Ocean Navigation Introduction

Corrections to Sextant, Time, Sunrise, Sunset, Twilight, Moonrise, Moonset, Finding GHA and Declination, Assumed Position and Local Hour Angle, Computed Altitude and Azimuth, Amplitudes, Interpolation, Altitude Intercept, Using Position Plotting Sheets, Plotting Lines of Position (Sun, Moon, Stars) LAN, Running Fixes.

This was designed to help you prepare yourself to pass the Coast Guard exam on celestial navigation oceans, or if you are just interested in learning celestial navigation. I have written this with three ideas in mind.

1. Make it as short as possible.
2. Make it in plain arithmetic and keep it in a form that is easy.
3. Use only the materials that will be available in the exam room.

You do not need a sextant to work these problems or the ones on the exam. Learning to use the sextant is a personal skill that is acquired by practice. The Coast Guard test has 10 multiple choice questions with a passing score of 90%.

The Coast Guard exam questions may cover:
1. Sight Reduction (Sun, Star, Moon)
2. Star Fixes
3. Running Fixes
4. Latitude by Meridian Altitude
5. Latitude by Polaris
6. Time of Local Apparent Noon
7. Time of (Sunrise, Sunset, Twilight, Moonrise and Moonset)
8. Deviation or Gyro Error by Azimuth
9. Deviation or Gyro Error by Amplitude
10. Identification of Unknown Stars and Planets
11. How to Select Stars for a Fix
12. Correction of Sextant Altitude
13. ETA Problems
14. Time Tick Problems

I will give you step by step instructions for doing all these problems. You will need PUB 229 (15-30) and a reprint of the 1981 Nautical Almanac, Bowditch volume 2, plotting sheets, and a starfinder, dividers, parallel rules, triangles, and a calculator.

I will also show you how to do sailing problems:
1. Great Circle
2. Mercator
3. Parallel
4. Mid-Latitude

Also included in this site will be Terrestial exam questions:

1. Compass problems with Leeway
2. Finding Deviation or Gyro error on a Range
3. Compass deviation table problems
4. Computing the Visibility of a light
5. Distance off by two bearings
6. Finding a course to steer with a known set and drift
7. Radar plotting problems
8. Computing the height of the tide
9. Computing the velocity of the tidal current
10. Fuel consumption
11. Speed by RPM
12. Zone time calculations

This site will be updated and is under construction.

Local Apparent Noon Problem #1

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Local Apparent Noon Problem #2

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How to Determine your Latitude by Local Apparent Noon (LAN)

The objective of this is to define how to compute a latitude line by using the sun at Local Apparent Noon (LAN).
Since the latitude of a position may be determined by finding the distance between the equinoctial and the zenith, you only need to know the declination and zenith distance (coaltitude) of a body to determine latitude. This has been used by mariners for centuries because of it's simplicity.

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Azimuth Exam Questions (Sun, Stars, Planets)

Azimuth Sun Only
On 31 May 1981, your vessel's 1420 zone time DR position is Lat. 29° 06.0' N, Long. 120° 06.0' W, when an azimuth of the Sun is observed. The bearing of the Sun per standard magnetic compass was 255.3°. The chronometer time of the observation is 10h 17m 24s. The chronometer error is 02m 32s slow. The variation for this area is 12.9° E. What is the deviation of the standard magnetic compass?
A. 2.5° W
B. 2.9° W
C. 2.9° E
D. 3.2° E

On 7 December 1981, your vessel's 0835 zone time DR position is Lat. 28° 30.0' N, Long. 125° 39.3' W, when an azimuth of the Sun is observed. The chronometer time of the sight is 04h 34m 48s, and Sun is bearing 113° per standard compass. The chronometer error 01 m 24s slow, and the variation in the area is 13.0 E. What is the deviation of the standard compass?
A. 0.5° E
B. 1.0° W
C. 2.5° E
D. 3.0° W

Azimuth Stars Only
On 16 June 1981, your 0430 zone time DR position is Lat. 29° 24.0' S, Long. 36° 16.0' E. At that time, you observe Vega bearing 341.0° psc. The chronometer reads 02h 32m 06s, and the chronometer error is 01 m 54s fast. The variation is 20.5° W. What is the deviation?
A. 3.2° E
B. 3.2° W
C. 2.4° W
D. 2.8° E

