.3 27909.2 37.8 5 18509.2 29146.4 54.2 33244.2 29.5 1051.9 52.3 29411.4 37.9
6 20011.6 30645.6 S2054.7 34745.4 S1129.9 2554.4 N0352.4 30913.6 S2037.9 7 21514.1 32144.8 55.1 246.5 30.4 4056.9 52.4 32415.8 37.9 8 23016.6 33644.1 55.5 1747.7 30.8 5559.3 52.4 33918.0 38.0 9 24519.0 35143.3 · · 56.0 3248.9 · · 31.3 7101.8 · · 52.4 35420.2 · · 38.0 10 26021.5 642.5 56.4 4750.0 31.7 8604.3 52.4 922.4 38.0 11 27523.9 2141.7 56.9 6251.2 32.2 10106.8 52.5 2424.6 38.1
12 29026.4 3641.0 S2057.3 7752.4 S1132.6 11609.3 N0352.5 3926.8 S2038.1 13 30528.9 5140.2 57.7 9253.5 33.1 13111.8 52.5 5429.0 38.1 14 32031.3 6639.4 58.2 10754.7 33.6 14614.2 52.5 6931.1 38.2 15 33533.8 8138.6 · · 58.6 12255.9 · · 34.0 16116.7 · · 52.6 8433.3 · · 38.2 16 35036.3 9637.9 59.1 13757.0 34.5 17619.2 52.6 9935.5 38.2 17 538.7 11137.1 59.5 15258.2 34.9 19121.7 52.6 11437.7 38.2
18 2041.2 12636.3 S2059.9 16759.4 S1135.4 20624.2 N0352.6 12939.9 S2038.3 19 3543.7 14135.5 2100.4 18300.5 35.8 22126.7 52.6 14442.1 38.3 20 5046.1 15634.8 00.8 19801.7 36.3 23629.2 52.7 15944.3 38.3 21 6548.6 17134.0 · · 01.2 21302.9 · · 36.7 25131.6 · · 52.7 17446.5 · · 38.4 22 8051.1 18633.2 01.6 22804.0 37.2 26634.1 52.7 18948.7 38.4 23 9553.5 20132.4 02.1 24305.2 37.6 28136.6 52.7 20450.9 38.4
Mer.pass.:16:37 v-0.8 d-0.5 m-3.9 v1.2 d-0.5 m1.1 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Tue GHA GHA Dec GHA Dec GHA Dec GHA Dec
0 11056.0 21631.6 S2102.5 25806.4 S1138.1 29639.1 N0352.8 21953.1 S2038.5 1 12558.4 23130.9 02.9 27307.6 38.5 31141.6 52.8 23455.3 38.5 2 14100.9 24630.1 03.4 28808.7 39.0 32644.1 52.8 24957.5 38.5 3 15603.4 26129.3 · · 03.8 30309.9 · · 39.4 34146.6 · · 52.8 26459.7 · · 38.6 4 17105.8 27628.5 04.2 31811.1 39.9 35649.1 52.8 28001.9 38.6 5 18608.3 29127.7 04.6 33312.2 40.3 1151.6 52.9 29504.1 38.6
6 20110.8 30627.0 S2105.0 34813.4 S1140.8 2654.0 N0352.9 31006.3 S2038.6 7 21613.2 32126.2 05.5 314.6 41.2 4156.5 52.9 32508.5 38.7 8 23115.7 33625.4 05.9 1815.7 41.7 5659.0 52.9 34010.7 38.7 9 24618.2 35124.6 · · 06.3 3316.9 · · 42.1 7201.5 · · 53.0 35512.9 · · 38.7 10 26120.6 623.8 06.7 4818.1 42.6 8704.0 53.0 1015.1 38.8 11 27623.1 2123.0 07.1 6319.3 43.0 10206.5 53.0 2517.3 38.8
