The Mathematical Dynamics of Celestial Navigation and Astronavigation
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Astro-Navigation
Astro-Navigation coincidence with a second star about goo in angular distance away from it in the heavens. Move the sextant about so that the observed stars are seen CHAPTER XXVII through different parts of the telescope's field. There is no collimation error if the star and star- Running Down a Position-Line image remain in coincidence. This is an unlikeiy error and, even if present, is scarcely worth worry- BY DAYLIGHT ing about unless large altitudes are being observed. OBSERVATIONS RESTRICTED Adjustment is made by altering the setting of the For most of the time in daylight only the sun can telescope collar. be observed. Occasionally the sun and a planet are both visible and on a few days in the month 1 sun and the moon can be observed together DEFECTIVE SHADES the during part of the day. Actually the moon is "up" A glare-screen may be bent by pressure from during nearly half the month's daylight, but for the metal frame gripping it. If the tr,vo faces are several days on each side of "new moonr" it is not parallel, rays passing through will be deviated too close to the sun for its position-Iine to make from their true path. The weakest screen can be a worthwhile cut with the srin's, and these ferv tested by first observing a planet without the days account for the greater portion ofits daylight screen, then with; the two readings should agree appearance. (if allowance is made for any change of altitude In short, for most of the time in daylight only during the interval). -
Basic Principles of Celestial Navigation James A
Basic principles of celestial navigation James A. Van Allena) Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242 ͑Received 16 January 2004; accepted 10 June 2004͒ Celestial navigation is a technique for determining one’s geographic position by the observation of identified stars, identified planets, the Sun, and the Moon. This subject has a multitude of refinements which, although valuable to a professional navigator, tend to obscure the basic principles. I describe these principles, give an analytical solution of the classical two-star-sight problem without any dependence on prior knowledge of position, and include several examples. Some approximations and simplifications are made in the interest of clarity. © 2004 American Association of Physics Teachers. ͓DOI: 10.1119/1.1778391͔ I. INTRODUCTION longitude ⌳ is between 0° and 360°, although often it is convenient to take the longitude westward of the prime me- Celestial navigation is a technique for determining one’s ridian to be between 0° and Ϫ180°. The longitude of P also geographic position by the observation of identified stars, can be specified by the plane angle in the equatorial plane identified planets, the Sun, and the Moon. Its basic principles whose vertex is at O with one radial line through the point at are a combination of rudimentary astronomical knowledge 1–3 which the meridian through P intersects the equatorial plane and spherical trigonometry. and the other radial line through the point G at which the Anyone who has been on a ship that is remote from any prime meridian intersects the equatorial plane ͑see Fig. -
Celestial Navigation Tutorial
NavSoft’s CELESTIAL NAVIGATION TUTORIAL Contents Using a Sextant Altitude 2 The Concept Celestial Navigation Position Lines 3 Sight Calculations and Obtaining a Position 6 Correcting a Sextant Altitude Calculating the Bearing and Distance ABC and Sight Reduction Tables Obtaining a Position Line Combining Position Lines Corrections 10 Index Error Dip Refraction Temperature and Pressure Corrections to Refraction Semi Diameter Augmentation of the Moon’s Semi-Diameter Parallax Reduction of the Moon’s Horizontal Parallax Examples Nautical Almanac Information 14 GHA & LHA Declination Examples Simplifications and Accuracy Methods for Calculating a Position 17 Plane Sailing Mercator Sailing Celestial Navigation and Spherical Trigonometry 19 The PZX Triangle Spherical Formulae Napier’s Rules The Concept of Using a Sextant Altitude Using the altitude of a celestial body is similar to using the altitude of a lighthouse or similar object of known height, to obtain a distance. One object or body provides a distance but the observer can be anywhere on a circle of that radius away from the object. At least two distances/ circles are necessary for a position. (Three avoids ambiguity.) In practice, only that part of the circle near an assumed position would be drawn. Using a Sextant for Celestial Navigation After a few corrections, a sextant gives the true distance of a body if measured on an imaginary sphere surrounding the earth. Using a Nautical Almanac to find the position of the body, the body’s position could be plotted on an appropriate chart and then a circle of the correct radius drawn around it. In practice the circles are usually thousands of miles in radius therefore distances are calculated and compared with an estimate. -
