The Nautical Almanac 1916 Nautical Almanac.pdf · As he has said, "The art of celestial navigation should be promoted, not discouraged, even in the modern day". To both of these men

TheNauticalAlmanac.com

The Nautical Almanac 1916In memory of

Frank Arthur WorsleyThe Navigator who saved the Shackleton expedition

"We knew it would be the hardest thing we had ever undertaken, for the Antarctic winter had set in, and we were

about to cross one of the worst seas in the world"

Shackleton led the men...but Worsely saved them.

The Nautical Almanac for 1916

Contents

Topic Page

Credits, Acknowledgment and Disclaimer 3

About Frank Worsely & Shackleton 4-9

Explanation of The Daily Pages 10-14

Equation of Time curve 15

Formulas 16-18

Useful Links 19

The 1916 Daily Pages (The Nautical Almanac) 20-263

Increments & Corrections (The Yellow Pages) 264-283

Corrections for Dip, Refraction and Moon Parallax 284

Conversion of Arc to Time 285

USNO Navigational Star Chart 286

1916tocr.odt June 13, 2020

Acknowledgment and Credits

Dr. Enno Rodegerdts

The Nautical Almanac Daily Pages and Sun Almanacs found herein and on our site were createdor derived from PyAlmanac written by the great Norwegian sailor Enno Rodegerdts. PyAlmanacuses PyEphem to generate the almanacs and LaTex provides 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 nowfound in the following Daily Pages. Attending foremost to the accuracy of data and thenformatting Mr. Bauer modified PyAlmanac to provide a clear arrangement of figures needed forcelestial navigation. To that end his work was determined, tireless and efficient. In our mutualwriting 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 themodern 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 orany 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 2019 TheNauticalAlmanac.com

You are free to copy and distribute this document in its entirety but never sell it.

freely ye received, freely give

Words of Frank Worsley

Captain Worsley's comment about the The Nautical Almanac being ruined by the weather and sea during the desperate voyage to South Georgia island-

"The Nautical Almanac shed its pages so rapidly before the onslaught of the seas that it was a racewhether or not the month of May would last to South Georgia"

About Shackleton, Worsley and Crean's glissade on the eastern slope of the South Georgia island-

“We seemed to shoot into space. For a moment my hair stood on end. Then quite suddenly I felt a glowand knew that I was grinning. I was actually enjoying it. It was most exhilarating. We were shootingdown the side of an almost precipitous mountain at nearly a mile a minute. I yelled with excitementand found that Shackleton and Crean were yelling too. It seemed ridiculously safe. To hell with therocks!”

After making it to Stromness and physically recovering enough to meet some of the workers-

“In the evening the manager told Sir Ernest that a number of old captains and sailors wished to speakto and shake hands with him and us. We went into a large, low room, full of captains and mates andsailors, and hazy with tobacco smoke. Three or four white-haired veterans of the sea came forward;one spoke in Norse, and manager translated. He said he had been at sea over forty years; that he knewthis stormy Southern Ocean intimately, from South Georgia to Cape Horn, from Elephant Island to theSouth Orkneys, and that never had he heard of such a wonderful feat of daring seamanship as bringingthe twenty-two foot open boat from Elephant Island to South Georgia, and then to crown it, trampingacross the ice and snow and rocky heights of the interior,and that he felt it an honour to meet andshake hands with Sir Ernest and his comrades. He finished with a dramatic gesture: ‘These are men!’”

After arriving at Elephant Island to rescue all the crew members left there-

“Rescued! August 30, 1916. All well! At last! All ahead full.”

Worsley and all of these men were part of the glorious era called the Golden Age of Exploration.Bold and tough of character and strength, never quitting, never giving up- the essense ofEndurance.

By Endurance we Conquer

To Him, that Fourth Man, He that standeth closer than a brother!

...fair winds...clear skies and following seas

TheNauticalAlmanac.com

The James Caird and brave mariners departing Elephant Island April 24, 1916.The crew were- Ernest Shackleton, Frank Worsley,

Tom Crean, John Vincent, Timothy McCarthy, Harry McNish.

Visit The James Caird SocietyJamesCairdSociety.com

Frank Worsley's sextant, pocket chronometer, binoculars, stop watch.

‘Thomas Mercer’ marine chronometer (Ser No. 5229, boxed with transit case)Kelvin & James White Ltd. Compass

Frank Worsley's nautical almanac is now located at The South Georgia Museum, located at Grytviken, South Georgia Island

S 54° 16.9' W 036° 30.5'

Closer views of Frank Worsley's nautical almanac.

Navigation instruments used during the Voyage of the James Caird

From- http://www.sebcoulthard.com/navigational-instruments.html

• ‘Heath & Co.’ Hezzanith "endless tangent" sextant (Ser No. L777, borrowed by Lt. Frank Worsley RNR from Lt. Huberht Hudson RN, navigator onboard Endurance)

• ‘Thomas Mercer’ marine chronometer (Ser No. 5229, boxed with transit case)

• ‘S. Smith & Son’ pocket chronometer (hours, minutes, seconds indicated)

• 'Kelvin & James White Ltd', Pattern 182 Admiralty boat compass (gimballed, alcohol filled compass to prevent freezing). 360º markings with ¼ points)

• Pocket watch (of unknown origin or make)

• Brass bilge pump made from ‘Flinders’ bar casing.

• Binoculars (with leather pouch)

• Admiralty charts (South Polar Charts)

• Navigation daily assistant & Logarithm tables

• Nautical Almanac

• Blue print chart of South Georgia (produced by Zweite Deutsche Antarktisexpedition 1911-12)

• Log book, diaries, and a handful of Frank Hurley photographic prints

• Boxed aneroid (unknown make, never used during the voyage of the James Caird according to Worsley)

http://sextantbook.com/2011/12/10/heath-and-companys-best-vernier-sextant/http://en.wikipedia.org/wiki/Manometer#Aneroidhttps://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCcQFjABahUKEwjo35TE5dTIAhWGAxoKHXlNBPU&url=https%3A%2F%2Fde.wikipedia.org%2Fwiki%2FZweite_Deutsche_Antarktisexpedition&usg=AFQjCNHUuq3kiZ_T1JPfTx3gPAaAh0RDOwhttp://www.jamescairdsociety.com/shackleton-news-108321.htmhttp://en.wikipedia.org/wiki/Admiralty_charthttp://www.davey.co.uk/pdf/pumps.pdfhttp://www.spri.cam.ac.uk/library/archives/shackleton/articles/N:_1054.htmlhttp://en.wikipedia.org/wiki/Gimbalhttp://en.wikipedia.org/wiki/Compasshttp://www.compassmuseum.com/images/nautical/dent_182_side_gr.jpghttp://www.spri.cam.ac.uk/library/archives/shackleton/articles/N:_999a.htmlhttp://en.wikipedia.org/wiki/Marine_chronometerhttp://www.thomasmercer.com/

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 timeof 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.

9SD- 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.

11SD- 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*

see notesat bottom

(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*

see notesat bottom

(morning) Twilight- Civil- the approximate GMT/UT of morning civil twilight starts when the geometric center of the sun is 6° below the horizon.


17*

see notesat bottom

Sunrise- the approximate GMT/UT when the Sun is 0° 50' (semi-diameter plus refraction) below the horizon.



17*

see notesat bottom

Sunset- the approximate GMT/UT when the Sun is 0° 50' (semi-diameter plus refraction) below the horizon.


17*

see notesat 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.


17*

see notesat bottom

(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.


18*

see notesat 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 notesat 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) andcan be condsidered as approximate LMT (Local Mean Time) with a tolerance of +/- 30 minutes depending on where you are within a time zone.

June 16, 2020

Explanation of The Nautical Almanac Daily Pages updated.odt


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www.TheNauticalAlmanac.comfile date- June 16 2020

2020 J anuary 01 to J an. 03h Sun Moon

Wed GHA Dec GHA ν Dec d HP0 179◦13.7 S23◦03.5 110◦56.9 15.3’ S09◦58.5 10.7’ 54.3’1 194◦13.4 03.3 125◦31.3 15.4’ 09◦47.8 10.7’ 54.3’2 209◦13.1 03.1 140◦05.7 15.4’ 09◦37.1 10.7’ 54.3’3 224◦12.8 · · 03.0 154◦40.1 15.5’ 09◦26.3 10.8’ 54.3’4 239◦12.5 02.8 169◦14.6 15.5’ 09◦15.5 10.8’ 54.3’5 254◦12.2 02.6 183◦49.1 15.5’ 09◦04.7 10.8’ 54.2’6 269◦11.9 S23◦02.4 198◦23.6 15.6’ S08◦53.8 10.9’ 54.2’7 284◦11.6 02.2 212◦58.2 15.6’ 08◦42.9 10.9’ 54.2’8 299◦11.3 02.0 227◦32.8 15.6’ 08◦32.0 10.9’ 54.2’9 314◦11.0 · · 01.8 242◦07.5 15.7’ 08◦21.0 11.0’ 54.2’10 329◦10.7 01.6 256◦42.2 15.7’ 08◦10.0 11.0’ 54.2’11 344◦10.4 01.4 271◦16.9 15.7’ 07◦59.0 11.0’ 54.2’12 359◦10.1 S23◦01.2 285◦51.7 15.8’ S07◦48.0 11.1’ 54.2’13 14◦09.8 01.0 300◦26.4 15.8’ 07◦36.9 11.1’ 54.2’14 29◦09.5 00.8 315◦01.2 15.8’ 07◦25.8 11.1’ 54.2’15 44◦09.2 · · 00.6 329◦36.1 15.9’ 07◦14.7 11.1’ 54.2’16 59◦08.9 00.4 344◦10.9 15.9’ 07◦03.5 11.2’ 54.2’17 74◦08.6 00.2 358◦45.8 15.9’ 06◦52.3 11.2’ 54.2’18 89◦08.3 S23◦00.0 13◦20.7 15.9’ S06◦41.1 11.2’ 54.2’19 104◦08.0 22◦59.7 27◦55.7 16.0’ 06◦29.9 11.2’ 54.2’20 119◦07.7 59.5 42◦30.7 16.0’ 06◦18.7 11.3’ 54.2’21 134◦07.5 · · 59.3 57◦05.6 16.0’ 06◦07.4 11.3’ 54.2’22 149◦07.2 59.1 71◦40.6 16.0’ 05◦56.1 11.3’ 54.2’23 164◦06.9 58.9 86◦15.7 16.0’ 05◦44.8 11.3’ 54.2’

SD.=16.3 d=0.2 S.D.=14.8Thu GHA Dec GHA ν Dec d HP0 179◦06.6 S22◦58.7 100◦50.7 16.1’ S05◦33.4 11.3’ 54.2’1 194◦06.3 58.5 115◦25.8 16.1’ 05◦22.1 11.4’ 54.2’2 209◦06.0 58.3 130◦00.9 16.1’ 05◦10.7 11.4’ 54.2’3 224◦05.7 · · 58.1 144◦36.0 16.1’ 04◦59.3 11.4’ 54.2’4 239◦05.4 57.9 159◦11.1 16.1’ 04◦47.9 11.4’ 54.2’5 254◦05.1 57.6 173◦46.3 16.1’ 04◦36.5 11.4’ 54.2’6 269◦04.8 S22◦57.4 188◦21.4 16.2’ S04◦25.0 11.5’ 54.2’7 284◦04.5 57.2 202◦56.6 16.2’ 04◦13.5 11.5’ 54.2’8 299◦04.2 57.0 217◦31.7 16.2’ 04◦02.1 11.5’ 54.2’9 314◦03.9 · · 56.8 232◦06.9 16.2’ 03◦50.6 11.5’ 54.2’10 329◦03.6 56.6 246◦42.1 16.2’ 03◦39.0 11.5’ 54.2’11 344◦03.3 56.3 261◦17.3 16.2’ 03◦27.5 11.5’ 54.2’12 359◦03.0 S22◦56.1 275◦52.6 16.2’ S03◦16.0 11.5’ 54.2’13 14◦02.8 55.9 290◦27.8 16.2’ 03◦04.4 11.6’ 54.2’14 29◦02.5 55.7 305◦03.0 16.2’ 02◦52.8 11.6’ 54.2’15 44◦02.2 · · 55.5 319◦38.3 16.2’ 02◦41.3 11.6’ 54.2’16 59◦01.9 55.2 334◦13.5 16.2’ 02◦29.7 11.6’ 54.2’17 74◦01.6 55.0 348◦48.8 16.3’ 02◦18.1 11.6’ 54.2’18 89◦01.3 S22◦54.8 3◦24.0 16.3’ S02◦06.5 11.6’ 54.2’19 104◦01.0 54.6 17◦59.3 16.3’ 01◦54.8 11.6’ 54.2’20 119◦00.7 54.3 32◦34.5 16.3’ 01◦43.2 11.6’ 54.2’21 134◦00.4 · · 54.1 47◦09.8 16.3’ 01◦31.6 11.6’ 54.2’22 149◦00.1 53.9 61◦45.0 16.3’ 01◦19.9 11.7’ 54.2’23 163◦59.8 53.7 76◦20.3 16.3’ 01◦08.2 11.7’ 54.3’