On 15 October 1981, your 0325 zone time DR position is Lat. 26° 51.0' N, Long. 138° 17.0' W. At that time, you observe Canopus bearing 167° pgc. The chronometer reads 00h 25m 36s, and the chronometer error is 00m 20s slow. The variation is 2° E. What is the gyro error?
A. 1.3° W
B. 3.2° W
C. 3.2° E
D. 4.1° W

Azimuth Planets Only
On 6 October 1981, your0416 zone time DR position is Lat. 25° 16.0' N, Long. 130° 25.0' E At that time, you observe Mars bearing 083° psc. The chronometer reads 07h 16m 22s, and the chronometer error is 00m 10s fast. The variation is 1.5° E. What is the deviation of the standard compass?
A. 0.4° E
B. 1.2° W
C. 3.5° E
D. 19.0 E

At 2326 ZT, on 22 June 1981, your vessel's position IS Lat. 28° 30.0' N, LONG 150° 04.0' W. An azimuth of the planet Jupiter is observed, and the standard compass bearing is 250.4° psc. The chronometer reads 09h 24m 36s and is 01m 12s slow. The variation of this area is 13.5° E. What is the deviation of the standard compass?
A. 3.0° W
B. 3.5° W
C. 1.5° E
D. 2.3° E

Azimuth of the Sun

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Azimuth of the Sun (short method)

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How to Determine the Deviation or Gyro Error by a Azimuth of a Celestial Body

I will explain how to use the azimuth circle to observe the azimuth of a celestial body and how to compute the azimuth of a celestial body.

Azimuth of the Sun
Computation of compass error at sea depends upon the observation of the azimuth of celestial bodies. The Sun is the most commonly used for this purpose. The observed azimuth is recorded, the time (to the nearest second) and the DR position are also noted. With DR position and time, the navigator computes Zn by using the Nautical Almanac and PUB 229 Sight Reduction Tables. The difference between pgc bearing and Zn (true bearing) is the gyro error (G.E.), and the difference between psc bearing and the magnetic bearing is the deviation. It should be appropriately labeled. Keep in mind that accuracy depends on the navigator's knowledge of position and the correct time.

In taking a azimuth of a celestial body, the azimuth circle is used. A azimuth circle is a nonmagnetic metal ring sized to fit on a 7-inch compass bowl or on a gyro repeater. The inner lip is graduated in degrees from 0° to 360° in a counterclockwise direction for the purpose of taking relative bearings. Two sighting vanes (the forward or far van containing a vertical wire, and the after or near vane containing a peep sight) facilitate the observation of bearings and azimuths. Two finger lugs are used to position the instrument exactly while aligning the vanes. A hinged reflector vane mounted althe base and beyond the forward vane is used for reflecting stars and planets when observing azimuths. Beneath the forward vane a reflecting mirror and the extended vertical wire are mounted, enabling the navigator to read the bearing or azimuth from the reflected portion of the compass card. For observing azimuths of the Sun, an additional reflecting mirror and housing are mounted on the ring, each midway between the forward and after vanes. The Sun's rays are reflected by the mirror to the housing where a vertical slit admits a line of light. This admitted light passes through a 45° reflecting prism and is projected on the compass card from which the azimuth is directly read. In observing both bearings and azimuths, two spirit levels, which are attached must be used to level the instrument. A azimuth is similar to a amplitude but it is taken at anytime, not at sunrise or sunset. When taking a azimuth it requires the use of Pub. 229 Sight Reduction Tables for Marine Navigation to obtain the Zn (true bearing).

Pub 229 Sight Reduction Tables for Marine Navigation
Pub. 229 Sight Reduction Tables for Marine Navigation is a set of six volumes of precalculated solutions for the computed altitude (Hc) and the azimuth angle (Z) of the navigational triangle. Each volume covers a 15 degree band of latitude with a 1° overlap occurring between volumes. When taking the Coast Guard exam you will be using Volume 2 - Latitudes 15° - 30°.

Entering arguments for the tables are local hour angle (LHA), latitude, and declination expressed in whole degrees. Values of Hc and Z are tabulated for each whole degree of each of the entering arguments. Tables inside the front and back covers of each volume allow for interpolation. Each volume contains two sets of tabulation for whole degrees of LHA between 0° and 360° The front half is for the first eight degrees of latitude (15° - 22°) covered by that volume, and the second half is for the remaining eight degrees of latitude (22° - 30°). The values of LHA are at the top and bottom of each page. The eight degrees of latitude form the horizontal argument and the declination is the vertical argument. Instructions at the top and bottom of each page indicate whether the tabulations on that page are for the latitude which is the same or contrary to the declination:

If both latitude and declination are north or both south, same name page. If they are of opposite names, north and south or vice versa south and north contrary page. The normal practice of navigation at sea is that the ship's compasses be checked frequently, it has been a custom to check for compass error at least once a day. There are two main celestial navigation methods of determining compass error, which are azimuths and amplitudes. Azimuth observations are simply bearings taken of celestial bodies using one of the ship's compasses. Normally, it is best to take an azimuth when the body's altitude is less than 20 degrees. Azimuths may be taken of any celestial body but the sun is preferred because it is the easiest to observe. The sight reduction calculations for solving azimuths are very similar to determining computed altitude (Hc) and azimuth (Zn) when solving a line of position sight.