12 29125.6 3622.3 S2107.5 7820.4 S1143.5 11709.0 N0353.0 4019.5 S2038.8 13 30628.0 5121.5 08.0 9321.6 43.9 13211.5 53.1 5521.7 38.9 14 32130.5 6620.7 08.4 10822.8 44.4 14714.0 53.1 7023.9 38.9 15 33632.9 8119.9 · · 08.8 12323.9 · · 44.8 16216.5 · · 53.1 8526.1 · · 38.9 16 35135.4 9619.1 09.2 13825.1 45.3 17719.0 53.1 10028.3 39.0 17 637.9 11118.3 09.6 15326.3 45.7 19221.5 53.2 11530.5 39.0
18 2140.3 12617.5 S2110.0 16827.4 S1146.2 20723.9 N0353.2 13032.7 S2039.0 19 3642.8 14116.8 10.4 18328.6 46.6 22226.4 53.2 14534.9 39.0 20 5145.3 15616.0 10.8 19829.8 47.1 23728.9 53.2 16037.1 39.1 21 6647.7 17115.2 · · 11.2 21331.0 · · 47.5 25231.4 · · 53.3 17539.3 · · 39.1 22 8150.2 18614.4 11.6 22832.1 48.0 26733.9 53.3 19041.5 39.1 23 9652.7 20113.6 12.0 24333.3 48.4 28236.4 53.3 20543.7 39.2
Mer.pass.:16:34 v-0.8 d-0.4 m-3.9 v1.2 d-0.5 m1.1 v2.5 d0.0 m-2.1 v2.2 d-0.0 m0.5
Stars SHA Dec
Alpheratz 35741.7 2910.8 Ankaa 35314.1 -4213.4
Schedar 34938.5 5637.7 Diphda 34854.2 -1754.1
Achernar 33525.5 -5709.7 Hamal 32758.7 2332.3 Polaris 31644.0 8920.1 Acamar 31516.9 -4014.8 Menkar 31413.1 409.0 Mirfak 30837.5 4955.1
Aldebaran 29047.1 1632.3 Rigel 28110.1 -811.3
Capella 28031.4 4600.7 Bellatrix 27829.8 621.6 Elnath 27810.1 2837.0 Alnilam 27544.3 -111.8
Betelgeuse 27059.1 724.3 Canopus 26354.8 -5242.5
Sirius 25831.8 -1644.6 Adhara 25510.7 -2859.9 Procyon 24457.6 510.8 Pollux 24325.2 2759.0 Avior 23416.6 -5933.8 Suhail 22250.7 -4329.9
Miaplacidus 22138.3 -6947.0 Alphard 21754.1 -843.8 Regulus 20741.4 1153.1 Dubhe 19349.3 6139.5
Denebola 18231.8 1428.8 Gienah 17550.4 -1737.8 Acrux 17307.0 -6311.0
Gacrux 17158.7 -5711.9 Alioth 16619.2 5552.1 Spica 15829.4 -1114.6 Alkaid 15257.7 4913.8 Hadar 14845.4 -6026.6
Menkent 14805.5 -3626.6 Arcturus 14554.3 1905.9
Rigil Kent. 13949.4 -6053.6 Kochab 13720.8 7405.2
Zuben’ubi 13703.6 -1606.3 Alphecca 12609.8 2639.7 Antares 11224.4 -2627.8
Atria 10725.0 -6903.0 Sabik 10210.8 -1544.4
Shaula 9619.9 -3706.6 Rasalhague 9605.1 1233.0
Eltanin 9045.8 5129.3 Kaus Aust. 8341.9 -3422.4
Vega 8038.2 3848.0 Nunki 7556.5 -2616.4 Altair 6206.9 854.8
Peacock 5317.2 -5640.9 Deneb 4930.7 4520.5
Enif 3345.7 957.0 Al Na’ir 2742.0 -4653.1
Fomalhaut 1522.3 -2932.4 Scheat 1351.8 2810.3 Markab 1336.8 1517.6