SD.=16.3 d=0.2 S.D.=14.8Fri GHA Dec GHA ν Dec d HP0 178◦59.5 S22◦53.4 90◦55.5 16.2’ S00◦56.6 11.7’ 54.3’1 193◦59.3 53.2 105◦30.8 16.2’ 00◦44.9 11.7’ 54.3’2 208◦59.0 53.0 120◦06.0 16.2’ 00◦33.2 11.7’ 54.3’3 223◦58.7 · · 52.7 134◦41.3 16.2’ 00◦21.5 11.7’ 54.3’4 238◦58.4 52.5 149◦16.5 16.2’ S00◦09.9 11.7’ 54.3’5 253◦58.1 52.3 163◦51.7 16.2’ N00◦01.8 11.7’ 54.3’6 268◦57.8 S22◦52.0 178◦26.9 16.2’ N00◦13.5 11.7’ 54.3’7 283◦57.5 51.8 193◦02.1 16.2’ 00◦25.2 11.7’ 54.3’8 298◦57.2 51.6 207◦37.3 16.2’ 00◦36.9 11.7’ 54.3’9 313◦56.9 · · 51.3 222◦12.5 16.2’ 00◦48.6 11.7’ 54.3’10 328◦56.6 51.1 236◦47.7 16.2’ 01◦00.3 11.7’ 54.3’11 343◦56.4 50.8 251◦22.8 16.1’ 01◦12.0 11.7’ 54.4’12 358◦56.1 S22◦50.6 265◦58.0 16.1’ N01◦23.7 11.7’ 54.4’13 13◦55.8 50.4 280◦33.1 16.1’ 01◦35.4 11.7’ 54.4’14 28◦55.5 50.1 295◦08.2 16.1’ 01◦47.1 11.7’ 54.4’15 43◦55.2 · · 49.9 309◦43.3 16.1’ 01◦58.8 11.7’ 54.4’16 58◦54.9 49.6 324◦18.4 16.1’ 02◦10.5 11.7’ 54.4’17 73◦54.6 49.4 338◦53.4 16.0’ 02◦22.2 11.7’ 54.4’18 88◦54.3 S22◦49.2 353◦28.4 16.0’ N02◦33.9 11.7’ 54.4’19 103◦54.0 48.9 8◦03.5 16.0’ 02◦45.6 11.7’ 54.4’20 118◦53.8 48.7 22◦38.4 16.0’ 02◦57.3 11.7’ 54.5’21 133◦53.5 · · 48.4 37◦13.4 16.0’ 03◦09.0 11.7’ 54.5’22 148◦53.2 48.2 51◦48.4 15.9’ 03◦20.6 11.7’ 54.5’23 163◦52.9 47.9 66◦23.3 15.9’ 03◦32.3 11.7’ 54.5’

SD.=16.3 d=0.2 S.D.=14.8

Lat. Twilight Sunrise Sunset TwilightNaut. Civil Civil Naut.N 72◦ 08:23 10:41 13:27 15:45N 70◦ 08:05 09:49 14:19 16:0368◦ 07:50 09:16 14:52 16:1866◦ 07:37 08:53 10:27 13:41 15:15 16:3164◦ 07:26 08:34 09:49 14:19 15:34 16:4162◦ 07:17 08:18 09:23 14:45 15:49 16:5160◦ 07:09 08:05 09:02 15:06 16:02 16:59

N 58◦ 07:02 07:54 08:45 15:23 16:14 17:0656◦ 06:56 07:44 08:31 15:37 16:24 17:1254◦ 06:50 07:35 08:19 15:49 16:32 17:1852◦ 06:44 07:28 08:08 16:00 16:40 17:2450◦ 06:39 07:20 07:58 16:09 16:47 17:2945◦ 06:28 07:05 07:38 16:29 17:03 17:40

N 40◦ 06:18 06:52 07:22 16:46 17:16 17:5035◦ 06:08 06:40 07:08 17:00 17:28 17:5930◦ 06:00 06:30 06:56 17:12 17:38 18:0820◦ 05:44 06:11 06:35 17:32 17:56 18:24

N 10◦ 05:28 05:54 06:17 17:50 18:13 18:400◦ 05:11 05:38 06:00 18:08 18:30 18:56

S 10◦ 04:53 05:20 05:43 18:25 18:48 19:1520◦ 04:31 05:00 05:24 18:43 19:08 19:3730◦ 04:02 04:35 05:03 19:05 19:32 20:0535◦ 03:44 04:20 04:50 19:17 19:47 20:2340◦ 03:21 04:03 04:35 19:32 20:05 20:4645◦ 02:52 03:41 04:18 19:50 20:27 21:15

S 50◦ 02:08 03:12 03:56 20:11 20:55 21:5952◦ 01:42 02:57 03:45 20:22 21:10 22:2454◦ 01:02 02:40 03:33 20:34 21:27 23:0356◦ 02:19 03:20 20:47 21:4858◦ 01:51 03:03 21:04 22:15

S 60◦ 01:08 02:44 21:23 22:58

Lat. Moonrise MoonsetWed Thu Fri Wed Thu FriN 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 –:– 00:0052◦ 10:12 11:18 12:25 23:45 –:– 00:0154◦ 10:08 11:17 12:25 23:47 –:– 00:0156◦ 10:05 11:15 12:26 23:49 –:– 00:0158◦ 10:01 11:14 12:27 23:52 –:– 00:02

S 60◦ 09:56 11:12 12:28 23:55 –:– 00:02

DaySun Moon

Eqn.of Time Mer. Mer.Pass. Age00h 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 04:4402 03:34 03:48 12:04 17:46 05:2603 04:02 04:16 12:04 18:27 06:06

3

1

117

18

103 119

3 12

13 14 15 16

www.TheNauticalAlmanac.comfile date- June 16 2020

Equation_of_Time_Curve.odt

Equation of Timefor the Sun

Tim

e in

min

u tes

Sun

is r

un n

ing

Sl o

w

Sun

is r

unn

ing

Fas

t

-20

-16

-12

-8

-4

0

4

8

12

16

20

January February March April May June July August September October November December

Celestial Navigation useful Formulas

About Calculators

The Casio fx-300ES Plus is an inexpensive calculator at about 11 USD. It features natural input soyou enter a formula just as it would be written on paper. Entering degrees, minutes and seconds isvery simple. The Casio fx-300ES Plus has 9 memory locations and you can review many of theprevious 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 ofLongitude (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 highestwhole degree figure then adding the DR. Longitude to GHA to obtain LHA. Only add the wholedegree DR. Longitude figure to the rounded up whole degree GHA figure. If the resulting LHAfigure 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 alot of printed out pages of Latitudes from Pub. No. 249 and Pub. No. 229. Pub. No. 249 Vol. 2 & 3don't cover any declination greater than 29 degrees so you'd have to use Pub. No. 229 which isextremely 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)

3- Latitude and declination Contrary name:

Latitude= (90o – Ho) – Declination

To get AP longitude (needed for plotting the LOP)

In Western longitudes

Combine the DR Longitude figure with only the minutes (of arc) of the total GHA figure. The Ap λfigure 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 seasTheNauticalAlmanac.com

Formula Sheet added to NA.odt

Useful Information

Time Signals- by telephone

WWV 303-499-7111 WWVH 808-335-4363

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

Pub. No. 249 Download individual Latitudes or Volumes

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

Sight Reduction Forms & Methods

https://www.TheNauticalAlmanac.com/Methods.html

Time Signals and Links.odt

https://TheNauticalAlmanac.com/Pub.%20No.%20229.htmlhttps://TheNauticalAlmanac.com/Pub.%20No.%20249.htmlhttps://TheNauticalAlmanac.com/TerrestrialAlmanac.html

January 01, 02, 03 (Sat., Sun., Mon.)

Aries Venus Mars Jupiter SaturnSat GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 99◦19.5 150◦04.9 S20◦20.0 306◦07.8 N14◦49.1 105◦59.5 S04◦14.7 354◦53.4 N22◦17.81 114◦21.9 165◦04.1 19.2 321◦10.2 49.2 121◦01.7 14.5 9◦56.1 17.82 129◦24.4 180◦03.4 18.5 336◦12.6 49.3 136◦03.8 14.4 24◦58.8 17.83 144◦26.9 195◦02.7 · · 17.7 351◦15.1 · · 49.4 151◦05.9 · · 14.2 40◦01.5 · · 17.84 159◦29.3 210◦01.9 16.9 6◦17.5 49.5 166◦08.1 14.1 55◦04.1 17.95 174◦31.8 225◦01.2 16.2 21◦19.9 49.6 181◦10.2 13.9 70◦06.8 17.9

6 189◦34.3 240◦00.4 S20◦15.4 36◦22.4 N14◦49.7 196◦12.3 S04◦13.8 85◦09.5 N22◦17.97 204◦36.7 254◦59.7 14.6 51◦24.8 49.8 211◦14.5 13.6 100◦12.2 17.98 219◦39.2 269◦59.0 13.8 66◦27.3 49.9 226◦16.6 13.5 115◦14.9 18.09 234◦41.7 284◦58.2 · · 13.1 81◦29.7 · · 50.0 241◦18.7 · · 13.3 130◦17.6 · · 18.010 249◦44.1 299◦57.5 12.3 96◦32.1 50.1 256◦20.9 13.2 145◦20.3 18.011 264◦46.6 314◦56.8 11.5 111◦34.6 50.2 271◦23.0 13.0 160◦22.9 18.0

12 279◦49.0 329◦56.0 S20◦10.7 126◦37.0 N14◦50.3 286◦25.1 S04◦12.9 175◦25.6 N22◦18.113 294◦51.5 344◦55.3 10.0 141◦39.5 50.4 301◦27.3 12.7 190◦28.3 18.114 309◦54.0 359◦54.5 09.2 156◦41.9 50.5 316◦29.4 12.6 205◦31.0 18.115 324◦56.4 14◦53.8 · · 08.4 171◦44.4 · · 50.6 331◦31.6 · · 12.4 220◦33.7 · · 18.116 339◦58.9 29◦53.1 07.6 186◦46.8 50.7 346◦33.7 12.3 235◦36.4 18.217 355◦01.4 44◦52.3 06.8 201◦49.3 50.8 1◦35.8 12.1 250◦39.1 18.2

18 10◦03.8 59◦51.6 S20◦06.1 216◦51.7 N14◦50.9 16◦38.0 S04◦12.0 265◦41.7 N22◦18.219 25◦06.3 74◦50.9 05.3 231◦54.2 51.0 31◦40.1 11.8 280◦44.4 18.220 40◦08.8 89◦50.2 04.5 246◦56.6 51.1 46◦42.2 11.7 295◦47.1 18.321 55◦11.2 104◦49.4 · · 03.7 261◦59.1 · · 51.2 61◦44.4 · · 11.5 310◦49.8 · · 18.322 70◦13.7 119◦48.7 02.9 277◦01.6 51.3 76◦46.5 11.4 325◦52.5 18.323 85◦16.1 134◦48.0 02.1 292◦04.0 51.4 91◦48.6 11.2 340◦55.2 18.3

Mer.pass.:17:19 v-0.7 d0.8 m-3.8 v2.4 d0.1 m-0.4 v2.1 d0.1 m-2.2 v2.7 d0.0 m-0.4

Sun GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 100◦18.6 149◦47.2 S20◦01.3 307◦06.5 N14◦51.5 106◦50.8 S04◦11.1 355◦57.9 N22◦18.31 115◦21.1 164◦46.5 20◦00.5 322◦08.9 51.6 121◦52.9 10.9 11◦00.5 18.42 130◦23.5 179◦45.8 19◦59.7 337◦11.4 51.7 136◦55.0 10.8 26◦03.2 18.43 145◦26.0 194◦45.0 · · 58.9 352◦13.9 · · 51.8 151◦57.1 · · 10.6 41◦05.9 · · 18.44 160◦28.5 209◦44.3 58.2 7◦16.3 51.9 166◦59.3 10.5 56◦08.6 18.45 175◦30.9 224◦43.6 57.4 22◦18.8 52.0 182◦01.4 10.3 71◦11.3 18.5

6 190◦33.4 239◦42.9 S19◦56.6 37◦21.3 N14◦52.1 197◦03.5 S04◦10.2 86◦14.0 N22◦18.57 205◦35.9 254◦42.1 55.8 52◦23.7 52.2 212◦05.7 10.0 101◦16.7 18.58 220◦38.3 269◦41.4 55.0 67◦26.2 52.3 227◦07.8 09.9 116◦19.3 18.59 235◦40.8 284◦40.7 · · 54.2 82◦28.7 · · 52.4 242◦09.9 · · 09.7 131◦22.0 · · 18.610 250◦43.3 299◦40.0 53.4 97◦31.2 52.5 257◦12.1 09.5 146◦24.7 18.611 265◦45.7 314◦39.2 52.6 112◦33.6 52.6 272◦14.2 09.4 161◦27.4 18.6