Amplitude of the Sun Exam Questions

Amplitude Sun (Celestial Horizon)
When computing an amplitude problem, you are to assume that a celestial body is on the celestial horizon when the stem of the question indicates that the body is on the "CELESTIAL HORIZON" or is at any elevation above the horizon, 1/2 to 2/3rds of a diameter or 21' of arc above the "VISIBLE HORIZON". Do not apply the Table 28, Correction of Amplitude as Observed on the Visible Horizon to the observed bearing. If the stem of an amplitude of the sun problem does not provide the zone time of observation (ZT) assume that sunrise is at 0600 ZT and sunset is at 1800 ZT in order to establish the correct chronometer time and or GMT / Date before entering the Nautical Almanac to compute the Sun's declination for the time of the observation.

1. On 8 December 1981, in DR position Lat. 21° 56.1' S, Long. 17° 21.6' E you observe an amplitude of the Sun. The Sun's center is on the celestial horizon and bears 240.5° psc. The chronometer reads 05h 27m 21s and is 00m 47s fast. Variation in the area is 3.3° E. What is the deviation of the standard magnetic compass?
A. 1.5°W
B. 0.3°W
C. 0.6° E
D. 1.5° E

2. On 11 January 1981, your vessel's 0655 zone time DR position is Lat. 24° 30.0' N, Long. 122° 02.0' W, when an amplitude of the Sun is observed. The Sun's center is on the celestial horizon and bears 101.0° per standard compass. Variation in the area is 11.6° E. The chronometer reads 02h 52m 48s and is 02m 12s slow. What is the deviation of the standard compass?
A. 1.4° E
B. 1.4° W
C. 4.6° E
D. 4.6° W

3. On 10 February 1981 in DR position Lat. 25° 32.0' N, Long. 135° 15.0' E, you observe an amplitude of the Sun. The Sun's center is on the celestial horizon and bears 109° psc. The chronometer reads 09h 43m 25s and is 03m 20s fast. Variation in the area is 4.5° W. What the deviation of the standard magnetic compass?
A. 1.6° E
B. 2.9° W
C. 10.5° E
D. 10.5° W

4. On 9 May 1981, your vessel's 1809 ZT DR position is Lat. 48° 13.7' N, Long. 168° 36.3' E, when an amplitude of the Sun is observed. The Sun's center is on the celestial horizon and bears 283.7° per standard compass. Variation in the area is 13.0° E. The chronometer reads 07h 13m 19s and is 02m 56s fast. What is the deviation of the standard compass?
A. 0.1° W
B. 1.1° W
C. 1.1° E
D. 1.9° W

Amplitude of the Sun (Visible Horizon)
A correction must be applied whenever the amplitude of a celestial body is observed on the "VISIBLE HORIZON". NEVER apply the Table 28, Correction of Amplitude as Observed on the Visible Horizon correction unless the stem of an amplitude problem specifically indicates that the center of a celestial body is on the "VISIBLE HORIZON". NEVER apply the Table 28, Correction of Amplitude as Observed on the Visible Horizon correction to the computed bearing or amplitude. The Table 28, Correction of Amplitude as Observed on the Visible Horizon correction should be applied to the observed bearing of a celestial body on the "VISIBLE HORIZON". For the sun, a planet, or a star, apply the correction to the observed bearing in the direction away from the elevated pole. For the moon apply half of the correction toward the elevated pole.

