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2021 Sun Only The Nautical Almanac 2021 For the Sun TheNauticalAlmanac.com Contents Credits, Acknowledgment and Disclaimer p. 3 Useful Links p. 4 Formulas p. 5 - 7 Equation of Time curve p. 8 The Daily Pages for the Sun p. 9 - 33 Increments & Corrections (The Yellow Pages) p. 34 - 53 Conversion of Arc to Time p. 54 Altitude Corrections for Sun, Planets, Stars (includes Refraction and Dip) p. 55 - 56 USNO Navigational Star Chart p. 57 Sun TOCR.odt 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 Skyfieldand 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 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 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 In Southern Latitudes LHA greater than 180°....Zn=Z LHA greater than 180°....Zn= 180° – Z LHA less than 180°...........Zn=360° – 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 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 Equation_of_Time_Curve.odt Time in minutes Sun is running Slow Sun is running Fast -20 -16 -12 12 16 20 -8 -4 0 4 8 January February March April May June July August September October November December November October September August July June May April MarchJanuary February Equation of Time of Equation for the Sun the for DUT1 = UT1-UTC = -1.2060 sec ∆T = TT-UT1 = +70.3900 sec 2021 January 01 to Jan. 15 UT 01 GHA Dec 04 GHA Dec 07 GHA Dec 10 GHA Dec 13 GHA Dec 0 179◦08.5 S23◦00.0 0 178◦47.7 S22◦43.1 0 178◦27.7 S22◦22.1 0 178◦08.9 S21◦57.3 0 177◦51.2 S21◦28.5 1 194◦08.2 22◦59.7 1 193◦47.4 42.8 1 193◦27.5 21.8 1 193◦08.6 56.9 1 192◦51.0 28.1 2 209◦07.9 59.5 2 208◦47.1 42.6 2 208◦27.2 21.5 2 208◦08.4 56.5 2 207◦50.8 27.6 3 224◦07.6 ·· 59.3 3 223◦46.8 ·· 42.3 3 223◦26.9 ·· 21.2 3 223◦08.1 ·· 56.1 3 222◦50.5 ·· 27.2 4 239◦07.3 59.1 4 238◦46.5 42.0 4 238◦26.7 20.9 4 238◦07.9 55.8 4 237◦50.3 26.8 5 254◦07.0 58.9 5 253◦46.3 41.8 5 253◦26.4 20.5 5 253◦07.6 55.4 5 252◦50.1 26.4 6 269◦06.7 S22◦58.7 6 268◦46.0 S22◦41.5 6 268◦26.1 S22◦20.2 6 268◦07.4 S21◦55.0 6 267◦49.8 S21◦25.9 7 284◦06.4 58.5 7 283◦45.7 41.2 7 283◦25.9 19.9 7 283◦07.1 54.6 7 282◦49.6 25.5 8 299◦06.1 58.3 8 298◦45.4 41.0 8 298◦25.6 19.6 8 298◦06.8 54.2 8 297◦49.4 25.1 9 314◦05.8 ·· 58.1 9 313◦45.1 ·· 40.7 9 313◦25.3 ·· 19.3 9 313◦06.6 ·· 53.9 9 312◦49.1 ·· 24.6 10 329◦05.5 57.9 10 328◦44.9 40.4 10 328◦25.1 18.9 10 328◦06.3 53.5 10 327◦48.9 24.2 11 344◦05.3 57.6 11 343◦44.6 40.1 11 343◦24.8 18.6 11 343◦06.1 53.1 11 342◦48.7 23.8 12 359◦05.0 S22◦57.4
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