12 280◦48.2 329◦38.5 S19◦51.8 127◦36.1 N14◦52.7 287◦16.3 S04◦09.2 176◦30.1 N22◦18.613 295◦50.6 344◦37.8 51.0 142◦38.6 52.9 302◦18.5 09.1 191◦32.8 18.714 310◦53.1 359◦37.1 50.2 157◦41.1 53.0 317◦20.6 08.9 206◦35.5 18.715 325◦55.6 14◦36.4 · · 49.4 172◦43.6 · · 53.1 332◦22.7 · · 08.8 221◦38.1 · · 18.716 340◦58.0 29◦35.6 48.5 187◦46.0 53.2 347◦24.8 08.6 236◦40.8 18.717 356◦00.5 44◦34.9 47.7 202◦48.5 53.3 2◦27.0 08.5 251◦43.5 18.8

18 11◦03.0 59◦34.2 S19◦46.9 217◦51.0 N14◦53.4 17◦29.1 S04◦08.3 266◦46.2 N22◦18.819 26◦05.4 74◦33.5 46.1 232◦53.5 53.5 32◦31.2 08.2 281◦48.9 18.820 41◦07.9 89◦32.8 45.3 247◦56.0 53.6 47◦33.4 08.0 296◦51.6 18.821 56◦10.4 104◦32.1 · · 44.5 262◦58.5 · · 53.7 62◦35.5 · · 07.9 311◦54.3 · · 18.922 71◦12.8 119◦31.3 43.7 278◦01.0 53.9 77◦37.6 07.7 326◦56.9 18.923 86◦15.3 134◦30.6 42.9 293◦03.4 54.0 92◦39.7 07.6 341◦59.6 18.9


Mon GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 101◦17.8 149◦29.9 S19◦42.1 308◦05.9 N14◦54.1 107◦41.9 S04◦07.4 357◦02.3 N22◦18.91 116◦20.2 164◦29.2 41.3 323◦08.4 54.2 122◦44.0 07.2 12◦05.0 19.02 131◦22.7 179◦28.5 40.4 338◦10.9 54.3 137◦46.1 07.1 27◦07.7 19.03 146◦25.1 194◦27.8 · · 39.6 353◦13.4 · · 54.4 152◦48.2 · · 06.9 42◦10.4 · · 19.04 161◦27.6 209◦27.0 38.8 8◦15.9 54.6 167◦50.4 06.8 57◦13.1 19.05 176◦30.1 224◦26.3 38.0 23◦18.4 54.7 182◦52.5 06.6 72◦15.7 19.1

6 191◦32.5 239◦25.6 S19◦37.2 38◦20.9 N14◦54.8 197◦54.6 S04◦06.5 87◦18.4 N22◦19.17 206◦35.0 254◦24.9 36.3 53◦23.4 54.9 212◦56.7 06.3 102◦21.1 19.18 221◦37.5 269◦24.2 35.5 68◦25.9 55.0 227◦58.9 06.2 117◦23.8 19.19 236◦39.9 284◦23.5 · · 34.7 83◦28.4 · · 55.1 243◦01.0 · · 06.0 132◦26.5 · · 19.210 251◦42.4 299◦22.8 33.9 98◦30.9 55.3 258◦03.1 05.9 147◦29.2 19.211 266◦44.9 314◦22.1 33.1 113◦33.4 55.4 273◦05.2 05.7 162◦31.9 19.2

12 281◦47.3 329◦21.4 S19◦32.2 128◦36.0 N14◦55.5 288◦07.4 S04◦05.5 177◦34.6 N22◦19.213 296◦49.8 344◦20.7 31.4 143◦38.5 55.6 303◦09.5 05.4 192◦37.2 19.314 311◦52.3 359◦20.0 30.6 158◦41.0 55.7 318◦11.6 05.2 207◦39.9 19.315 326◦54.7 14◦19.2 · · 29.7 173◦43.5 · · 55.9 333◦13.7 · · 05.1 222◦42.6 · · 19.316 341◦57.2 29◦18.5 28.9 188◦46.0 56.0 348◦15.9 04.9 237◦45.3 19.317 356◦59.6 44◦17.8 28.1 203◦48.5 56.1 3◦18.0 04.8 252◦48.0 19.4

18 12◦02.1 59◦17.1 S19◦27.3 218◦51.0 N14◦56.2 18◦20.1 S04◦04.6 267◦50.7 N22◦19.419 27◦04.6 74◦16.4 26.4 233◦53.6 56.4 33◦22.2 04.5 282◦53.4 19.420 42◦07.0 89◦15.7 25.6 248◦56.1 56.5 48◦24.4 04.3 297◦56.0 19.421 57◦09.5 104◦15.0 · · 24.8 263◦58.6 · · 56.6 63◦26.5 · · 04.1 312◦58.7 · · 19.522 72◦12.0 119◦14.3 23.9 279◦01.1 56.7 78◦28.6 04.0 328◦01.4 19.523 87◦14.4 134◦13.6 23.1 294◦03.6 56.9 93◦30.7 03.8 343◦04.1 19.5


StarsSHA Dec

Alpheratz 358◦59.3 28◦37.8Ankaa 354◦27.8 -42◦45.9

Schedar 351◦04.0 56◦05.0Diphda 350◦09.2 -18◦26.9

Achernar 336◦20.7 -57◦40.0Hamal 329◦23.2 23◦04.2Polaris 337◦32.5 88◦51.9Acamar 316◦13.4 -40◦38.5Menkar 315◦31.3 3◦45.8Mirfak 310◦24.7 49◦34.1

Aldebaran 292◦13.0 16◦20.6Rigel 282◦22.0 -8◦17.8

Capella 282◦22.1 45◦55.0Bellatrix 279◦50.1 6◦16.6Elnath 279◦44.7 28◦32.4Alnilam 277◦00.2 -1◦15.2

Betelgeuse 272◦20.1 7◦23.6Canopus 264◦28.1 -52◦38.9

Sirius 259◦37.8 -16◦35.9Adhara 256◦09.6 -28◦51.4Procyon 246◦15.9 5◦26.5Pollux 244◦56.7 28◦13.8Avior 234◦47.5 -59◦14.2Suhail 223◦46.0 -43◦05.5

Miaplacidus 221◦55.1 -69◦22.1Alphard 219◦07.7 -8◦17.6Regulus 209◦01.1 12◦22.6Dubhe 195◦20.9 62◦11.9

Denebola 183◦48.1 15◦02.3Gienah 177◦07.5 -17◦04.5Acrux 174◦31.1 -62◦37.8

Gacrux 173◦22.4 -56◦38.4Alioth 167◦24.7 56◦24.5Spica 159◦48.4 -10◦43.5Alkaid 153◦56.4 49◦43.6Hadar 150◦31.8 -59◦58.0

Menkent 149◦34.0 -35◦57.4Arcturus 147◦02.5 19◦36.9

Rigil Kent. 141◦31.6 -60◦28.9Kochab 137◦16.4 74◦29.5

Zuben’ubi 138◦26.6 -15◦41.7Alphecca 127◦13.1 26◦59.5Antares 113◦56.3 -26◦14.8

Atria 110◦04.1 -68◦52.5Sabik 103◦36.7 -15◦37.4

Shaula 98◦01.6 -37◦02.7Rasalhague 97◦14.6 12◦37.1

Eltanin 91◦20.6 51◦29.7Kaus Aust. 85◦21.2 -34◦25.6

Vega 81◦28.9 38◦42.2Nunki 77◦29.3 -26◦24.2Altair 63◦19.9 8◦38.7

Peacock 55◦15.0 -57◦00.5Deneb 50◦21.8 44◦58.9

Enif 34◦59.2 9◦29.4Al Na’ir 29◦15.8 -47◦22.3

Fomalhaut 16◦44.7 -30◦04.2Scheat 15◦04.5 27◦37.8Markab 14◦51.3 14◦45.3

Jan 01 Sat SHA Mer.passVenus 50◦45.4 14:00Mars 206◦48.3 03:35

Jupiter 6◦40.0 16:54Saturn 255◦33.9 00:20

Jan 02 Sun SHA Mer.passVenus 49◦28.6 14:02Mars 206◦47.9 03:31

Jupiter 6◦32.1 16:50Saturn 255◦39.2 00:16

Jan 03 Mon SHA Mer.passVenus 48◦12.1 14:03Mars 206◦48.2 03:27

Jupiter 6◦24.1 16:47Saturn 255◦44.6 00:12

Horizontal parallaxVenus: 0.1Mars: 0.2

2

1916 January 01 to Jan. 03

h Sun MoonSat GHA Dec GHA ν Dec d HP

0 179◦15.8 S23◦07.8 242◦48.0 7.4’ S19◦59.2 -11.3’ 59.5’1 194◦15.5 07.6 257◦14.3 7.3’ 20◦10.5 -11.2’ 59.6’2 209◦15.2 07.4 271◦40.6 7.2’ 20◦21.7 -11.1’ 59.6’3 224◦14.9 · · 07.2 286◦06.7 7.0’ 20◦32.8 -11.0’ 59.6’4 239◦14.6 07.1 300◦32.6 6.9’ 20◦43.7 -10.9’ 59.7’5 254◦14.3 06.9 314◦58.4 6.8’ 20◦54.6 -10.8’ 59.7’

6 269◦14.0 S23◦06.7 329◦24.1 6.6’ S21◦05.3 -10.7’ 59.7’7 284◦13.7 06.5 343◦49.7 6.5’ 21◦15.9 -10.5’ 59.8’8 299◦13.4 06.3 358◦15.1 6.4’ 21◦26.4 -10.4’ 59.8’9 314◦13.1 · · 06.1 12◦40.4 6.2’ 21◦36.8 -10.3’ 59.8’10 329◦12.8 06.0 27◦05.6 6.1’ 21◦47.0 -10.2’ 59.9’11 344◦12.5 05.8 41◦30.6 6.0’ 21◦57.1 -10.0’ 59.9’

12 359◦12.2 S23◦05.6 55◦55.5 5.8’ S22◦07.1 -9.9’ 59.9’13 14◦11.9 05.4 70◦20.3 5.7’ 22◦16.9 -9.8’ 60.0’14 29◦11.6 05.2 84◦44.9 5.6’ 22◦26.6 -9.6’ 60.0’15 44◦11.3 · · 05.0 99◦09.4 5.4’ 22◦36.2 -9.5’ 60.0’16 59◦11.1 04.8 113◦33.8 5.3’ 22◦45.7 -9.4’ 60.1’17 74◦10.8 04.6 127◦58.0 5.2’ 22◦55.0 -9.2’ 60.1’

18 89◦10.5 S23◦04.4 142◦22.1 5.0’ S23◦04.1 -9.1’ 60.1’19 104◦10.2 04.3 156◦46.1 4.9’ 23◦13.1 -8.9’ 60.2’20 119◦09.9 04.1 171◦09.9 4.8’ 23◦22.0 -8.8’ 60.2’21 134◦09.6 · · 03.9 185◦33.6 4.7’ 23◦30.7 -8.6’ 60.2’22 149◦09.3 03.7 199◦57.2 4.5’ 23◦39.3 -8.5’ 60.3’23 164◦09.0 03.5 214◦20.7 4.4’ 23◦47.7 -8.3’ 60.3’

SD.=16.3 d=0.2 S.D.=16.2

Sun GHA Dec GHA ν Dec d HP

0 179◦08.7 S23◦03.3 228◦44.0 4.3’ S23◦55.9 -8.2’ 60.3’1 194◦08.4 03.1 243◦07.2 4.1’ 24◦04.0 -8.0’ 60.3’2 209◦08.1 02.9 257◦30.3 4.0’ 24◦12.0 -7.9’ 60.4’3 224◦07.8 · · 02.7 271◦53.3 3.9’ 24◦19.7 -7.7’ 60.4’4 239◦07.5 02.5 286◦16.1 3.8’ 24◦27.4 -7.5’ 60.4’5 254◦07.2 02.3 300◦38.8 3.7’ 24◦34.8 -7.4’ 60.5’

6 269◦06.9 S23◦02.1 315◦01.5 3.5’ S24◦42.1 -7.2’ 60.5’7 284◦06.6 01.9 329◦23.9 3.4’ 24◦49.2 -7.0’ 60.5’8 299◦06.3 01.7 343◦46.3 3.3’ 24◦56.2 -6.9’ 60.5’9 314◦06.0 · · 01.5 358◦08.6 3.2’ 25◦02.9 -6.7’ 60.6’10 329◦05.7 01.3 12◦30.7 3.1’ 25◦09.5 -6.5’ 60.6’11 344◦05.4 01.1 26◦52.8 3.0’ 25◦15.9 -6.3’ 60.6’

12 359◦05.1 S23◦00.9 41◦14.7 2.9’ S25◦22.2 -6.2’ 60.7’13 14◦04.8 00.7 55◦36.5 2.8’ 25◦28.2 -6.0’ 60.7’14 29◦04.5 00.5 69◦58.2 2.7’ 25◦34.1 -5.8’ 60.7’15 44◦04.2 · · 00.2 84◦19.9 2.6’ 25◦39.8 -5.6’ 60.7’16 59◦03.9 23◦00.0 98◦41.4 2.5’ 25◦45.3 -5.4’ 60.8’17 74◦03.6 22◦59.8 113◦02.8 2.4’ 25◦50.7 -5.2’ 60.8’