5. On Sunday, 8 November 1981, your ship is enroute from Texas City, TX, to Portland, ME. At 0632 ZT, you fix your position by Loran at Lat. 27° 06.0' N, Long. 90° 36.0' W. When the lower limb of the Sun was two-thirds of a diameter above the visible horizon, the Sun bore 105° per standard magnetic compass. At this time the chronometer read 12h 39m 20s and is 3m 20s slow. If the variation is 3° E, determine the deviation of the standard compass?
A. 0.8° E
B. 0.8 W
C. 3.8° E
D. 3.8° W

6. On 15 July 1981, in DR position Lat. 22° 19.0' N, Long. 154° 37.0' W, you observe an amplitude of the Sun. The Sun's center is on the visible horizon and bears 298° psc. The chronometer reads 04h 45m 19s and is 01m 56s slow. Variation in the area is 7.5° W. What is the deviation of the standard magnetic compass?
A. 2.7° W
B. 3.0° E
C. 3.6° W
D. 3.9° E

7. On 23 August 1981, at 0604 ZT, in DR position Lat. 16° 42.3' S, Long. 28° 19.3' W, you observed an amplitude of the Sun. The lower limb was a little above the horizon, and the Sun bore 076.0° pgc. At the time of the observation, the helmsman reported that he was heading 143° pgc and 167° per magnetic compass. The variation in the area was 23° W. What were the gyro error and deviation for that heading?
A. 1° W GE / 2° W DEV
B. 1° E GE / 1° E DEV
C. 2° W GE / 1° E DEV
D. 2° E GE / 1° E DEV

8. On 20 June 1981, your vessel's 1955 ZT DR position is Lat. 52° 38.9' N, Long. 03° 42.7' E, when an amplitude of the Sun is observed. The Sun's center is on the visible horizon and bear 311° per gyrocompass. Variation in the area is 6° W. At the time of the observation, the helmsman noted that he was heading 352° per gyrocompass and 358° per steering compass. What is the gyro error and deviation for that heading?
A. 1.3° W GE / 1.3° E DEV
B. 0.0° GE / 0.0° DEV
C. 1.3° W GE / 1.3° W DEV
D.1.3° E GE / 1.3° E DEV

How to Determine the Amplitude of the Sun

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Latitude by Polaris Exam Questions

1. On 5 May 1981, at 1953 zone time, you take a sextant observation of Polaris. Your vessel's DR position is Lat. 29° 30.0' N, Long. 66° 25.7' W, and your sextant reads 29° 07.2'. Your chronometer reads 11h 51m 45s, and your chronometer error is 01m 36s slow. Your height of eye is 56 feet, and the index error for your sextant is 1.5' on the arc. What is the latitude of your vessel from your observation of Polaris?
A. 29° 14.3' N
B. 29° 23.6' N
C. 29° 32.3' N
D. 29° 38.8' N

2. On 14 March 1981, your 1846 ZT DR position is Lat. 21° 57.6' N, Long. 132° 16.2' W. At that time you observe Polaris with a sextant altitude (hs) of 22° 16.8'. The chronometer time of the sight is 03h 45m 10s, and the chronometer error is 01m 32s slow. The index error is 3.2' off the arc, and the height of eye is 44.9 feet. What is your latitude by Polaris?
A. 21° 32.4' N
B. 21° 49.8' N
C. 21° 51.0' N
D. 21° 53.1' N

3. On 24 September 1981, your 1841 zone time DR position is Lat. 25° 15.0' N, Long. 129° 34.5' E. At that time you observe Polaris with a sextant altitude (hs) of 25° 20.8'. The chronometer time of the sight is 09h 38m 12s, and the chronometer error is 03m 12s slow. The index error is 4.3' off the arc, and the height of eye is 52.0 feet. What is your latitude by Polaris?
A. 24° 28.4' N
B. 25° 16.0' N
C. 25° 37.6' N
D. 25° 42.3' N

4. On 16 January 1981, at 1804 zone time, you take a sextant observation of Polaris. Your vessel's DR position is Lat. 36° 12.0' N, Long. 124° 36.0' W, and your sextant reads (hs) 37° 16.4'. Your chronometer reads 02h 02m 12s, and is 01in 36s slow. Your height of eye is 60 feet, and the index error is 1.5' on the arc. From your observation of Polaris, what is the latitude of your vessel?
A. 36° 12.6' N
B. 36° 14.4' N
C. 36° 17.9' N
D. 36° 20.2' N

5. On 29 July 1981, your 1930 zone time DR position is Long. 164° 26.0'E. At that time you observe Polaris with a sextant altitude (hs) of 23° 46.8'. The chronometer time of the sight is 08h 32m 18s, and the chronometer error is 02m 26s fast. The index error is 2.7' on the arc, and the height of eye is 56.0 feet. What is your latitude by Polaris?
A. 24° 01.9' N
B. 24° 19.5' N
C. 24° 31.7' N
D. 25° 19.6' N