Air Corps Field Manual Air Navigation Chapter 1 General * 1
MHI Copy 3 FM 1-30 WAUI DEPARTMENT AIR CORPS FIELD MANUAL AIR NAVIGATION ;ren't - .', 1?+6e :_ FM 1 AIR CORPS FIELD MANUAL AIR NAVIGATION Prepared under direction of the Chief of the Air Corps UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON: 1940 For sale by the Superintendent of Documents. Washington, D.C.- Price 15 cents WAR DEPARTMENT, WASHINGTON, AUgUst 30, 1940. FM 1-30, Air Corps Field Manual, Air Navigation, is pub- lished for the information and guidance of all concerned. [A. G. 062.11 (5-28-40).] BY ORDER OF THE SECRETARY OF WAR: G. C. MARSHALL, Chief of Staff. OFFICIAL: E. S. ADAMS, Major General, The Adjutant General. TABLE OF CONTENTS Paragraph Page CHAPTER 1. GENERAL -___-_______________________ 1-6 1 CHAPTER 2. PILOTAGE AND DEAD RECKONING. Section I. General -_______________--________ 7-9 3 II. Pilot-navigator ___:_-- __________ 10-14 3 II. Navigator __---___--____-- ________ 15-19 6 CHAPTER 3. RADIO NAVIGATION. Section I. Facilities and equipment__________ 20-26 14 II. Practice -______________----------- 27-30 18 CHAPTER 4. CELESTIAL NAVIGATION. Section I. General__________________________-31-33 22 II. Instruments and equipment_-__-__ 34-39 22 III. Celestial line of position -------__ 40-47 23 IV. Preflight preparation ------------- 48-50 30 V. Practice _________________________ 51-59 30 APPENDIX. GLOSSARY OF TERMS ____.__________________-- 35 INDEX --________ ------------------ ----- - 39 III FN. AIR CORPS FIELD MANUAL AIR NAVIGATION CHAPTER 1 GENERAL * 1. SCOPE.-This manual is a general treatise on all methods and technique of air navigation and a brief summary of instruments and equipment used. -
Printable Celestial Navigation Work Forms
S T A R P A T H ® S c h o o l o f N a v i g a t i o n PRINTABLE CELESTIAL NAVIGATION WORK FORMS For detailed instructions and numerical examples, see the companion booklet listed below. FORM 104 — All bodies, using Pub 249 or Pub 229 FORM 106 — All Bodies, Using NAO Tables FORM 108 — All Bodies, Almanac, and NAO Tables FORM 109 — Solar Index Correction FORM 107 — Latitude at LAN FORM 110 — Latitude by Polaris FORM 117 — Lat, Lon at LAN plus Polaris FORM 111 — Pub 249, Vol. 1 Selected Stars Other Starpath publications on Celestial Navigation Celestial Navigation Starpath Celestial Navigation Work Forms Hawaii by Sextant How to Use Plastic Sextants The Star Finder Book GPS Backup with a Mark 3 Sextant Emergency Navigation Stark Tables for Clearing the Lunar Distance Long Term Almanac 2000 to 2050 Celestial Navigation Work Form Form 104, All Sights, Pub. 249 or Pub. 229 WT h m s date body Hs ° ´ WE DR log index corr. 1 +S -F Lat + off - on ZD DR HE DIP +W -E Lon ft - UTC h m s UTC date / LOP label Ha ° ´ GHA v Dec d HP ° ´ moon ° ´ + 2 hr. planets hr - moon GHA + d additional ° ´ + ´ altitude corr. m.s. corr. - moon, mars, venus 3 SHA + stars Dec Dec altitude corr. or ° ´ or ° ´ all sights v corr. moon, planets min GHA upper limb moon ° ´ tens d subtract 30’ d upper Ho units d ° ´ a-Lon ° ´ d lower -W+E dsd dsd T LHA corr. + Hc 00´ W / 60´ E ° d. -
A History of Maritime Radio- Navigation Positioning Systems Used in Poland
THE JOURNAL OF NAVIGATION (2016), 69, 468–480. © The Royal Institute of Navigation 2016 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/S0373463315000879 A History of Maritime Radio- Navigation Positioning Systems used in Poland Cezary Specht, Adam Weintrit and Mariusz Specht (Gdynia Maritime University, Gdynia, Poland) (E-mail: [email protected]) This paper describes the genesis, the principle of operation and characteristics of selected radio-navigation positioning systems, which in addition to terrestrial methods formed a system of navigational marking constituting the primary method for determining the location in the sea areas of Poland in the years 1948–2000, and sometimes even later. The major ones are: maritime circular radiobeacons (RC), Decca-Navigator System (DNS) and Differential GPS (DGPS), as well as solutions forgotten today: AD-2 and SYLEDIS. In this paper, due to its limited volume, the authors have omitted the description of the solutions used by the Polish Navy (RYM, BRAS, JEMIOŁUSZKA, TSIKADA) and the global or continental systems (TRANSIT, GPS, GLONASS, OMEGA, EGNOS, LORAN, CONSOL) - described widely in world literature. KEYWORDS 1. Radio-Navigation. 2. Positioning systems. 3. Decca-Navigator System (DNS). 4. Maritime circular radiobeacons (RC). 5. AD-2 system. 6. SYLEDIS. 7. Differential GPS (DGPS). Submitted: 21 June 2015. Accepted: 30 October 2015. First published online: 11 January 2016. 1. INTRODUCTION. Navigation is the process of object motion control (Specht, 2007), thus determination of position is its essence. -
6.- Methods for Latitude and Longitude Measurement