18 89◦03.3 S22◦59.6 127◦24.1 2.3’ S25◦55.8 -5.0’ 60.8’19 104◦03.0 59.4 141◦45.4 2.2’ 26◦00.7 -4.9’ 60.8’20 119◦02.7 59.2 156◦06.5 2.1’ 26◦05.5 -4.7’ 60.8’21 134◦02.4 · · 59.0 170◦27.5 2.0’ 26◦10.1 -4.5’ 60.9’22 149◦02.1 58.8 184◦48.5 1.9’ 26◦14.4 -4.3’ 60.9’23 164◦01.8 58.5 199◦09.4 1.8’ 26◦18.6 -4.1’ 60.9’

SD.=16.3 d=0.2 S.D.=16.5

Mon GHA Dec GHA ν Dec d HP

0 179◦01.5 S22◦58.3 213◦30.2 1.8’ S26◦22.6 -3.9’ 60.9’1 194◦01.3 58.1 227◦50.9 1.7’ 26◦26.3 -3.7’ 61.0’2 209◦01.0 57.9 242◦11.6 1.6’ 26◦29.9 -3.5’ 61.0’3 224◦00.7 · · 57.7 256◦32.2 1.5’ 26◦33.3 -3.3’ 61.0’4 239◦00.4 57.5 270◦52.7 1.5’ 26◦36.5 -3.1’ 61.0’5 254◦00.1 57.2 285◦13.1 1.4’ 26◦39.4 -2.9’ 61.0’

6 268◦59.8 S22◦57.0 299◦33.5 1.4’ S26◦42.2 -2.7’ 61.0’7 283◦59.5 56.8 313◦53.8 1.3’ 26◦44.7 -2.5’ 61.1’8 298◦59.2 56.6 328◦14.1 1.2’ 26◦47.1 -2.2’ 61.1’9 313◦58.9 · · 56.4 342◦34.3 1.2’ 26◦49.2 -2.0’ 61.1’10 328◦58.6 56.1 356◦54.4 1.1’ 26◦51.2 -1.8’ 61.1’11 343◦58.3 55.9 11◦14.6 1.1’ 26◦52.9 -1.6’ 61.1’

12 358◦58.0 S22◦55.7 25◦34.6 1.0’ S26◦54.4 -1.4’ 61.1’13 13◦57.7 55.5 39◦54.7 1.0’ 26◦55.7 -1.2’ 61.2’14 28◦57.4 55.2 54◦14.7 1.0’ 26◦56.8 -1.0’ 61.2’15 43◦57.1 · · 55.0 68◦34.6 0.9’ 26◦57.7 -0.8’ 61.2’16 58◦56.8 54.8 82◦54.5 0.9’ 26◦58.4 -0.6’ 61.2’17 73◦56.6 54.6 97◦14.4 0.9’ 26◦58.8 -0.4’ 61.2’

18 88◦56.3 S22◦54.3 111◦34.3 0.9’ S26◦59.1 -0.1’ 61.2’19 103◦56.0 54.1 125◦54.2 0.8’ 26◦59.1 0.1’ 61.2’20 118◦55.7 53.9 140◦14.0 0.8’ 26◦58.9 0.3’ 61.2’21 133◦55.4 · · 53.6 154◦33.8 0.8’ 26◦58.5 0.5’ 61.3’22 148◦55.1 53.4 168◦53.7 0.8’ 26◦57.9 0.7’ 61.3’23 163◦54.8 53.2 183◦13.5 0.8’ 26◦57.1 0.9’ 61.3’

SD.=16.3 d=0.2 S.D.=16.6

Lat.Twilight

Sunrise SunsetTwilight

Naut. Civil Civil Naut.

N 72◦ 08:25 10:44 13:24 15:43

N 70◦ 08:06 09:50 14:17 16:0268◦ 07:50 09:18 14:50 16:1766◦ 07:38 08:54 10:29 13:39 15:14 16:3064◦ 07:27 08:35 09:50 14:17 15:33 16:4162◦ 07:18 08:19 09:23 14:44 15:48 16:5060◦ 07:10 08:06 09:03 15:05 16:02 16:58

N 58◦ 07:02 07:55 08:46 15:22 16:13 17:0556◦ 06:56 07:45 08:32 15:36 16:23 17:1254◦ 06:50 07:36 08:19 15:48 16:32 17:1852◦ 06:44 07:28 08:08 15:59 16:40 17:2350◦ 06:39 07:21 07:59 16:09 16:47 17:2845◦ 06:28 07:05 07:39 16:29 17:03 17:40

N 40◦ 06:18 06:52 07:22 16:45 17:16 17:5035◦ 06:09 06:40 07:08 16:59 17:27 17:5930◦ 06:00 06:30 06:56 17:11 17:38 18:0720◦ 05:44 06:11 06:35 17:32 17:56 18:23

N 10◦ 05:28 05:54 06:17 17:50 18:13 18:390◦ 05:11 05:37 06:00 18:07 18:30 18:56

S 10◦ 04:53 05:20 05:43 18:25 18:48 19:1520◦ 04:30 05:00 05:24 18:43 19:08 19:3730◦ 04:02 04:35 05:02 19:05 19:32 20:0535◦ 03:43 04:20 04:50 19:18 19:47 20:2440◦ 03:21 04:02 04:35 19:32 20:05 20:4645◦ 02:51 03:40 04:17 19:50 20:27 21:16

S 50◦ 02:07 03:11 03:55 20:12 20:56 22:0052◦ 01:41 02:56 03:44 20:22 21:10 22:2654◦ 01:00 02:39 03:32 20:34 21:28 23:0556◦ 02:18 03:19 20:48 21:4958◦ 01:49 03:02 21:04 22:17

S 60◦ 01:05 02:43 21:24 23:00

Lat.Moonrise Moonset

Sat Sun Mon Sat Sun Mon

N 72◦

N 70◦

68◦ 07:11 08:4766◦ 06:06 09:5364◦ 05:31 08:00 10:29 10:0662◦ 05:06 07:08 09:03 10:55 10:59 11:2060◦ 04:47 06:36 08:15 11:15 11:31 12:09

N 58◦ 04:31 06:12 07:44 11:32 11:55 12:3956◦ 04:17 05:53 07:21 11:46 12:15 13:0354◦ 04:05 05:37 07:02 11:59 12:31 13:2252◦ 03:55 05:24 06:46 12:10 12:45 13:3850◦ 03:45 05:12 06:32 12:20 12:58 13:5245◦ 03:26 04:47 06:04 12:40 13:23 14:20

N 40◦ 03:10 04:27 05:42 12:57 13:44 14:4335◦ 02:57 04:11 05:24 13:11 14:01 15:0130◦ 02:46 03:57 05:08 13:24 14:16 15:1720◦ 02:26 03:33 04:41 13:45 14:41 15:44

N 10◦ 02:09 03:12 04:18 14:04 15:03 16:070◦ 01:54 02:53 03:57 14:21 15:23 16:29

S 10◦ 01:38 02:34 03:36 14:39 15:43 16:5020◦ 01:22 02:14 03:13 14:57 16:05 17:1430◦ 01:03 01:50 02:47 15:19 16:30 17:4035◦ 00:52 01:37 02:32 15:32 16:45 17:5640◦ 00:40 01:21 02:14 15:47 17:03 18:1445◦ 00:25 01:03 01:53 16:04 17:24 18:37

S 50◦ 00:07 00:40 01:26 16:26 17:50 19:0552◦ –:– 00:29 01:13 16:36 18:03 19:1854◦ –:– 00:16 00:58 16:48 18:18 19:3456◦ –:– 00:02 00:40 17:02 18:35 19:5358◦ 23:46 –:– 00:19 17:18 18:56 20:15

S 60◦ 23:26 23:52 –:– 17:37 19:22 20:45

Day

Sun MoonEqn.of Time Mer. Mer.Pass. Age

00h 12h Pass Upper Lower 26-28mm:ss mm:ss hh:mm hh:mm hh:mm 19-4%

01 02:57 03:11 12:03 08:07 20:3702 03:25 03:40 12:04 09:08 21:4003 03:54 04:08 12:04 10:13 22:46

3

January 04, 05, 06 (Tue., Wed., Thu.)

Aries Venus Mars Jupiter SaturnTue GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 102◦16.9 149◦12.9 S19◦22.3 309◦06.2 N14◦57.0 108◦32.8 S04◦03.7 358◦06.8 N22◦19.51 117◦19.4 164◦12.2 21.4 324◦08.7 57.1 123◦35.0 03.5 13◦09.5 19.62 132◦21.8 179◦11.5 20.6 339◦11.2 57.2 138◦37.1 03.4 28◦12.2 19.63 147◦24.3 194◦10.8 · · 19.7 354◦13.8 · · 57.4 153◦39.2 · · 03.2 43◦14.8 · · 19.64 162◦26.8 209◦10.1 18.9 9◦16.3 57.5 168◦41.3 03.0 58◦17.5 19.65 177◦29.2 224◦09.4 18.1 24◦18.8 57.6 183◦43.4 02.9 73◦20.2 19.7

6 192◦31.7 239◦08.7 S19◦17.2 39◦21.3 N14◦57.8 198◦45.6 S04◦02.7 88◦22.9 N22◦19.77 207◦34.1 254◦08.0 16.4 54◦23.9 57.9 213◦47.7 02.6 103◦25.6 19.78 222◦36.6 269◦07.3 15.5 69◦26.4 58.0 228◦49.8 02.4 118◦28.3 19.79 237◦39.1 284◦06.6 · · 14.7 84◦29.0 · · 58.1 243◦51.9 · · 02.3 133◦31.0 · · 19.810 252◦41.5 299◦05.9 13.8 99◦31.5 58.3 258◦54.0 02.1 148◦33.6 19.811 267◦44.0 314◦05.2 13.0 114◦34.0 58.4 273◦56.2 01.9 163◦36.3 19.8

12 282◦46.5 329◦04.6 S19◦12.1 129◦36.6 N14◦58.5 288◦58.3 S04◦01.8 178◦39.0 N22◦19.813 297◦48.9 344◦03.9 11.3 144◦39.1 58.7 304◦00.4 01.6 193◦41.7 19.914 312◦51.4 359◦03.2 10.4 159◦41.7 58.8 319◦02.5 01.5 208◦44.4 19.915 327◦53.9 14◦02.5 · · 09.6 174◦44.2 · · 58.9 334◦04.6 · · 01.3 223◦47.1 · · 19.916 342◦56.3 29◦01.8 08.7 189◦46.8 59.1 349◦06.8 01.2 238◦49.8 19.917 357◦58.8 44◦01.1 07.9 204◦49.3 59.2 4◦08.9 01.0 253◦52.5 19.9

18 13◦01.3 59◦00.4 S19◦07.0 219◦51.9 N14◦59.3 19◦11.0 S04◦00.8 268◦55.1 N22◦20.019 28◦03.7 73◦59.7 06.2 234◦54.4 59.5 34◦13.1 00.7 283◦57.8 20.020 43◦06.2 88◦59.0 05.3 249◦57.0 59.6 49◦15.2 00.5 299◦00.5 20.021 58◦08.6 103◦58.3 · · 04.5 264◦59.5 · · 59.8 64◦17.3 · · 00.4 314◦03.2 · · 20.022 73◦11.1 118◦57.6 03.6 280◦02.1 14◦59.9 79◦19.5 00.2 329◦05.9 20.123 88◦13.6 133◦57.0 02.8 295◦04.6 15◦00.0 94◦21.6 00.0 344◦08.6 20.1


Wed GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 103◦16.0 148◦56.3 S19◦01.9 310◦07.2 N15◦00.2 109◦23.7 S03◦59.9 359◦11.3 N22◦20.11 118◦18.5 163◦55.6 01.0 325◦09.7 00.3 124◦25.8 59.7 14◦13.9 20.12 133◦21.0 178◦54.9 19◦00.2 340◦12.3 00.4 139◦27.9 59.6 29◦16.6 20.23 148◦23.4 193◦54.2 18◦59.3 355◦14.9 · · 00.6 154◦30.0 · · 59.4 44◦19.3 · · 20.24 163◦25.9 208◦53.5 58.4 10◦17.4 00.7 169◦32.2 59.3 59◦22.0 20.25 178◦28.4 223◦52.9 57.6 25◦20.0 00.9 184◦34.3 59.1 74◦24.7 20.2

6 193◦30.8 238◦52.2 S18◦56.7 40◦22.5 N15◦01.0 199◦36.4 S03◦58.9 89◦27.4 N22◦20.37 208◦33.3 253◦51.5 55.9 55◦25.1 01.1 214◦38.5 58.8 104◦30.1 20.38 223◦35.8 268◦50.8 55.0 70◦27.7 01.3 229◦40.6 58.6 119◦32.7 20.39 238◦38.2 283◦50.1 · · 54.1 85◦30.3 · · 01.4 244◦42.7 · · 58.5 134◦35.4 · · 20.310 253◦40.7 298◦49.4 53.2 100◦32.8 01.6 259◦44.8 58.3 149◦38.1 20.411 268◦43.1 313◦48.8 52.4 115◦35.4 01.7 274◦47.0 58.1 164◦40.8 20.4