6. On 7 December 1981, your 0350 ZT position is LAT 350 42' N, LONG 17° 38' E. You observe Polaris bearing 359.7° pgc. At the time of the observation the helmsman noted that he was heading 016° pgc and 014° psc. The variation is 1.0° E. What is the deviation for that heading?
A. 0.5° E
B. 0.0°
C. 0.5° W
D. 1.5° W

7. On 11 January 1981, your 0450 ZT position is Lat. 38° 42.0' N, Long. 14° 16.0' W. You observe Polaris bearing 358.5° pgc. At the time of the observation the helmsman noted that he was heading 160° pgc and 173° psc. The variation is 9° W. What is the deviation for that heading?
A. 1° E
B. 1° W
C. 3° W
D. 13° W

8. On 11 July 1981, your 0240 ZT position is Lat. 14° 52.0' N, Long. 34° 23.0' W. You observe Polaris bearing 359.8° pgc. At the time of the observation the helmsman noted that he was heading 279° pgc and 299° psc. The variation is 19° W. What is the deviation for that heading?
A. 0.0°
B. 1° E
C. 1° W
D. 3° W

How to Determine your Latitude by Polaris

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How to Select the Best Stars or Planets for a Fix

Star selection problems are one of the more difficult and time consuming of the problems found on USCG license exams. In star selection problems, you have four choices of combinations of three stars, planets, and or the moon in each problem. You must determine which of the four combinations would result in the most reliable fix for the date, time, and DR position. In making a choice the following three things must be considered, listed from highest priority to least priority:

First Priority - The azimuth differences between the bodies should be sufficient to give a reliable fix. The ideal azimuth spread would be for the bearings of the bodies to differ by 120 degrees.

Second Priority - The bodies should be at altitudes between 15 degrees and 70 degrees. Unusual refraction can introduce large errors in low altitude sights, and accurate sights at very high altitudes are difficult to obtain.

Third Priority - The magnitude of the star. Obviously, first magnitude stars are easier to see and to shoot while the horizon is still clearly defined.

In analyzing the four choices the following should be avoided.
1. Two of three bodies are very close together in bearing.
2. All three bodies azimuths fall within the same 180 degrees of bearing.
3. Two of the bodies are reciprocal in bearing or nearly so.

To make a list of stars and planets available for observation at morning or evening twilight for a fix, you would setup the starfinder with the LHA (Aries) and have the planets plotted. Then use the following guide lines for selection of bodies:
1. Altitude 10° to 65°
2. 1st magnitude
3. Bearing 120° apart
4. Always try to get Polaris, it gives you a latitude line of position if you are in the northern hemisphere, and any body who has a bearing of 000° - 180° will do the same thing.
5. To check your course, select bodies with bearings perpendicular to your course.
6. To check your speed, select bodies that are parallel to your course.

In working these Coast Guard exam problems, some groups can be eliminated if one of the bodies in the group is below the horizon for that observer's DR position and time of star time.

Here is a Coast Guard exam problem.
On 23 July 1981, your 1700 zone time DR position is Lat. 27° 29.0' N, Long. 129° 26.0' W. You are on course 079° T at a speed of 20 knots. Considering their magnitude, azimuth, and altitude, which group includes the three bodies best suited for a fix at star time?

A. Arcturus, Jupiter, Denebola
B. Spica, Sabik, Vega
C. Antares, Polaris, Altair
D. Jupiter, Saturn, Polaris

Step 1: Compute the ZT of evening twilight or star time (approx. 1857), use this DR position for your form.

Step 2: Compute the LHA (Aries) and the RA and Declination of the planets.

Step 3: Plot the planets on your starfinder, and then place your blue template over the star base on your LHA (Aries). This will be the stars and planets available at star time.

Step 4: Find the best answer. I use a diagram to help me locate the answers.

How to Plot Planets on the Rude Starfinder

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How to Compute Unidentified Star (Celestial Navigation)

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Rude Starfinder 2102-D

The objective of this is to describe the procedure to use the Rude Starfinder and to be able to identify an unknown body, plot the planets on the Starfinder, and to select the best stars or planets for a fix.

To solve the navigational triangle for a computed altitude and true azimuth, the navigator must know beforehand or be able to determine afterwards the name of the celestial body observed, so that you can obtain its GHA and declination from the Nautical Almanac. Several aids are available to the navigator to assist in identifying and locating celestial bodies, among which is the starfinder. Starfinders are intended to furnish the approximate altitude and true azimuth of celestial bodies either before or after navigational observations. One of the best and most common is the Rude Starfinder.