Jan 10 Sun SHA Mer.pass Venus 10810.9 09:32 Mars 14812.7 06:51
Jupiter 18542.3 04:21 Saturn 10910.1 09:26
Jan 11 Mon SHA Mer.pass Venus 10653.4 09:33 Mars 14741.5 06:49
Jupiter 18542.6 04:17 Saturn 10903.6 09:23
Jan 12 Tue SHA Mer.pass Venus 10535.7 09:34 Mars 14710.4 06:47
Jupiter 18543.1 04:13 Saturn 10857.1 09:19
Horizontal parallax Venus: 0.1 Mars: 0.1
8
DUT1 = UT1-UTC = +0.0655 sec T = TT-UT1 = +68.1185 sec 2016 January 10 to Jan. 12 UT
h Sun Moon Sun GHA Dec GHA ν Dec d HP
0 17813.4 S2204.0 17943.3 8.0’ S1736.9 3.2’ 57.8’ 1 19313.1 03.6 19410.4 8.0’ 1733.6 3.3’ 57.8’ 2 20812.9 03.2 20837.4 8.0’ 1730.2 3.4’ 57.8’ 3 22312.6 · · 02.9 22304.4 8.0’ 1726.7 3.6’ 57.8’ 4 23812.4 02.5 23731.4 8.0’ 1723.1 3.7’ 57.9’ 5 25312.1 02.2 25158.5 8.0’ 1719.4 3.8’ 57.9’
6 26811.9 S2201.8 26625.5 8.0’ S1715.6 3.9’ 57.9’ 7 28311.6 01.4 28052.5 8.0’ 1711.7 4.0’ 57.9’ 8 29811.3 01.1 29519.5 8.0’ 1707.6 4.1’ 58.0’ 9 31311.1 · · 00.7 30946.5 8.0’ 1703.5 4.2’ 58.0’ 10 32810.8 00.3 32413.5 8.0’ 1659.2 4.3’ 58.0’ 11 34310.6 2200.0 33840.5 8.0’ 1654.9 4.4’ 58.0’
12 35810.3 S2159.6 35307.5 8.0’ S1650.4 4.5’ 58.1’ 13 1310.1 59.2 734.5 8.0’ 1645.9 4.6’ 58.1’ 14 2809.8 58.9 2201.4 8.0’ 1641.2 4.7’ 58.1’ 15 4309.6 · · 58.5 3628.4 8.0’ 1636.5 4.8’ 58.1’ 16 5809.3 58.1 5055.4 8.0’ 1631.6 4.9’ 58.1’ 17 7309.0 57.8 6522.4 8.0’ 1626.6 5.0’ 58.2’
18 8808.8 S2157.4 7949.5 8.0’ S1621.5 5.1’ 58.2’ 19 10308.5 57.0 9416.5 8.0’ 1616.4 5.2’ 58.2’ 20 11808.3 56.6 10843.5 8.0’ 1611.1 5.3’ 58.2’ 21 13308.0 · · 56.3 12310.5 8.0’ 1605.7 5.4’ 58.3’ 22 14807.8 55.9 13737.5 8.0’ 1600.2 5.5’ 58.3’ 23 16307.5 55.5 15204.6 8.0’ 1554.6 5.6’ 58.3’
SD.=16.3 d=0.4 S.D.=15.8
Mon GHA Dec GHA ν Dec d HP
0 17807.3 S2155.1 16631.6 8.1’ S1549.0 5.7’ 58.3’ 1 19307.0 54.8 18058.7 8.1’ 1543.2 5.8’ 58.3’ 2 20806.8 54.4 19525.8 8.1’ 1537.3 5.9’ 58.4’ 3 22306.5 · · 54.0 20952.8 8.1’ 1531.3 6.0’ 58.4’ 4 23806.3 53.6 22419.9 8.1’ 1525.2 6.1’ 58.4’ 5 25306.0 53.2 23847.0 8.1’ 1519.1 6.2’ 58.4’
6 26805.8 S2152.9 25314.1 8.1’ S1512.8 6.3’ 58.4’ 7 28305.5 52.5 26741.3 8.1’ 1506.4 6.4’ 58.5’ 8 29805.3 52.1 28208.4 8.1’ 1500.0 6.5’ 58.5’ 9 31305.0 · · 51.7 29635.6 8.2’ 1453.4 6.6’ 58.5’ 10 32804.8 51.3 31102.7 8.2’ 1446.8 6.7’ 58.5’ 11 34304.5 50.9 32529.9 8.2’ 1440.1 6.8’ 58.5’