12 283◦45.6 328◦48.1 S18◦51.5 130◦38.0 N15◦01.9 289◦49.1 S03◦58.0 179◦43.5 N22◦20.413 298◦48.1 343◦47.4 50.6 145◦40.5 02.0 304◦51.2 57.8 194◦46.2 20.414 313◦50.5 358◦46.7 49.8 160◦43.1 02.1 319◦53.3 57.7 209◦48.9 20.515 328◦53.0 13◦46.0 · · 48.9 175◦45.7 · · 02.3 334◦55.4 · · 57.5 224◦51.6 · · 20.516 343◦55.5 28◦45.4 48.0 190◦48.3 02.4 349◦57.5 57.3 239◦54.2 20.517 358◦57.9 43◦44.7 47.1 205◦50.9 02.6 4◦59.6 57.2 254◦56.9 20.5

18 14◦00.4 58◦44.0 S18◦46.3 220◦53.4 N15◦02.7 20◦01.7 S03◦57.0 269◦59.6 N22◦20.619 29◦02.9 73◦43.3 45.4 235◦56.0 02.9 35◦03.9 56.9 285◦02.3 20.620 44◦05.3 88◦42.7 44.5 250◦58.6 03.0 50◦06.0 56.7 300◦05.0 20.621 59◦07.8 103◦42.0 · · 43.6 266◦01.2 · · 03.2 65◦08.1 · · 56.5 315◦07.7 · · 20.622 74◦10.3 118◦41.3 42.8 281◦03.8 03.3 80◦10.2 56.4 330◦10.4 20.723 89◦12.7 133◦40.7 41.9 296◦06.4 03.5 95◦12.3 56.2 345◦13.0 20.7


Thu GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 104◦15.2 148◦40.0 S18◦41.0 311◦09.0 N15◦03.6 110◦14.4 S03◦56.1 0◦15.7 N22◦20.71 119◦17.6 163◦39.3 40.1 326◦11.6 03.8 125◦16.5 55.9 15◦18.4 20.72 134◦20.1 178◦38.6 39.2 341◦14.1 03.9 140◦18.6 55.7 30◦21.1 20.83 149◦22.6 193◦38.0 · · 38.3 356◦16.7 · · 04.1 155◦20.8 · · 55.6 45◦23.8 · · 20.84 164◦25.0 208◦37.3 37.5 11◦19.3 04.2 170◦22.9 55.4 60◦26.5 20.85 179◦27.5 223◦36.6 36.6 26◦21.9 04.4 185◦25.0 55.2 75◦29.2 20.8

6 194◦30.0 238◦36.0 S18◦35.7 41◦24.5 N15◦04.5 200◦27.1 S03◦55.1 90◦31.8 N22◦20.97 209◦32.4 253◦35.3 34.8 56◦27.1 04.7 215◦29.2 54.9 105◦34.5 20.98 224◦34.9 268◦34.6 33.9 71◦29.7 04.8 230◦31.3 54.8 120◦37.2 20.99 239◦37.4 283◦34.0 · · 33.0 86◦32.3 · · 05.0 245◦33.4 · · 54.6 135◦39.9 · · 20.910 254◦39.8 298◦33.3 32.1 101◦34.9 05.1 260◦35.5 54.4 150◦42.6 21.011 269◦42.3 313◦32.6 31.2 116◦37.5 05.3 275◦37.6 54.3 165◦45.3 21.0

12 284◦44.8 328◦32.0 S18◦30.4 131◦40.2 N15◦05.5 290◦39.7 S03◦54.1 180◦48.0 N22◦21.013 299◦47.2 343◦31.3 29.5 146◦42.8 05.6 305◦41.8 54.0 195◦50.6 21.014 314◦49.7 358◦30.6 28.6 161◦45.4 05.8 320◦44.0 53.8 210◦53.3 21.115 329◦52.1 13◦30.0 · · 27.7 176◦48.0 · · 05.9 335◦46.1 · · 53.6 225◦56.0 · · 21.116 344◦54.6 28◦29.3 26.8 191◦50.6 06.1 350◦48.2 53.5 240◦58.7 21.117 359◦57.1 43◦28.6 25.9 206◦53.2 06.2 5◦50.3 53.3 256◦01.4 21.1

18 14◦59.5 58◦28.0 S18◦25.0 221◦55.8 N15◦06.4 20◦52.4 S03◦53.1 271◦04.1 N22◦21.119 30◦02.0 73◦27.3 24.1 236◦58.4 06.6 35◦54.5 53.0 286◦06.8 21.220 45◦04.5 88◦26.7 23.2 252◦01.1 06.7 50◦56.6 52.8 301◦09.5 21.221 60◦06.9 103◦26.0 · · 22.3 267◦03.7 · · 06.9 65◦58.7 · · 52.7 316◦12.1 · · 21.222 75◦09.4 118◦25.3 21.4 282◦06.3 07.0 81◦00.8 52.5 331◦14.8 21.223 90◦11.9 133◦24.7 20.5 297◦08.9 07.2 96◦02.9 52.3 346◦17.5 21.3


StarsSHA Dec

Alpheratz 358◦59.3 28◦37.8Ankaa 354◦27.8 -42◦45.9

Schedar 351◦04.0 56◦05.0Diphda 350◦09.2 -18◦26.9


Aldebaran 292◦13.0 16◦20.6Rigel 282◦22.0 -8◦17.8










Atria 110◦04.0 -68◦52.5Sabik 103◦36.7 -15◦37.4




Peacock 55◦15.0 -57◦00.5Deneb 50◦21.8 44◦58.9

Enif 34◦59.2 9◦29.4Al Na’ir 29◦15.8 -47◦22.3


Jan 04 Tue SHA Mer.passVenus 46◦56.0 14:04Mars 206◦49.3 03:23

Jupiter 6◦15.9 16:43Saturn 255◦49.9 00:08

Jan 05 Wed SHA Mer.passVenus 45◦40.2 14:05Mars 206◦51.1 03:19

Jupiter 6◦07.7 16:40Saturn 255◦55.2 00:03

Jan 06 Thu SHA Mer.passVenus 44◦24.8 14:06Mars 206◦53.8 03:15

Jupiter 5◦59.2 16:37Saturn 256◦00.5 23:55


4


h Sun MoonTue GHA Dec GHA ν Dec d HP

0 178◦54.5 S22◦52.9 197◦33.3 0.8’ S26◦56.0 1.1’ 61.3’1 193◦54.2 52.7 211◦53.1 0.8’ 26◦54.8 1.4’ 61.3’2 208◦53.9 52.5 226◦12.9 0.8’ 26◦53.3 1.6’ 61.3’3 223◦53.6 · · 52.2 240◦32.7 0.8’ 26◦51.6 1.8’ 61.3’4 238◦53.4 52.0 254◦52.6 0.8’ 26◦49.7 2.0’ 61.3’5 253◦53.1 51.7 269◦12.4 0.9’ 26◦47.6 2.2’ 61.3’

6 268◦52.8 S22◦51.5 283◦32.3 0.9’ S26◦45.3 2.4’ 61.3’7 283◦52.5 51.3 297◦52.2 0.9’ 26◦42.8 2.6’ 61.3’8 298◦52.2 51.0 312◦12.1 0.9’ 26◦40.0 2.9’ 61.3’9 313◦51.9 · · 50.8 326◦32.1 1.0’ 26◦37.1 3.1’ 61.3’10 328◦51.6 50.5 340◦52.0 1.0’ 26◦33.9 3.3’ 61.3’11 343◦51.3 50.3 355◦12.1 1.0’ 26◦30.5 3.5’ 61.3’

12 358◦51.0 S22◦50.1 9◦32.1 1.1’ S26◦26.9 3.7’ 61.3’13 13◦50.7 49.8 23◦52.2 1.1’ 26◦23.1 3.9’ 61.3’14 28◦50.5 49.6 38◦12.4 1.2’ 26◦19.1 4.1’ 61.3’15 43◦50.2 · · 49.3 52◦32.5 1.2’ 26◦14.9 4.3’ 61.3’16 58◦49.9 49.1 66◦52.8 1.3’ 26◦10.5 4.5’ 61.3’17 73◦49.6 48.8 81◦13.1 1.3’ 26◦05.9 4.7’ 61.3’

18 88◦49.3 S22◦48.6 95◦33.4 1.4’ S26◦01.0 4.9’ 61.3’19 103◦49.0 48.3 109◦53.9 1.5’ 25◦56.0 5.1’ 61.3’20 118◦48.7 48.1 124◦14.3 1.5’ 25◦50.8 5.3’ 61.3’21 133◦48.4 · · 47.8 138◦34.9 1.6’ 25◦45.3 5.5’ 61.3’22 148◦48.1 47.6 152◦55.5 1.7’ 25◦39.7 5.7’ 61.3’23 163◦47.9 47.3 167◦16.2 1.7’ 25◦33.9 5.9’ 61.3’

SD.=16.3 d=0.2 S.D.=16.7

Wed GHA Dec GHA ν Dec d HP

0 178◦47.6 S22◦47.1 181◦37.0 1.8’ S25◦27.8 6.1’ 61.3’1 193◦47.3 46.8 195◦57.8 1.9’ 25◦21.6 6.3’ 61.3’2 208◦47.0 46.6 210◦18.8 2.0’ 25◦15.2 6.5’ 61.3’3 223◦46.7 · · 46.3 224◦39.8 2.1’ 25◦08.6 6.7’ 61.3’4 238◦46.4 46.0 239◦00.9 2.1’ 25◦01.8 6.9’ 61.3’5 253◦46.1 45.8 253◦22.1 2.2’ 24◦54.8 7.1’ 61.3’

6 268◦45.9 S22◦45.5 267◦43.3 2.3’ S24◦47.6 7.3’ 61.3’7 283◦45.6 45.3 282◦04.7 2.4’ 24◦40.2 7.5’ 61.3’8 298◦45.3 45.0 296◦26.2 2.5’ 24◦32.7 7.6’ 61.3’9 313◦45.0 · · 44.8 310◦47.7 2.6’ 24◦25.0 7.8’ 61.2’10 328◦44.7 44.5 325◦09.4 2.7’ 24◦17.1 8.0’ 61.2’11 343◦44.4 44.2 339◦31.1 2.8’ 24◦09.0 8.2’ 61.2’

12 358◦44.1 S22◦44.0 353◦53.0 2.9’ S24◦00.7 8.3’ 61.2’13 13◦43.9 43.7 8◦15.0 3.0’ 23◦52.3 8.5’ 61.2’14 28◦43.6 43.4 22◦37.1 3.1’ 23◦43.7 8.7’ 61.2’15 43◦43.3 · · 43.2 36◦59.2 3.2’ 23◦34.9 8.9’ 61.2’16 58◦43.0 42.9 51◦21.5 3.4’ 23◦25.9 9.0’ 61.2’17 73◦42.7 42.6 65◦43.9 3.5’ 23◦16.8 9.2’ 61.1’

18 88◦42.4 S22◦42.4 80◦06.5 3.6’ S23◦07.6 9.4’ 61.1’19 103◦42.1 42.1 94◦29.1 3.7’ 22◦58.1 9.5’ 61.1’20 118◦41.9 41.8 108◦51.9 3.8’ 22◦48.5 9.7’ 61.1’21 133◦41.6 · · 41.6 123◦14.7 3.9’ 22◦38.8 9.8’ 61.1’22 148◦41.3 41.3 137◦37.7 4.0’ 22◦28.8 10.0’ 61.1’23 163◦41.0 41.0 152◦00.8 4.2’ 22◦18.8 10.1’ 61.0’

SD.=16.3 d=0.3 S.D.=16.7

Thu GHA Dec GHA ν Dec d HP

0 178◦40.7 S22◦40.8 166◦24.0 4.3’ S22◦08.5 10.3’ 61.0’1 193◦40.4 40.5 180◦47.4 4.4’ 21◦58.2 10.4’ 61.0’2 208◦40.2 40.2 195◦10.9 4.5’ 21◦47.7 10.6’ 61.0’3 223◦39.9 · · 39.9 209◦34.4 4.7’ 21◦37.0 10.7’ 61.0’4 238◦39.6 39.7 223◦58.2 4.8’ 21◦26.2 10.9’ 60.9’5 253◦39.3 39.4 238◦22.0 4.9’ 21◦15.3 11.0’ 60.9’

6 268◦39.0 S22◦39.1 252◦46.0 5.0’ S21◦04.2 11.2’ 60.9’7 283◦38.8 38.8 267◦10.1 5.2’ 20◦53.0 11.3’ 60.9’8 298◦38.5 38.5 281◦34.3 5.3’ 20◦41.6 11.4’ 60.8’9 313◦38.2 · · 38.3 295◦58.6 5.4’ 20◦30.1 11.5’ 60.8’10 328◦37.9 38.0 310◦23.1 5.5’ 20◦18.5 11.7’ 60.8’11 343◦37.6 37.7 324◦47.7 5.7’ 20◦06.8 11.8’ 60.8’

12 358◦37.3 S22◦37.4 339◦12.4 5.8’ S19◦54.9 11.9’ 60.7’13 13◦37.1 37.1 353◦37.3 5.9’ 19◦42.9 12.0’ 60.7’14 28◦36.8 36.9 8◦02.2 6.0’ 19◦30.8 12.2’ 60.7’15 43◦36.5 · · 36.6 22◦27.3 6.2’ 19◦18.6 12.3’ 60.7’16 58◦36.2 36.3 36◦52.6 6.3’ 19◦06.3 12.4’ 60.6’17 73◦35.9 36.0 51◦17.9 6.4’ 18◦53.8 12.5’ 60.6’