Star Identification
As a navigator, you may be required to obtain a fix from two or more stars. Actually, only a few of the of stars are used regularly for celestial navigation, and they are not too difficult to locate and identify. No matter where you may be navigating, you can manage very well if you are able to recognize 20 or so. The Nautical Almanac consists of 57 principal stars as well as tables for finding latitude by the North Star (Polaris).

Relative brightness of stars is called magnitudes the lower the magnitude, the brighter the star. Sirius, brightest of them all, has a magnitude of - 1.6, Acamar, dimmest of the navigational stars, is listed at + 3.1 magnitude.

First magnitude stars range from magnitude - 1.6 to magnitude +1.50

Second magnitude stars are those from +1.51 to +2.50

Stars of third magnitude range from +2.51 to +3.50, and so on.

Stars of the sixth magnitude are barely visible to the unaided eye.The magnitudes given here of principal stars are only a fraction of the navigational celestial bodies. Selected navigational planet magnitudes vary due to atmospheric conditions. Mars magnitude, for example, varies from + 1.6 to -2.8. The moon usually has a magnitude of 12.6, however, its "phase" must be considered prior to use. The king of celestial bodies, with a magnitude of -26.7, is the sun, limited only by nighttime and atmospheric conditions. The magnitude of the planets is listed at the top of daily pages and stars at the end of the white pages in the Nautical Almanac.


One or more of the stars in a constellation may be navigational stars. Obviously, if you can recognize a constellation and know which of its stars may be used, you can identify them whenever the group is visible in the sky. The stars and constellations that might be familiar to you are not always visible from where you may happen to be. For this reason, you must have some means of identifying navigational bodies when nothing you know by sight can be seen overhead. One method by which you can identify those celestial bodies is to use the Star Finder.

The Rude Starfinder consists of the star base, an opaque white plastic circular base plate fitted with a peg in the center, and ten circular transparent templates. On one side of the star base the north celestial pole appears at the center, and on the other side the south celestial pole.


Description of the Rude Starfinder
The Rude Starfinder, 2102-D, is designed to permit the determination of the approximate apparent altitude and azimuth of any of the 57 selected navigational stars tabulated in the Nautical Almanac. All of the 57 navigational stars are shown on each side at their positions

relative to the appropriate pole in a type of projection called an azimuthal equidistant projection. In this projection, the positions of the stars relative to one another are distorted, but their true declinations and azimuths relative to the pole are correct, the pattern of the stars on the star base does not correspond to their apparent positions as seen in the sky. Each star on the base is labeled, and its magnitude is indicated by its symbol, a large heavy ring indicates first magnitude, an intermediate sized ring second magnitude, and a small thin ring third magnitude. The celestial equator appears as a solid circle about four inches in diameter on each side of the star base, and the boundary of each side is graduated to a half-degree of LHA of Aries.


There are 10 templates included for use with the star base. Nine of these are printed with blue ink and are designed for apparent altitude and azimuth determinations, while the tenth, printed in red ink, is intended for the plotting of bodies other than the 57 selected stars on the base plate. There is one blue template for every 10° of latitude between 5° and 85°, one side of each template is for use in north latitudes, the other for south latitudes. Each of these "latitude" templates is printed with a set of oval blue altitude curves at 5° intervals, with the outermost curve representing the observer's celestial horizon, and a second set of radial azimuth curves, also at 5° intervals. The red template is printed with a set of concentric declination circles, one for each 10° of declination, and a set of radial meridian angle lines. The appropriate template is snapped in place on the star base.


Using the Star Finder
The star finder may be used either to:
1. Identify an unknown body whose altitude and azimuth have been observed.
2. Make a list of the stars and planets available for observation at morning or evening twilight for a fix.

To use the star finder, first determine GHA of Aries for your time of observation from the Nautical Almanac. Next, determine LHA of Aries by subtracting your longitude from GHA of Aries if in west longitude or by adding your longitude of GHA Aries if in east longitude. Select the template nearest your DR latitude and place it on the northern or southern base, depending on whether you are north or south of the equator. Ensure that the proper side of the template is up, north to north, south to south. Rotate the blue template until the 000° to 180° arrow on the template is over the LHA Aries on the base plate. The stars or planets available to you at that time, will be under the grid system of your blue template. DIRECTLY OVERHEAD (Zenith) then is represented by the cross at the center of the open space on the template. The sky overhead or dome is now shown in the part of the base covered by the curves on the template. The approximate azimuth and altitude of any navigational star within these curves can be found by following the lines on the template.


