celestial navigation.pdf

A Short Guide to

Celestial Navigation

Revised January 2, 2003

Index

Preface

Chapter 1

The Elements of Celestial Navigation

Chapter 2

Altitude Measurement

Chapter 3

The Geographic Position of a Celestial Body

Chapter 4

Finding One's Position (Sight Reduction)

Chapter 5

Finding the Position of a Traveling Vessel

Chapter 6

Methods for Latitude and Longitude Measurement

Chapter 7

Finding Time and Longitude by Lunar Observations

Chapter 8

Rise, Set, Twilight

Chapter 9

Geodetic Aspects of Celestial Navigation

Chapter 10

Spherical Trigonometry

Chapter 11

The Navigational Triangle

Chapter 12

Other Navigational Formulas

Chapter 13

Mercator Charts and Plotting Sheets

Chapter 14

Magnetic Declination

Chapter 15

Ephemerides of the Sun

Chapter 16

Navigational Errors

Appendix

Legal Notice

Carpe diem.

Horace

Preface

Why should anybody still use celestial navigation in the era of electronics and GPS? You might as well ask why some

people still develop black and white photos in their darkroom instead of using a high-color digital camera and image

processing software. The answer would be the same: because it is a noble art, and because it is fun. Reading a GPS

display is easy and not very exciting as soon as you have got used to it. Celestial navigation, however, will always be a

challenge because each scenario is different. Finding your geographic position by means of astronomical observations

requires knowledge, judgement, and the ability to handle delicate instruments. In other words, you play an active part

during the whole process, and you have to use your brains. Everyone who ever reduced a sight knows the thrill I am

talking about. The way is the goal.

It took centuries and generations of navigators, astronomers, geographers, mathematicians, and instrument makers to

develop the art and science of celestial navigation to its present state, and the knowledge thus accumulated is too

precious to be forgotten. After all, celestial navigation will always be a valuable alternative if a GPS receiver happens to

fail.

Years ago, when I read my first book on navigation, the chapter on celestial navigation with its fascinating diagrams and

formulas immediately caught my particular interest although I was a little deterred by its complexity at first. As I became

more advanced, I realized that celestial navigation is not as difficult as it seems to be at first glance. Further, I found that

many publications on this subject, although packed with information, are more confusing than enlightening, probably

because most of them have been written by experts and for experts.

I decided to write something like a compact guide-book for my personal use which had to include operating instructions

as well as all important formulas and diagrams. The idea to publish it came in 1997 when I became interested in the

internet and found that it is the ideal medium to share one's knowledge with others. I took my manuscript, rewrote it in

the form of a structured manual, and redesigned the layout to make it more attractive to the public. After converting

everything to the HTML format, I published it on my web site. Since then, I have revised text and graphic images

several times and added a couple of new chapters.

Following the recent trend, I decided to convert the manual to the PDF format, which has become an established

standard for internet publishing. In contrast to HTML documents, the page-oriented PDF documents retain their layout

when printed. The HTML version is no longer available since keeping two versions in different formats synchronized

was too much work. In my opinion, a printed manual is more useful anyway.

Since people keep asking me how I wrote the documents and how I created the graphic images, a short description of

the procedure and software used is given below:

Drawings and diagrams were made with good old CorelDraw! 3.0 and exported as gif files. The manual was designed

and written with Star Office 5. The Star Office (.sdw) documents were then converted to Postscript (.ps) files with the

AdobePS printer driver (available at www.adobe.com). Finally, the Postscript files were converted to pdf files with

GsView and Ghostscript (www.ghostscript.com).

I apologize for misspellings, grammar errors, and wrong punctuation. I did my best, but after all, English is not my

native language.

I hope the new version will find as many readers as the old one. Please contact me if you find errors. Due to the

increasing number of questions I get every day, I am lagging far behind with my correspondence, and I am no longer

able to provide individual support. I really appreciate the interest in my web site, but I still have a few other things to

do, e. g., working for my living. Remember, this is just a hobby.

Last but not least, I owe my wife an apology for spending countless hours in front of the PC, staying up late, neglecting

household chores, etc. I'll try to mend my ways. Some day ...