18 88◦35.7 S22◦35.7 65◦43.4 6.6’ S18◦41.2 12.6’ 60.6’19 103◦35.4 35.4 80◦09.1 6.7’ 18◦28.6 12.7’ 60.6’20 118◦35.1 35.1 94◦34.8 6.8’ 18◦15.8 12.8’ 60.5’21 133◦34.8 · · 34.9 109◦00.7 6.9’ 18◦02.9 12.9’ 60.5’22 148◦34.5 34.6 123◦26.7 7.1’ 17◦49.9 13.0’ 60.5’23 163◦34.3 34.3 137◦52.8 7.2’ 17◦36.9 13.1’ 60.4’

SD.=16.3 d=0.3 S.D.=16.6

Lat.Twilight



N 72◦ 08:22 10:35 13:36 15:49

N 70◦ 08:03 09:46 14:25 16:0768◦ 07:48 09:14 11:42 12:29 14:56 16:2266◦ 07:36 08:51 10:23 13:47 15:19 16:3464◦ 07:26 08:33 09:47 14:24 15:38 16:4562◦ 07:17 08:18 09:21 14:49 15:53 16:5460◦ 07:09 08:05 09:01 15:09 16:06 17:01

N 58◦ 07:02 07:54 08:45 15:26 16:17 17:0956◦ 06:55 07:44 08:31 15:40 16:26 17:1554◦ 06:50 07:35 08:19 15:52 16:35 17:2152◦ 06:44 07:28 08:08 16:02 16:43 17:2650◦ 06:39 07:20 07:58 16:12 16:50 17:3145◦ 06:28 07:05 07:39 16:32 17:05 17:42

N 40◦ 06:18 06:52 07:22 16:48 17:18 17:5235◦ 06:09 06:41 07:09 17:02 17:30 18:0130◦ 06:01 06:31 06:57 17:14 17:40 18:0920◦ 05:45 06:12 06:36 17:34 17:58 18:25

N 10◦ 05:29 05:56 06:18 17:52 18:15 18:410◦ 05:13 05:39 06:01 18:09 18:31 18:57

S 10◦ 04:54 05:21 05:44 18:26 18:49 19:1620◦ 04:32 05:01 05:26 18:44 19:09 19:3830◦ 04:04 04:37 05:05 19:05 19:33 20:0635◦ 03:46 04:22 04:52 19:18 19:47 20:2440◦ 03:24 04:05 04:37 19:32 20:05 20:4645◦ 02:54 03:43 04:20 19:50 20:27 21:15

S 50◦ 02:12 03:15 03:58 20:11 20:55 21:5852◦ 01:46 03:00 03:48 20:22 21:09 22:2254◦ 01:09 02:43 03:36 20:33 21:26 22:5956◦ 02:22 03:23 20:47 21:4758◦ 01:55 03:07 21:03 22:13

S 60◦ 01:15 02:47 21:22 22:53


Tue Wed Thu Tue Wed Thu

N 72◦

N 70◦ 13:00 14:1468◦ 11:43 15:2966◦ 11:05 16:0664◦ 10:54 10:38 14:09 16:3262◦ 10:02 10:15 10:17 12:43 14:47 16:5260◦ 09:18 09:47 10:00 13:26 15:14 17:08

N 58◦ 08:49 09:26 09:45 13:55 15:35 17:2256◦ 08:27 09:08 09:33 14:17 15:52 17:3454◦ 08:08 08:53 09:22 14:36 16:07 17:4452◦ 07:53 08:40 09:12 14:51 16:19 17:5350◦ 07:39 08:28 09:03 15:05 16:31 18:0145◦ 07:11 08:04 08:45 15:32 16:54 18:18

N 40◦ 06:49 07:45 08:29 15:54 17:12 18:3235◦ 06:31 07:29 08:16 16:12 17:27 18:4430◦ 06:15 07:15 08:05 16:27 17:41 18:5420◦ 05:48 06:51 07:46 16:53 18:03 19:11

N 10◦ 05:26 06:30 07:29 17:15 18:23 19:260◦ 05:04 06:10 07:13 17:36 18:40 19:40

S 10◦ 04:43 05:51 06:56 17:57 18:58 19:5420◦ 04:20 05:30 06:39 18:19 19:17 20:0930◦ 03:53 05:06 06:19 18:44 19:39 20:2635◦ 03:38 04:51 06:08 18:59 19:52 20:3540◦ 03:19 04:35 05:54 19:16 20:06 20:4645◦ 02:57 04:15 05:38 19:37 20:23 20:59

S 50◦ 02:29 03:50 05:18 20:03 20:45 21:1452◦ 02:16 03:37 05:09 20:15 20:55 21:2254◦ 02:00 03:23 04:58 20:29 21:06 21:3056◦ 01:41 03:07 04:46 20:46 21:18 21:3958◦ 01:19 02:48 04:32 21:06 21:33 21:49

S 60◦ 00:49 02:24 04:16 21:30 21:50 22:00

Day



04 04:22 04:36 12:05 11:20 23:5305 04:50 05:04 12:05 12:26 –:–06 05:17 05:31 12:06 13:27 00:57

5

January 07, 08, 09 (Fri., Sat., Sun.)

Aries Venus Mars Jupiter SaturnFri GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 105◦14.3 148◦24.0 S18◦19.6 312◦11.5 N15◦07.4 111◦05.0 S03◦52.2 1◦20.2 N22◦21.31 120◦16.8 163◦23.4 18.7 327◦14.2 07.5 126◦07.1 52.0 16◦22.9 21.32 135◦19.3 178◦22.7 17.8 342◦16.8 07.7 141◦09.2 51.8 31◦25.6 21.33 150◦21.7 193◦22.1 · · 16.9 357◦19.4 · · 07.8 156◦11.3 · · 51.7 46◦28.3 · · 21.44 165◦24.2 208◦21.4 16.0 12◦22.0 08.0 171◦13.4 51.5 61◦30.9 21.45 180◦26.6 223◦20.8 15.1 27◦24.7 08.2 186◦15.5 51.3 76◦33.6 21.4

6 195◦29.1 238◦20.1 S18◦14.2 42◦27.3 N15◦08.3 201◦17.7 S03◦51.2 91◦36.3 N22◦21.47 210◦31.6 253◦19.4 13.2 57◦29.9 08.5 216◦19.8 51.0 106◦39.0 21.58 225◦34.0 268◦18.8 12.3 72◦32.6 08.7 231◦21.9 50.9 121◦41.7 21.59 240◦36.5 283◦18.1 · · 11.4 87◦35.2 · · 08.8 246◦24.0 · · 50.7 136◦44.4 · · 21.510 255◦39.0 298◦17.5 10.5 102◦37.8 09.0 261◦26.1 50.5 151◦47.1 21.511 270◦41.4 313◦16.8 09.6 117◦40.5 09.2 276◦28.2 50.4 166◦49.7 21.6

12 285◦43.9 328◦16.2 S18◦08.7 132◦43.1 N15◦09.3 291◦30.3 S03◦50.2 181◦52.4 N22◦21.613 300◦46.4 343◦15.5 07.8 147◦45.8 09.5 306◦32.4 50.0 196◦55.1 21.614 315◦48.8 358◦14.9 06.9 162◦48.4 09.7 321◦34.5 49.9 211◦57.8 21.615 330◦51.3 13◦14.2 · · 05.9 177◦51.0 · · 09.8 336◦36.6 · · 49.7 227◦00.5 · · 21.716 345◦53.7 28◦13.6 05.0 192◦53.7 10.0 351◦38.7 49.5 242◦03.2 21.717 0◦56.2 43◦12.9 04.1 207◦56.3 10.2 6◦40.8 49.4 257◦05.9 21.7

18 15◦58.7 58◦12.3 S18◦03.2 222◦59.0 N15◦10.3 21◦42.9 S03◦49.2 272◦08.5 N22◦21.719 31◦01.1 73◦11.7 02.3 238◦01.6 10.5 36◦45.0 49.1 287◦11.2 21.820 46◦03.6 88◦11.0 01.4 253◦04.3 10.7 51◦47.1 48.9 302◦13.9 21.821 61◦06.1 103◦10.4 18◦00.4 268◦06.9 · · 10.8 66◦49.2 · · 48.7 317◦16.6 · · 21.822 76◦08.5 118◦09.7 17◦59.5 283◦09.6 11.0 81◦51.3 48.6 332◦19.3 21.823 91◦11.0 133◦09.1 58.6 298◦12.2 11.2 96◦53.4 48.4 347◦22.0 21.9


Sat GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 106◦13.5 148◦08.4 S17◦57.7 313◦14.9 N15◦11.4 111◦55.5 S03◦48.2 2◦24.7 N22◦21.91 121◦15.9 163◦07.8 56.7 328◦17.6 11.5 126◦57.6 48.1 17◦27.3 21.92 136◦18.4 178◦07.1 55.8 343◦20.2 11.7 141◦59.7 47.9 32◦30.0 21.93 151◦20.9 193◦06.5 · · 54.9 358◦22.9 · · 11.9 157◦01.8 · · 47.7 47◦32.7 · · 22.04 166◦23.3 208◦05.9 54.0 13◦25.5 12.1 172◦03.9 47.6 62◦35.4 22.05 181◦25.8 223◦05.2 53.0 28◦28.2 12.2 187◦06.0 47.4 77◦38.1 22.0

6 196◦28.2 238◦04.6 S17◦52.1 43◦30.9 N15◦12.4 202◦08.1 S03◦47.2 92◦40.8 N22◦22.07 211◦30.7 253◦03.9 51.2 58◦33.5 12.6 217◦10.2 47.1 107◦43.5 22.08 226◦33.2 268◦03.3 50.2 73◦36.2 12.8 232◦12.3 46.9 122◦46.1 22.19 241◦35.6 283◦02.7 · · 49.3 88◦38.9 · · 12.9 247◦14.4 · · 46.7 137◦48.8 · · 22.110 256◦38.1 298◦02.0 48.4 103◦41.5 13.1 262◦16.5 46.6 152◦51.5 22.111 271◦40.6 313◦01.4 47.5 118◦44.2 13.3 277◦18.6 46.4 167◦54.2 22.1

12 286◦43.0 328◦00.8 S17◦46.5 133◦46.9 N15◦13.5 292◦20.7 S03◦46.2 182◦56.9 N22◦22.213 301◦45.5 343◦00.1 45.6 148◦49.6 13.6 307◦22.8 46.1 197◦59.6 22.214 316◦48.0 357◦59.5 44.6 163◦52.2 13.8 322◦24.9 45.9 213◦02.3 22.215 331◦50.4 12◦58.9 · · 43.7 178◦54.9 · · 14.0 337◦27.0 · · 45.7 228◦04.9 · · 22.216 346◦52.9 27◦58.2 42.8 193◦57.6 14.2 352◦29.1 45.6 243◦07.6 22.317 1◦55.4 42◦57.6 41.8 209◦00.3 14.4 7◦31.2 45.4 258◦10.3 22.3

18 16◦57.8 57◦57.0 S17◦40.9 224◦02.9 N15◦14.5 22◦33.3 S03◦45.2 273◦13.0 N22◦22.319 32◦00.3 72◦56.3 40.0 239◦05.6 14.7 37◦35.4 45.1 288◦15.7 22.320 47◦02.7 87◦55.7 39.0 254◦08.3 14.9 52◦37.5 44.9 303◦18.4 22.421 62◦05.2 102◦55.1 · · 38.1 269◦11.0 · · 15.1 67◦39.6 · · 44.7 318◦21.1 · · 22.422 77◦07.7 117◦54.4 37.1 284◦13.7 15.3 82◦41.7 44.6 333◦23.7 22.423 92◦10.1 132◦53.8 36.2 299◦16.4 15.5 97◦43.8 44.4 348◦26.4 22.4


Sun GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 107◦12.6 147◦53.2 S17◦35.2 314◦19.1 N15◦15.6 112◦45.9 S03◦44.2 3◦29.1 N22◦22.51 122◦15.1 162◦52.6 34.3 329◦21.7 15.8 127◦48.0 44.1 18◦31.8 22.52 137◦17.5 177◦51.9 33.4 344◦24.4 16.0 142◦50.1 43.9 33◦34.5 22.53 152◦20.0 192◦51.3 · · 32.4 359◦27.1 · · 16.2 157◦52.2 · · 43.7 48◦37.2 · · 22.54 167◦22.5 207◦50.7 31.5 14◦29.8 16.4 172◦54.2 43.6 63◦39.8 22.65 182◦24.9 222◦50.0 30.5 29◦32.5 16.6 187◦56.3 43.4 78◦42.5 22.6

6 197◦27.4 237◦49.4 S17◦29.6 44◦35.2 N15◦16.8 202◦58.4 S03◦43.2 93◦45.2 N22◦22.67 212◦29.8 252◦48.8 28.6 59◦37.9 16.9 218◦00.5 43.1 108◦47.9 22.68 227◦32.3 267◦48.2 27.7 74◦40.6 17.1 233◦02.6 42.9 123◦50.6 22.79 242◦34.8 282◦47.6 · · 26.7 89◦43.3 · · 17.3 248◦04.7 · · 42.7 138◦53.3 · · 22.710 257◦37.2 297◦46.9 25.8 104◦46.0 17.5 263◦06.8 42.6 153◦56.0 22.711 272◦39.7 312◦46.3 24.8 119◦48.7 17.7 278◦08.9 42.4 168◦58.6 22.7