12 35804.3 S2150.6 33957.1 8.2’ S1433.2 6.9’ 58.5’ 13 1304.0 50.2 35424.3 8.2’ 1426.3 7.0’ 58.6’ 14 2803.8 49.8 851.5 8.2’ 1419.3 7.1’ 58.6’ 15 4303.5 · · 49.4 2318.8 8.3’ 1412.2 7.1’ 58.6’ 16 5803.3 49.0 3746.1 8.3’ 1405.0 7.2’ 58.6’ 17 7303.0 48.6 5213.3 8.3’ 1357.7 7.3’ 58.6’
18 8802.8 S2148.2 6640.6 8.3’ S1350.3 7.4’ 58.7’ 19 10302.5 47.8 8108.0 8.3’ 1342.9 7.5’ 58.7’ 20 11802.3 47.4 9535.3 8.3’ 1335.3 7.6’ 58.7’ 21 13302.0 · · 47.1 11002.7 8.4’ 1327.7 7.7’ 58.7’ 22 14801.8 46.7 12430.0 8.4’ 1320.0 7.8’ 58.7’ 23 16301.5 46.3 13857.4 8.4’ 1312.2 7.8’ 58.7’
SD.=16.3 d=0.4 S.D.=16.0
Tue GHA Dec GHA ν Dec d HP
0 17801.3 S2145.9 15324.9 8.4’ S1304.3 7.9’ 58.8’ 1 19301.0 45.5 16752.3 8.4’ 1256.4 8.0’ 58.8’ 2 20800.8 45.1 18219.7 8.5’ 1248.3 8.1’ 58.8’ 3 22300.5 · · 44.7 19647.2 8.5’ 1240.2 8.2’ 58.8’ 4 23800.3 44.3 21114.7 8.5’ 1232.0 8.2’ 58.8’ 5 25300.0 43.9 22542.3 8.5’ 1223.7 8.3’ 58.8’
6 26759.8 S2143.5 24009.8 8.6’ S1215.4 8.4’ 58.8’ 7 28259.6 43.1 25437.4 8.6’ 1206.9 8.5’ 58.9’ 8 29759.3 42.7 26905.0 8.6’ 1158.4 8.5’ 58.9’ 9 31259.1 · · 42.3 28332.6 8.6’ 1149.8 8.6’ 58.9’ 10 32758.8 41.9 29800.2 8.6’ 1141.2 8.7’ 58.9’ 11 34258.6 41.5 31227.9 8.7’ 1132.4 8.8’ 58.9’
12 35758.3 S2141.1 32655.6 8.7’ S1123.6 8.8’ 58.9’ 13 1258.1 40.7 34123.3 8.7’ 1114.8 8.9’ 58.9’ 14 2757.8 40.3 35551.0 8.7’ 1105.8 9.0’ 59.0’ 15 4257.6 · · 39.9 1018.7 8.8’ 1056.8 9.0’ 59.0’ 16 5757.4 39.5 2446.5 8.8’ 1047.7 9.1’ 59.0’ 17 7257.1 39.1 3914.3 8.8’ 1038.6 9.2’ 59.0’
18 8756.9 S2138.7 5342.1 8.8’ S1029.4 9.2’ 59.0’ 19 10256.6 38.3 6810.0 8.9’ 1020.1 9.3’ 59.0’ 20 11756.4 37.8 8237.8 8.9’ 1010.7 9.4’ 59.0’ 21 13256.1 · · 37.4 9705.7 8.9’ 1001.3 9.4’ 59.0’ 22 14755.9 37.0 11133.6 8.9’ 0951.9 9.5’ 59.0’ 23 16255.7 36.6 12601.6 8.9’ 0942.3 9.6’ 59.1’
SD.=16.3 d=0.4 S.D.=16.1
Lat. Twilight
N 72 08:10 10:10 14:07 16:06
N 70 07:54 09:30 14:46 16:22 68 07:41 09:03 10:55 13:21 15:13 16:35 66 07:30 08:42 10:06 14:10 15:34 16:46 64 07:20 08:26 09:35 14:41 15:50 16:56 62 07:12 08:12 09:12 15:04 16:04 17:04 60 07:05 08:00 08:54 15:22 16:16 17:11