Chapter 6 Copyright © 1997-2004 Henning Umland All Rights Reserved Methods for Latitude and Longitude Measurement Latitude by Polaris The observed altitude of a star being vertically above the geographic north pole would be numerically equal to the latitude of the observer ( Fig. 6-1 ). This is nearly the case with the pole star (Polaris). However, since there is a measurable angular distance between Polaris and the polar axis of the earth (presently ca. 1°), the altitude of Polaris is a function of the local hour angle. The altitude of Polaris is also affected by nutation. To obtain the accurate latitude, several corrections have to be applied: = − ° + + + Lat Ho 1 a0 a1 a2 The corrections a0, a1, and a2 depend on LHA Aries , the observer's estimated latitude, and the number of the month. They are given in the Polaris Tables of the Nautical Almanac [12]. To extract the data, the observer has to know his approximate position and the approximate time. When using a computer almanac instead of the N. A., we can calculate Lat with the following simple procedure. Lat E is our estimated latitude, Dec is the declination of Polaris, and t is the meridian angle of Polaris (calculated from GHA and our estimated longitude). Hc is the computed altitude, Ho is the observed altitude (see chapter 4). = ( ⋅ + ⋅ ⋅ ) Hc arcsin sin Lat E sin Dec cos Lat E cos Dec cos t ∆ H = Ho − Hc Adding the altitude difference, ∆H, to the estimated latitude, we obtain the improved latitude: ≈ + ∆ Lat Lat E H The error of Lat is smaller than 0.1' when Lat E is smaller than 70° and when the error of Lat E is smaller than 2°, provided the exact longitude is known. -
Celestial Navigation At
Celestial Navigation at Sea Agenda • Moments in History • LOP (Bearing “Line of Position”) -- in piloting and celestial navigation • DR Navigation: Cornerstone of Navigation at Sea • Ocean Navigation: Combining DR Navigation with a fix of celestial body • Tools of the Celestial Navigator (a Selection, including Sextant) • Sextant Basics • Celestial Geometry • Time Categories and Time Zones (West and East) • From Measured Altitude Angles (the Sun) to LOP • Plotting a Sun Fix • Landfall Strategies: From NGA-Ocean Plotting Sheet to Coastal Chart Disclaimer! M0MENTS IN HISTORY 1731 John Hadley (English) and Thomas Godfrey (Am. Colonies) invent the Sextant 1736 John Harrison (English) invents the Marine Chronometer. Longitude can now be calculated (Time/Speed/Distance) 1766 First Nautical Almanac by Nevil Maskelyne (English) 1830 U.S. Naval Observatory founded (Nautical Almanac) An Ancient Practice, again Alive Today! Celestial Navigation Today • To no-one’s surprise, for most boaters today, navigation = electronics to navigate. • The Navy has long relied on it’s GPS-based Voyage Management System. (GPS had first been developed as a U.S. military “tool”.) • If celestial navigation comes to mind, it may bring up romantic notions or longing: Sailing or navigating “by the stars” • Yet, some study, teach and practice Celestial Navigation to keep the skill alive—and, once again, to keep our nation safe Celestial Navigation comes up in literature and film to this day: • Master and Commander with Russell Crowe and Paul Bettany. Film based on: • The “Aubrey and Maturin” novels by Patrick O’Brian • Horatio Hornblower novels by C. S. Forester • The Horatio Hornblower TV series, etc. • Airborne by William F. -
Lunar Distances Final
A (NOT SO) BRIEF HISTORY OF LUNAR DISTANCES: LUNAR LONGITUDE DETERMINATION AT SEA BEFORE THE CHRONOMETER Richard de Grijs Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Email: [email protected] Abstract: Longitude determination at sea gained increasing commercial importance in the late Middle Ages, spawned by a commensurate increase in long-distance merchant shipping activity. Prior to the successful development of an accurate marine timepiece in the late-eighteenth century, marine navigators relied predominantly on the Moon for their time and longitude determinations. Lunar eclipses had been used for relative position determinations since Antiquity, but their rare occurrences precludes their routine use as reliable way markers. Measuring lunar distances, using the projected positions on the sky of the Moon and bright reference objects—the Sun or one or more bright stars—became the method of choice. It gained in profile and importance through the British Board of Longitude’s endorsement in 1765 of the establishment of a Nautical Almanac. Numerous ‘projectors’ jumped onto the bandwagon, leading to a proliferation of lunar ephemeris tables. Chronometers became both more affordable and more commonplace by the mid-nineteenth century, signaling the beginning of the end for the lunar distance method as a means to determine one’s longitude at sea. Keywords: lunar eclipses, lunar distance method, longitude determination, almanacs, ephemeris tables 1 THE MOON AS A RELIABLE GUIDE FOR NAVIGATION As European nations increasingly ventured beyond their home waters from the late Middle Ages onwards, developing the means to determine one’s position at sea, out of view of familiar shorelines, became an increasingly pressing problem. -