12 287◦42.2 327◦45.7 S17◦23.9 134◦51.4 N15◦17.9 293◦11.0 S03◦42.2 184◦01.3 N22◦22.713 302◦44.6 342◦45.1 22.9 149◦54.1 18.1 308◦13.1 42.1 199◦04.0 22.814 317◦47.1 357◦44.4 21.9 164◦56.8 18.3 323◦15.2 41.9 214◦06.7 22.815 332◦49.6 12◦43.8 · · 21.0 179◦59.6 · · 18.5 338◦17.3 · · 41.7 229◦09.4 · · 22.816 347◦52.0 27◦43.2 20.0 195◦02.3 18.6 353◦19.4 41.6 244◦12.1 22.817 2◦54.5 42◦42.6 19.1 210◦05.0 18.8 8◦21.5 41.4 259◦14.8 22.9

18 17◦57.0 57◦42.0 S17◦18.1 225◦07.7 N15◦19.0 23◦23.6 S03◦41.2 274◦17.4 N22◦22.919 32◦59.4 72◦41.4 17.2 240◦10.4 19.2 38◦25.7 41.0 289◦20.1 22.920 48◦01.9 87◦40.7 16.2 255◦13.1 19.4 53◦27.7 40.9 304◦22.8 22.921 63◦04.3 102◦40.1 · · 15.2 270◦15.8 · · 19.6 68◦29.8 · · 40.7 319◦25.5 · · 23.022 78◦06.8 117◦39.5 14.3 285◦18.6 19.8 83◦31.9 40.5 334◦28.2 23.023 93◦09.3 132◦38.9 13.3 300◦21.3 20.0 98◦34.0 40.4 349◦30.9 23.0


StarsSHA Dec

Alpheratz 358◦59.3 28◦37.8Ankaa 354◦27.8 -42◦45.9

Schedar 351◦04.0 56◦05.0Diphda 350◦09.2 -18◦26.9


Aldebaran 292◦13.0 16◦20.6Rigel 282◦22.0 -8◦17.8










Atria 110◦04.0 -68◦52.5Sabik 103◦36.7 -15◦37.4




Peacock 55◦15.0 -57◦00.4Deneb 50◦21.8 44◦58.8

Enif 34◦59.2 9◦29.4Al Na’ir 29◦15.8 -47◦22.3


Jan 07 Fri SHA Mer.passVenus 43◦09.7 14:07Mars 206◦57.2 03:11

Jupiter 5◦50.7 16:33Saturn 256◦05.9 23:50

Jan 08 Sat SHA Mer.passVenus 41◦55.0 14:08Mars 207◦01.4 03:06

Jupiter 5◦42.0 16:30Saturn 256◦11.2 23:46

Jan 09 Sun SHA Mer.passVenus 40◦40.6 14:09Mars 207◦06.5 03:02

Jupiter 5◦33.3 16:27Saturn 256◦16.5 23:42


6


h Sun MoonFri GHA Dec GHA ν Dec d HP

0 178◦34.0 S22◦34.0 152◦19.0 7.3’ S17◦23.7 13.2’ 60.4’1 193◦33.7 33.7 166◦45.4 7.4’ 17◦10.4 13.3’ 60.4’2 208◦33.4 33.4 181◦11.9 7.6’ 16◦57.1 13.4’ 60.4’3 223◦33.2 · · 33.1 195◦38.5 7.7’ 16◦43.6 13.5’ 60.3’4 238◦32.9 32.8 210◦05.3 7.8’ 16◦30.1 13.6’ 60.3’5 253◦32.6 32.5 224◦32.2 7.9’ 16◦16.4 13.7’ 60.3’

6 268◦32.3 S22◦32.2 238◦59.2 8.1’ S16◦02.7 13.8’ 60.2’7 283◦32.0 31.9 253◦26.3 8.2’ 15◦48.9 13.8’ 60.2’8 298◦31.8 31.6 267◦53.5 8.3’ 15◦35.1 13.9’ 60.2’9 313◦31.5 · · 31.3 282◦20.9 8.4’ 15◦21.1 14.0’ 60.1’10 328◦31.2 31.0 296◦48.4 8.5’ 15◦07.1 14.1’ 60.1’11 343◦30.9 30.7 311◦16.0 8.7’ 14◦53.0 14.1’ 60.1’

12 358◦30.7 S22◦30.4 325◦43.7 8.8’ S14◦38.8 14.2’ 60.0’13 13◦30.4 30.1 340◦11.5 8.9’ 14◦24.6 14.3’ 60.0’14 28◦30.1 29.8 354◦39.5 9.0’ 14◦10.3 14.3’ 60.0’15 43◦29.8 · · 29.5 9◦07.5 9.1’ 13◦55.9 14.4’ 59.9’16 58◦29.6 29.2 23◦35.7 9.2’ 13◦41.5 14.5’ 59.9’17 73◦29.3 28.9 38◦04.0 9.3’ 13◦27.0 14.5’ 59.9’

18 88◦29.0 S22◦28.6 52◦32.4 9.5’ S13◦12.5 14.6’ 59.8’19 103◦28.7 28.3 67◦00.9 9.6’ 12◦57.9 14.6’ 59.8’20 118◦28.5 28.0 81◦29.5 9.7’ 12◦43.2 14.7’ 59.7’21 133◦28.2 · · 27.7 95◦58.3 9.8’ 12◦28.5 14.7’ 59.7’22 148◦27.9 27.4 110◦27.1 9.9’ 12◦13.7 14.8’ 59.7’23 163◦27.6 27.1 124◦56.0 10.0’ 11◦58.9 14.8’ 59.6’

SD.=16.3 d=0.3 S.D.=16.5

Sat GHA Dec GHA ν Dec d HP

0 178◦27.4 S22◦26.8 139◦25.1 10.1’ S11◦44.1 14.9’ 59.6’1 193◦27.1 26.5 153◦54.3 10.2’ 11◦29.2 14.9’ 59.6’2 208◦26.8 26.2 168◦23.5 10.3’ 11◦14.2 15.0’ 59.5’3 223◦26.6 · · 25.8 182◦52.9 10.4’ 10◦59.2 15.0’ 59.5’4 238◦26.3 25.5 197◦22.4 10.5’ 10◦44.2 15.0’ 59.4’5 253◦26.0 25.2 211◦51.9 10.6’ 10◦29.2 15.1’ 59.4’

6 268◦25.7 S22◦24.9 226◦21.6 10.7’ S10◦14.1 15.1’ 59.4’7 283◦25.5 24.6 240◦51.3 10.8’ 09◦58.9 15.1’ 59.3’8 298◦25.2 24.3 255◦21.2 10.9’ 09◦43.8 15.2’ 59.3’9 313◦24.9 · · 24.0 269◦51.1 11.0’ 09◦28.6 15.2’ 59.2’10 328◦24.6 23.6 284◦21.2 11.1’ 09◦13.4 15.2’ 59.2’11 343◦24.4 23.3 298◦51.3 11.2’ 08◦58.1 15.3’ 59.2’

12 358◦24.1 S22◦23.0 313◦21.6 11.3’ S08◦42.8 15.3’ 59.1’13 13◦23.8 22.7 327◦51.9 11.4’ 08◦27.5 15.3’ 59.1’14 28◦23.6 22.4 342◦22.3 11.4’ 08◦12.2 15.3’ 59.1’15 43◦23.3 · · 22.0 356◦52.8 11.5’ 07◦56.9 15.3’ 59.0’16 58◦23.0 21.7 11◦23.4 11.6’ 07◦41.5 15.4’ 59.0’17 73◦22.8 21.4 25◦54.0 11.7’ 07◦26.2 15.4’ 58.9’

18 88◦22.5 S22◦21.1 40◦24.8 11.8’ S07◦10.8 15.4’ 58.9’19 103◦22.2 20.8 54◦55.6 11.9’ 06◦55.4 15.4’ 58.9’20 118◦21.9 20.4 69◦26.5 11.9’ 06◦39.9 15.4’ 58.8’21 133◦21.7 · · 20.1 83◦57.5 12.0’ 06◦24.5 15.4’ 58.8’22 148◦21.4 19.8 98◦28.5 12.1’ 06◦09.1 15.4’ 58.7’23 163◦21.1 19.5 112◦59.7 12.2’ 05◦53.6 15.4’ 58.7’

SD.=16.3 d=0.3 S.D.=16.3

Sun GHA Dec GHA ν Dec d HP

0 178◦20.9 S22◦19.1 127◦30.9 12.3’ S05◦38.2 15.5’ 58.6’1 193◦20.6 18.8 142◦02.2 12.3’ 05◦22.7 15.5’ 58.6’2 208◦20.3 18.5 156◦33.5 12.4’ 05◦07.3 15.5’ 58.6’3 223◦20.1 · · 18.1 171◦05.0 12.5’ 04◦51.8 15.5’ 58.5’4 238◦19.8 17.8 185◦36.5 12.5’ 04◦36.3 15.5’ 58.5’5 253◦19.5 17.5 200◦08.0 12.6’ 04◦20.9 15.5’ 58.4’

6 268◦19.3 S22◦17.1 214◦39.7 12.7’ S04◦05.4 15.5’ 58.4’7 283◦19.0 16.8 229◦11.4 12.7’ 03◦49.9 15.5’ 58.4’8 298◦18.7 16.5 243◦43.1 12.8’ 03◦34.5 15.5’ 58.3’9 313◦18.5 · · 16.1 258◦15.0 12.9’ 03◦19.0 15.4’ 58.3’10 328◦18.2 15.8 272◦46.9 12.9’ 03◦03.6 15.4’ 58.2’11 343◦17.9 15.5 287◦18.8 13.0’ 02◦48.2 15.4’ 58.2’

12 358◦17.7 S22◦15.1 301◦50.8 13.0’ S02◦32.7 15.4’ 58.2’13 13◦17.4 14.8 316◦22.9 13.1’ 02◦17.3 15.4’ 58.1’14 28◦17.1 14.5 330◦55.0 13.1’ 02◦01.9 15.4’ 58.1’15 43◦16.9 · · 14.1 345◦27.2 13.2’ 01◦46.5 15.4’ 58.0’16 58◦16.6 13.8 359◦59.4 13.3’ 01◦31.2 15.4’ 58.0’17 73◦16.4 13.4 14◦31.7 13.3’ 01◦15.8 15.4’ 58.0’

18 88◦16.1 S22◦13.1 29◦04.0 13.4’ S01◦00.5 15.3’ 57.9’19 103◦15.8 12.8 43◦36.4 13.4’ 00◦45.1 15.3’ 57.9’20 118◦15.6 12.4 58◦08.8 13.4’ 00◦29.8 15.3’ 57.8’21 133◦15.3 · · 12.1 72◦41.3 13.5’ S00◦14.5 15.3’ 57.8’22 148◦15.0 11.7 87◦13.8 13.5’ N00◦00.7 15.3’ 57.8’23 163◦14.8 11.4 101◦46.4 13.6’ 00◦16.0 15.2’ 57.7’

SD.=16.3 d=0.3 S.D.=16.0

Lat.Twilight



N 72◦ 08:17 10:24 13:49 15:56

N 70◦ 08:00 09:40 14:34 16:1468◦ 07:46 09:10 11:18 12:56 15:03 16:2866◦ 07:34 08:48 10:16 13:57 15:25 16:3964◦ 07:24 08:30 09:42 14:31 15:43 16:4962◦ 07:15 08:16 09:18 14:55 15:58 16:5860◦ 07:08 08:03 08:58 15:15 16:10 17:06

N 58◦ 07:01 07:52 08:43 15:31 16:21 17:1256◦ 06:55 07:43 08:29 15:44 16:30 17:1954◦ 06:49 07:34 08:17 15:56 16:39 17:2452◦ 06:44 07:27 08:07 16:06 16:46 17:2950◦ 06:39 07:20 07:58 16:15 16:53 17:3445◦ 06:28 07:05 07:38 16:35 17:08 17:45

N 40◦ 06:18 06:52 07:22 16:51 17:21 17:5535◦ 06:10 06:41 07:09 17:04 17:32 18:0330◦ 06:01 06:31 06:57 17:16 17:42 18:1220◦ 05:46 06:13 06:37 17:36 18:00 18:27

N 10◦ 05:30 05:57 06:19 17:54 18:16 18:420◦ 05:14 05:40 06:03 18:10 18:32 18:58

S 10◦ 04:56 05:23 05:46 18:27 18:50 19:1720◦ 04:35 05:04 05:28 18:45 19:09 19:3830◦ 04:07 04:40 05:07 19:06 19:33 20:0635◦ 03:49 04:25 04:54 19:18 19:47 20:2340◦ 03:27 04:08 04:40 19:32 20:05 20:4545◦ 02:58 03:47 04:23 19:49 20:26 21:14