N 58 06:58 07:49 08:39 15:37 16:26 17:17 56 06:53 07:40 08:26 15:50 16:35 17:23 54 06:47 07:32 08:15 16:01 16:44 17:29 52 06:42 07:25 08:05 16:11 16:51 17:34 50 06:38 07:18 07:56 16:20 16:58 17:38 45 06:27 07:04 07:37 16:39 17:12 17:49
N 40 06:18 06:51 07:21 16:54 17:24 17:58 35 06:09 06:41 07:08 17:07 17:35 18:06 30 06:01 06:31 06:57 17:19 17:45 18:14 20 05:46 06:14 06:37 17:38 18:02 18:29
N 10 05:32 05:58 06:20 17:55 18:18 18:44 0 05:16 05:42 06:04 18:11 18:34 19:00
S 10 04:58 05:25 05:48 18:28 18:50 19:17 20 04:37 05:06 05:30 18:45 19:09 19:38 30 04:10 04:43 05:10 19:06 19:32 20:05 35 03:53 04:29 04:58 19:17 19:47 20:22 40 03:31 04:12 04:44 19:31 20:03 20:43 45 03:04 03:51 04:27 19:48 20:24 21:11
S 50 02:24 03:24 04:07 20:08 20:50 21:50 52 02:02 03:11 03:57 20:18 21:04 22:12 54 01:31 02:55 03:46 20:29 21:19 22:42 56 00:25 02:36 03:33 20:41 21:38 23:39 58 02:12 03:18 20:56 22:01
S 60 01:39 03:01 21:13 22:34
Lat. Moonrise Moonset
N 72 11:08 10:56 10:48 13:58 16:04 18:04
N 70 10:15 10:24 10:29 14:50 16:35 18:22 68 09:42 10:01 10:13 15:23 16:57 18:37 66 09:17 09:43 10:00 15:47 17:14 18:48 64 08:58 09:28 09:50 16:05 17:29 18:58 62 08:43 09:15 09:41 16:20 17:40 19:06 60 08:30 09:05 09:33 16:33 17:50 19:13
N 58 08:19 08:55 09:26 16:44 17:59 19:19 56 08:09 08:47 09:20 16:53 18:07 19:25 54 08:00 08:40 09:14 17:02 18:14 19:30 52 07:52 08:34 09:09 17:09 18:20 19:34 50 07:45 08:28 09:05 17:16 18:25 19:38 45 07:30 08:15 08:55 17:30 18:37 19:47
N 40 07:18 08:04 08:47 17:42 18:47 19:54 35 07:08 07:55 08:40 17:52 18:55 20:00 30 06:58 07:47 08:34 18:01 19:02 20:05 20 06:42 07:34 08:23 18:16 19:15 20:14
N 10 06:28 07:22 08:13 18:29 19:26 20:22 0 06:15 07:10 08:04 18:42 19:36 20:30
S 10 06:02 06:59 07:56 18:54 19:46 20:37 20 05:48 06:47 07:46 19:07 19:57 20:45 30 05:33 06:33 07:35 19:22 20:09 20:54 35 05:23 06:25 07:29 19:30 20:16 20:59 40 05:13 06:16 07:22 19:40 20:24 21:05 45 05:00 06:05 07:13 19:51 20:34 21:12
S 50 04:45 05:52 07:03 20:05 20:45 21:20 52 04:38 05:46 06:59 20:12 20:50 21:23 54 04:30 05:39 06:53 20:19 20:56 21:27 56 04:21 05:32 06:48 20:27 21:02 21:32 58 04:11 05:23 06:41 20:35 21:09 21:37
S 60 04:00 05:14 06:34 20:46 21:17 21:42
Day
Sun Moon Eqn.of Time Mer. Mer.Pass. Age
00h 12h Pass Upper Lower 0-2 mm:ss mm:ss hh:mm