Celestial Navigation Practical Theory and Application of Principles
Celestial Navigation Practical Theory and Application of Principles By Ron Davidson 1 Contents Preface .................................................................................................................................................................................. 3 The Essence of Celestial Navigation ...................................................................................................................................... 4 Altitudes and Co-Altitudes .................................................................................................................................................... 6 The Concepts at Work ........................................................................................................................................................ 12 A Bit of History .................................................................................................................................................................... 12 The Mariner’s Angle ........................................................................................................................................................ 13 The Equal-Altitude Line of Position (Circle of Position) ................................................................................................... 14 Using the Nautical Almanac ............................................................................................................................................ 15 The Limitations of Mechanical Methods ........................................................................................................................ -
Chapter 19 Sight Reduction
CHAPTER 19 SIGHT REDUCTION BASIC PROCEDURES 1900. Computer Sight Reduction 1901. Tabular Sight Reduction The purely mathematical process of sight reduction is The process of deriving from celestial observations the an ideal candidate for computerization, and a number of information needed for establishing a line of position, different hand-held calculators, apps, and computer LOP, is called sight reduction. The observation itself con- programs have been developed to relieve the tedium of sists of measuring the altitude of the celestial body above working out sights by tabular or mathematical methods. the visible horizon and noting the time. The civilian navigator can choose from a wide variety of This chapter concentrates on sight reduction using the hand-held calculators and computer programs that require Nautical Almanac and Pub. No. 229: Sight Reduction Ta- only the entry of the DR position, measured altitude of the bles for Marine Navigation. Pub 229 is available on the body, and the time of observation. Even knowing the name NGA website. The method described here is one of many of the body is unnecessary because the computer can methods of reducing a sight. Use of the Nautical Almanac identify it based on the entered data. Calculators, apps, and and Pub. 229 provide the most precise sight reduction prac- computers can provide more accurate solutions than tabular tical, 0.'1 (or about 180 meters). and mathematical methods because they can be based on The Nautical Almanac contains a set of concise sight precise analytical computations rather than rounded values reduction tables and instruction on their use. It also contains inherent in tabular data. -
Exercises in Archaeoastronomy -2 -The Passage Mound of Newgrange Amelia Carolina Sparavigna
Exercises in Archaeoastronomy -2 -The passage mound of Newgrange Amelia Carolina Sparavigna To cite this version: Amelia Carolina Sparavigna. Exercises in Archaeoastronomy -2 -The passage mound of Newgrange. Philica, Philica, 2018. hal-01712819 HAL Id: hal-01712819 https://hal.archives-ouvertes.fr/hal-01712819 Submitted on 19 Feb 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Exercises in Archaeoastronomy - 2 - The passage mound of Newgrange Amelia Carolina Sparavigna (Department of Applied Science and Technology, Politecnico di Torino) Published in enviro.philica.com Abstract Here it is given the second article of a series proposing exercises in archaeoastronomy. The reader can find exercises about the apparent motion of the sun, and its azimuth and altitude given in the horizontal coordinate system. As case study, we investigate the orientation of the prehistoric passage mound of Newgrange. In the previous article [1], we have introduced a series of exercises in archaeoastronomy. Let us start the series by studying the sun and its horizontal coordinates. After exercises on azimuth and altitude of the sun, we consider some prehistoric monuments. In particular we propose exercises on the passage mound of Newgrange, as a case study.