January 2, 2003

Henning Umland

Correspondence address:

Dr. Henning Umland

Rabenhorst 6

21244 Buchholz i. d. N.

Germany

Fax: +49 89 2443 68325

E-mail: astro@celnav.de

Chapter 1

The Elements of Celestial Navigation

Celestial navigation , a branch of applied astronomy, is the art and science of finding one's geographic position through

astronomical observations, particularly by measuring altitudes of celestial bodies – sun, moon, planets, or stars.

An observer watching the night sky without knowing anything about geography and astronomy might spontaneously get

the impression of being on a plane located at the center of a huge, hollow sphere with the celestial bodies attached to its

inner surface. Indeed, this naive model of the universe was in use for millennia and developed to a high degree of

perfection by ancient astronomers. Still today, it is a useful tool for celestial navigation since the navigator, like the

astronomers of old, measures apparent positions of bodies in the sky but not their absolute positions in space.

Following the above scenario, the apparent position of a body in the sky is defined by the horizon system of

coordinates . In this system, the observer is located at the center of a fictitious hollow sphere of infinite diameter, the

celestial sphere , which is divided into two hemispheres by the plane of the celestial horizon ( Fig. 1-1 ). The altitude ,

H , is the vertical angle between the line of sight to the respective body and the celestial horizon, measured from 0°

through +90° when the body is above the horizon (visible) and from 0° through -90° when the body is below the horizon

(invisible). The zenith distance , z , is the corresponding angular distance between the body and the zenith , an imaginary

point vertically overhead. The zenith distance is measured from 0° through 180°. The point opposite to the zenith is

called nadir (z = 180°). H and z are complementary angles (H + z = 90°). The azimuth , Az N , is the horizontal

direction of the body with respect to the geographic (true) north point on the horizon, measured clockwise from 0°

through 360°.

In reality, the observer is not located at the celestial horizon but at the the sensible horizon. Fig. 1-2 shows the three

horizontal planes relevant to celestial navigation:

The sensible horizon is the horizontal plane passing through the observer's eye. The celestial horizon is the horizontal

plane passing through the center of the earth which coincides with the center of the celestial sphere. Moreover, there is

the geoidal horizon, the horizontal plane tangent to the earth at the observer's position. These three planes are parallel

to each other.

The sensible horizon merges into the geoidal horizon when the observer's eye is at sea or ground level. Since both

horizons are usually very close to each other, they can be considered as identical under practical conditions. None of the

above horizontal planes coincides with the visible horizon , the line where the earth's surface and the sky appear to meet.

Calculations of celestial navigation always refer to the geocentric altitude of a body, the altitude with respect to a

fictitious observer being at the celestial horizon and at the center of the earth which coincides the center of the

celestial sphere. Since there is no way to measure this altitude directly, it has to be derived from the altitude with

respect to the visible or sensible horizon (altitude corrections, chapter 2).

A marine sextant is an instrument designed to measure the altitude of a body with reference to the visible sea horizon.

Instruments with any kind of an artificial horizon measure the altitude referring to the sensible horizon (chapter 2).

Altitude and zenith distance of a celestial body depend on the distance between a terrestrial observer and the

geographic position of the body , GP . GP is the point where a straight line from the body to the center of the earth, C,

intersects the earth's surface ( Fig. 1-3 ).

A body appears in the zenith (z = 0°, H = 90°) when GP is identical with the observer's position. A terrestrial observer

moving away from GP will observe that the altitude of the body decreases as his distance from GP increases. The body

is on the celestial horizon (H = 0°, z = 90°) when the observer is one quarter of the circumference of the earth away

from GP.

For a given altitude of a body, there is an infinite number of positions having the same distance from GP and forming a

circle on the earth's surface whose center is on the line C–GP, below the earth's surface. Such a circle is called a circle

of equal altitude . An observer traveling along a circle of equal altitude will measure a constant altitude and zenith

distance of the respective body, no matter where on the circle he is. The radius of the circle, r, measured along the

surface of the earth, is directly proportional to the observed zenith distance, z ( Fig 1-4 ).

[ ]

Perimeter

Earth

[ ]

[ °

360

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