Finding an Unknown Star or Planet
After a long period of heavy weather, you may see the navigator out on the bridge wing scanning the heavens, his sextant in hand. He is hoping that the overcast will break long enough for him to have a shot at even a single star. If the navigator should manage to pull a star down, the star's identity may not be known. This is where one uses the star finder. An azimuth (bearing) of the star should be taken at the instant of observation. When the correct template is oriented properly on the star base, the name of the star can be read at the intersection of the azimuth and altitude lines on the grid. The Star Finder is designed to help locate and identify, by altitude and azimuth, the 57 stars listed in the Nautical Almanac or any other celestial bodies that may be plotted on the star base. Because the unit uses an Azimuthal Equidistant Projection, it can not be compared directly with the heavens due to distortion. The complete unit consists of one star base, ten templates, and instructions.


To Find or Identify Celestial Bodies
1. From the Nautical Almanac determine the GHA of Aries for GMT of the observation.
2. Convert GHA Aries to LHA Aries by subtracting DR longitude if west, or adding DR longitude if east. When this answer is negative add 360°, or if the answer is over 360° subtract 360°.
3. Select blue-line template for latitude nearest your DR position. Center selected template over star base so that template and star base both conform to hemisphere (N or S) of observer. Rotate the template until arrow is over LHA Aries. The approximate altitudes and azimuths of celestial bodies above the horizon are then indicated by the curves.


To plot the Sun, Moon, Planets, or additional Stars From the Nautical Almanac, determine the body's declination and right ascension (RA). The body's RA is obtained by:
When GHA body is zero, GHA Aries equals RA. Center red-line template over star base, use correct hemisphere on both, then rotate until arrow (0°) points to RA body. If the body's declination is the same as the hemisphere in center of base, then position will be plotted towards center from celestial equator. If declination is opposite, then position will be plotted away from celestial equator towards edge of base. With a pencil through the cut-out slot, mark the body's declination.


Identifying Unknown Bodies
Using the appropriate blue-line template and base side, align index arrow to LHA Aries for the time of sighting. Locate intersection of altitude and azimuth of shot. If no star is near intersection, the body may be a planet or unmarked star. Keeping blue-line template in place, put red-line template on top and rotate until the cut-out slot is over the altitude / azimuth intersection of sight. Determine declination and SHA of body, then refer to the Nautical Almanac for identification.

Celestial Navigation Problems GHA, LHA, DEC

The following practice problems are Coast Guard celestial navigation exam questions. Compute the GHA, LHA, and Declination for the Sun, Stars, and Planets.

Sun Only
1. On 26 February 1981, your vessel's 1615 ZT position is Lat. 25° 14.0' S, Long. 57° 22.0' W, when an azimuth the of Sun is observed. The chronometer time of the sight is 8h 13m 19s. The chronometer error is 01m 46s slow.
Answers
GHA 120° 33.3'
LHA 63° 11.3'
DEC 8° 30.8' S

2. On 9 February 1981, your 0739 zone time DR position is Lat. 23° 31.0' N, Long. 143° 41.0' E. At that time you observe the Sun. The chronometer reads 09h 37m 12s, and the chronometer error is 01m 52s slow.
Answers
GHA 141° 12.2'
LHA 284° 53.2'
DEC 14° 47.9' S

3. On 6 August 1981, your 1552 zone time DR position is Lat. 24° 26.0' S, Long. 73° 19.0' E. At that time you observe the Sun. The chronometer reads 10h 55m 07s, and the chronometer error is 02m 38s fast.
Answers
GHA 341° 39.9'
LHA 54° 58.9'
DEC 16° 39.8' N

4. On 6 November 1981, your vessel's 0706 zone time DR position is Lat. 25° 30.0' N, Long. 85° 35.0' W, when the Sun is observed. The chronometer time of the sight is 01h 03m 30s. The chronometer error is 02m 30s slow.
Answers
GHA 20° 35.0'
LHA 295° 00.0'
DEC 16° 03.1' S

Stars Only
1. On 16 June 1981, your 0430 zone time DR position is Lat. 29° 24.0' S, Long. 36° 16.0' E. At that time, you observe Vega. The chronometer reads 02h 32m 06s, and the chronometer error is 01m 54s fast.
Answers
GHA 22° 44.7'
LHA 59° 00.7'
DEC 38° 46.0' N