S 50◦ 02:17 03:19 04:02 20:10 20:53 21:5552◦ 01:53 03:05 03:52 20:20 21:07 22:1854◦ 01:18 02:48 03:40 20:32 21:24 22:5256◦ 02:28 03:27 20:45 21:4358◦ 02:02 03:12 21:00 22:09

S 60◦ 01:25 02:53 21:19 22:45


Fri Sat Sun Fri Sat Sun

N 72◦ 11:55 11:03 10:28 17:17 19:56 22:10

N 70◦ 11:25 10:50 10:24 17:45 20:06 22:1068◦ 11:02 10:39 10:21 18:06 20:14 22:1166◦ 10:44 10:29 10:18 18:23 20:21 22:1164◦ 10:29 10:22 10:15 18:36 20:27 22:1162◦ 10:17 10:15 10:13 18:47 20:32 22:1160◦ 10:06 10:09 10:11 18:56 20:37 22:11

N 58◦ 09:57 10:04 10:10 19:04 20:40 22:1156◦ 09:48 09:59 10:08 19:12 20:44 22:1154◦ 09:41 09:55 10:07 19:18 20:47 22:1152◦ 09:35 09:51 10:06 19:24 20:50 22:1150◦ 09:29 09:48 10:04 19:29 20:52 22:1145◦ 09:16 09:41 10:02 19:40 20:57 22:11

N 40◦ 09:05 09:34 10:00 19:49 21:02 22:1135◦ 08:56 09:29 09:58 19:57 21:06 22:1130◦ 08:48 09:24 09:57 20:03 21:09 22:1120◦ 08:33 09:16 09:54 20:15 21:15 22:11

N 10◦ 08:21 09:08 09:51 20:25 21:20 22:110◦ 08:09 09:01 09:49 20:35 21:24 22:11

S 10◦ 07:58 08:54 09:47 20:44 21:29 22:1120◦ 07:45 08:47 09:44 20:54 21:34 22:1130◦ 07:31 08:38 09:42 21:05 21:39 22:1135◦ 07:22 08:33 09:40 21:11 21:42 22:1140◦ 07:13 08:28 09:38 21:18 21:46 22:1145◦ 07:01 08:21 09:36 21:27 21:50 22:10

S 50◦ 06:48 08:13 09:34 21:37 21:55 22:1052◦ 06:41 08:09 09:33 21:41 21:57 22:1054◦ 06:34 08:05 09:31 21:46 21:59 22:1056◦ 06:26 08:01 09:30 21:52 22:02 22:1058◦ 06:17 07:56 09:28 21:58 22:05 22:10

S 60◦ 06:07 07:50 09:27 22:05 22:08 22:10

Day



07 05:44 05:57 12:06 14:22 01:5508 06:11 06:24 12:06 15:13 02:4809 06:37 06:49 12:07 16:00 03:37

7

January 10, 11, 12 (Mon., Tue., Wed.)

Aries Venus Mars Jupiter SaturnMon GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 108◦11.7 147◦38.3 S17◦12.4 315◦24.0 N15◦20.2 113◦36.1 S03◦40.2 4◦33.5 N22◦23.01 123◦14.2 162◦37.7 11.4 330◦26.7 20.4 128◦38.2 40.0 19◦36.2 23.12 138◦16.7 177◦37.1 10.4 345◦29.5 20.6 143◦40.3 39.9 34◦38.9 23.13 153◦19.1 192◦36.4 · · 09.5 0◦32.2 · · 20.8 158◦42.4 · · 39.7 49◦41.6 · · 23.14 168◦21.6 207◦35.8 08.5 15◦34.9 21.0 173◦44.5 39.5 64◦44.3 23.15 183◦24.1 222◦35.2 07.5 30◦37.6 21.2 188◦46.6 39.4 79◦47.0 23.2

6 198◦26.5 237◦34.6 S17◦06.6 45◦40.4 N15◦21.4 203◦48.7 S03◦39.2 94◦49.7 N22◦23.27 213◦29.0 252◦34.0 05.6 60◦43.1 21.6 218◦50.7 39.0 109◦52.3 23.28 228◦31.5 267◦33.4 04.6 75◦45.8 21.8 233◦52.8 38.8 124◦55.0 23.29 243◦33.9 282◦32.8 · · 03.6 90◦48.6 · · 22.0 248◦54.9 · · 38.7 139◦57.7 · · 23.310 258◦36.4 297◦32.2 02.7 105◦51.3 22.2 263◦57.0 38.5 155◦00.4 23.311 273◦38.8 312◦31.6 01.7 120◦54.0 22.4 278◦59.1 38.3 170◦03.1 23.3

12 288◦41.3 327◦31.0 S17◦00.7 135◦56.8 N15◦22.6 294◦01.2 S03◦38.2 185◦05.8 N22◦23.313 303◦43.8 342◦30.4 16◦59.8 150◦59.5 22.8 309◦03.3 38.0 200◦08.4 23.314 318◦46.2 357◦29.8 58.8 166◦02.3 23.0 324◦05.4 37.8 215◦11.1 23.415 333◦48.7 12◦29.1 · · 57.8 181◦05.0 · · 23.2 339◦07.5 · · 37.7 230◦13.8 · · 23.416 348◦51.2 27◦28.5 56.8 196◦07.8 23.4 354◦09.5 37.5 245◦16.5 23.417 3◦53.6 42◦27.9 55.9 211◦10.5 23.6 9◦11.6 37.3 260◦19.2 23.4

18 18◦56.1 57◦27.3 S16◦54.9 226◦13.2 N15◦23.8 24◦13.7 S03◦37.1 275◦21.9 N22◦23.519 33◦58.6 72◦26.7 53.9 241◦16.0 24.0 39◦15.8 37.0 290◦24.5 23.520 49◦01.0 87◦26.1 52.9 256◦18.7 24.2 54◦17.9 36.8 305◦27.2 23.521 64◦03.5 102◦25.5 · · 51.9 271◦21.5 · · 24.4 69◦20.0 · · 36.6 320◦29.9 · · 23.522 79◦05.9 117◦24.9 51.0 286◦24.2 24.6 84◦22.1 36.5 335◦32.6 23.623 94◦08.4 132◦24.3 50.0 301◦27.0 24.8 99◦24.2 36.3 350◦35.3 23.6


Tue GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 109◦10.9 147◦23.7 S16◦49.0 316◦29.8 N15◦25.0 114◦26.2 S03◦36.1 5◦38.0 N22◦23.61 124◦13.3 162◦23.1 48.0 331◦32.5 25.2 129◦28.3 35.9 20◦40.6 23.62 139◦15.8 177◦22.5 47.0 346◦35.3 25.4 144◦30.4 35.8 35◦43.3 23.73 154◦18.3 192◦21.9 · · 46.0 1◦38.0 · · 25.6 159◦32.5 · · 35.6 50◦46.0 · · 23.74 169◦20.7 207◦21.3 45.0 16◦40.8 25.8 174◦34.6 35.4 65◦48.7 23.75 184◦23.2 222◦20.7 44.1 31◦43.6 26.0 189◦36.7 35.3 80◦51.4 23.7

6 199◦25.7 237◦20.1 S16◦43.1 46◦46.3 N15◦26.2 204◦38.8 S03◦35.1 95◦54.1 N22◦23.87 214◦28.1 252◦19.6 42.1 61◦49.1 26.5 219◦40.8 34.9 110◦56.8 23.88 229◦30.6 267◦19.0 41.1 76◦51.9 26.7 234◦42.9 34.7 125◦59.4 23.89 244◦33.1 282◦18.4 · · 40.1 91◦54.6 · · 26.9 249◦45.0 · · 34.6 141◦02.1 · · 23.810 259◦35.5 297◦17.8 39.1 106◦57.4 27.1 264◦47.1 34.4 156◦04.8 23.811 274◦38.0 312◦17.2 38.1 122◦00.2 27.3 279◦49.2 34.2 171◦07.5 23.9

12 289◦40.4 327◦16.6 S16◦37.1 137◦02.9 N15◦27.5 294◦51.3 S03◦34.1 186◦10.2 N22◦23.913 304◦42.9 342◦16.0 36.1 152◦05.7 27.7 309◦53.3 33.9 201◦12.9 23.914 319◦45.4 357◦15.4 35.1 167◦08.5 27.9 324◦55.4 33.7 216◦15.5 23.915 334◦47.8 12◦14.8 · · 34.2 182◦11.3 · · 28.1 339◦57.5 · · 33.5 231◦18.2 · · 24.016 349◦50.3 27◦14.2 33.2 197◦14.0 28.4 354◦59.6 33.4 246◦20.9 24.017 4◦52.8 42◦13.6 32.2 212◦16.8 28.6 10◦01.7 33.2 261◦23.6 24.0

18 19◦55.2 57◦13.0 S16◦31.2 227◦19.6 N15◦28.8 25◦03.8 S03◦33.0 276◦26.3 N22◦24.019 34◦57.7 72◦12.5 30.2 242◦22.4 29.0 40◦05.8 32.8 291◦29.0 24.120 50◦00.2 87◦11.9 29.2 257◦25.2 29.2 55◦07.9 32.7 306◦31.6 24.121 65◦02.6 102◦11.3 · · 28.2 272◦27.9 · · 29.4 70◦10.0 · · 32.5 321◦34.3 · · 24.122 80◦05.1 117◦10.7 27.2 287◦30.7 29.6 85◦12.1 32.3 336◦37.0 24.123 95◦07.5 132◦10.1 26.2 302◦33.5 29.9 100◦14.2 32.2 351◦39.7 24.2


Wed GHA GHA Dec GHA Dec GHA Dec GHA Dec

0 110◦10.0 147◦09.5 S16◦25.2 317◦36.3 N15◦30.1 115◦16.3 S03◦32.0 6◦42.4 N22◦24.21 125◦12.5 162◦08.9 24.2 332◦39.1 30.3 130◦18.3 31.8 21◦45.0 24.22 140◦14.9 177◦08.4 23.2 347◦41.9 30.5 145◦20.4 31.6 36◦47.7 24.23 155◦17.4 192◦07.8 · · 22.2 2◦44.7 · · 30.7 160◦22.5 · · 31.5 51◦50.4 · · 24.34 170◦19.9 207◦07.2 21.2 17◦47.5 30.9 175◦24.6 31.3 66◦53.1 24.35 185◦22.3 222◦06.6 20.2 32◦50.3 31.2 190◦26.7 31.1 81◦55.8 24.3

6 200◦24.8 237◦06.0 S16◦19.1 47◦53.1 N15◦31.4 205◦28.7 S03◦30.9 96◦58.5 N22◦24.37 215◦27.3 252◦05.5 18.1 62◦55.9 31.6 220◦30.8 30.8 112◦01.1 24.38 230◦29.7 267◦04.9 17.1 77◦58.7 31.8 235◦32.9 30.6 127◦03.8 24.49 245◦32.2 282◦04.3 · · 16.1 93◦01.5 · · 32.0 250◦35.0 · · 30.4 142◦06.5 · · 24.410 260◦34.7 297◦03.7 15.1 108◦04.3 32.3 265◦37.1 30.2 157◦09.2 24.411 275◦37.1 312◦03.1 14.1 123◦07.1 32.5 280◦39.1 30.1 172◦11.9 24.4

12 290◦39.6 327◦02.6 S16◦13.1 138◦09.9 N15◦32.7 295◦41.2 S03◦29.9 187◦14.6 N22◦24.513 305◦42.0 342◦02.0 12.1 153◦12.7 32.9 310◦43.3 29.7 202◦17.2 24.514 320◦44.5 357◦01.4 11.1 168◦15.5 33.2 325◦45.4 29.5 217◦19.9 24.515 335◦47.0 12◦00.8 · · 10.1 183◦18.3 · · 33.4 340◦47.5 · · 29.4 232◦22.6 · · 24.516 350◦49.4 27◦00.3 09.0 198◦21.1 33.6 355◦49.5 29.2 247◦25.3 24.617 5◦51.9 41◦59.7 08.0 213◦23.9 33.8 10◦51.6 29.0 262◦28.0 24.6

18 20◦54.4 56◦59.1 S16◦07.0 228◦26.7 N15◦34.0 25◦53.7 S03◦28.8 277◦30.7 N22◦24.619 35◦56.8 71◦58.5 06.0 243◦29.6 34.3 40◦55.8 28.7 292◦33.3 24.620 50◦59.3 86◦58.0 05.0 258◦32.4 34.5 55◦57.8 28.5 307◦36.0 24.721 66◦01.8 101◦57.4 · · 04.0 273◦35.2 · · 34.7 70◦59.9 · · 28.3 322◦38.7 · · 24.722 81◦04.2 116◦56.8 02.9 288◦38.0 34.9 86◦02.0 28.1 337◦41.4 24.723 96◦06.7 131◦56.2 01.9 303◦40.8 35.2 101◦04.1 28.0 352◦44.1 24.7


StarsSHA Dec

Alpheratz 358◦59.3 28◦37.8Ankaa 354◦27.8 -42◦45.9

Schedar 351◦04.0 56◦05.0Diphda 350◦09.2 -18◦26.9


Aldebaran 292◦1

Documents

The Nautical Almanac 1916 Nautical Almanac.pdf · As he has said, "The art of celestial navigation should be promoted, not discouraged, even in the modern day". To both of these men