2. On 15 October 1981, your 0325 zone time DR position is Lat. 26° 51.0' N, Long. 138° 17.0' W. At that time, you observe Canopus. The chronometer reads 00h 25m 36s, and the chronometer error is 00m 20s slow.
Answers
GHA 114° 32.6'
LHA 336° 15.6'
DEC 52° 40.9' S

3. On 25 August 1981, your 1926 zone time DR position is Lat. 24° 17.0' S, Long. 5° 47.0' W. At that time you observe Fomalhaut. The chronometer reads 07h 26m 52s, and the chronometer error is 00m 15s fast.
Answers
GHA 281° 27.6'
LHA 275° 40.6'
DEC 29° 43.1' S

4. On 22 April 1981 , your 0344 zone time DR position is Lat. 21° 16.0' N, Long. 107° 32.0' W. At that time, you observe Spica. The chronometer reads 10h 45m 16s, and the chronometer error is 00m 25s fast.
Answers
GHA 170° 33.9'
LHA 63° 01.9'
DEC 11° 03.8' S

Planets Only
1. On 11 December 1981. your 1816 ZT DR position is Lat. 26° 30.0' N, Long. 140° 35.0' E. At That time you observe Venus. The chronometer reads 09h 14m 52s and the chronometer error is 01 m 02s slow.
Answers
GHA 274° 34.3'
LHA 55° 09.3'
DEC 21° 47.2' S

2. On 27 June 1981, your 1905 ZT DR position is Lat. 24° 35.0' N, Long. 50° 15.0' W. At that time you observe Saturn. The chronometer reads 10h 04m 26s and the chronometer error is 01m 20s slow.
Answers
GHA 63° 15.4'
LHA 13° 00.4'
DEC 0° 51.1' N

3. On 6 October 1981 , your 0416 zone time DR position is Lat. 25° 16.0' N, Long. 130° 25.0' E. At that time you observe Mars. The chronometer reads 07h 16m 22s, and the chronometer error is 00m 10s fast.
Answers
GHA 159° 40.7
LHA 290° 05.7'
DEC 15° 45.6' N

4. At 2326 ZT, on 22 June 1981, your vessel's position is Lat. 28° 30.0' N, Long. 150° 04.0' W. The planet Jupiter is observed. The chronometer reads 09h 24m 36s and is 01m 12s slow.
Answers
GHA 231°01.4'
LHA 80° 57.4'
DEC 0° 37.7' N

How to find a Stars GHA, LHA, and Declination

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How to find a Planets GHA, LHA, and Declination

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How to find the Sun's GHA, LHA, and Declination

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How to Compute the Observed Altitude (Ho) Planets

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How to Compute the Observed Altitude (Ho) Stars

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How to Compute the Observed Altitude (Ho) Sun Upper Limb

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How to Compute the Observed Altitude (Ho) Sun Lower Limb

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The Marine Sextant its Use and Adjustments

A sextant is not difficult to use but it does take practice to get a sight quickly and accurately, especially aboard a bouncing vessel. The instrument is held vertically in the right hand and the sighting is made through the telescope. The horizon is observed in the horizon glass while the celestial object is found in the mirror and positioned such that it is in line with the horizon. In the case of the Sun or Moon, the edge of the disk is placed on the horizon. If the lower edge is used, the sight is referred to as a lower limb sight. An upper limb sight is less used with the Sun but is necessary with the Moon since the lower edge may not actually be a circular one, depending on the phase.

Once the body is lined up properly, the sextant is "rocked" or pivoted as if the top of the index arm were attached to the rod of a pendulum and the arc were at the bottom with the swinging action. This is done to insure that the sextant is held vertically when the sight is taken. As the rocking is done, the celestial body will seem to trace an arc with respect to the horizon. The sextant is vertical or plumb when the body is at the bottom of the arc. The sight is then marked, the observer says "mark" to his timekeeper or observes the time himself.

The angular height of the celestial body is read on the arc and on the micrometer drum. The arc displays the degrees whereas the drum displays the minutes and tenths of minutes (or in some cases minutes and seconds). An arrow on the index arm points to the degrees on the arc. The degree is chosen that rests just to the right of the arrow. If the arrow pointing to the micro­meter drum lies between two minutes, an estimation is made as to how many tenths of the way between it is or sometimes a vernier is available on the index arm for that purpose.

There are several techniques of getting the celestial body in the field of view. In sighting the Sun, assuming reasonably good sea conditions, the observer can get the horizon under the Sun in the glass and then move the index arm back and forth, homing in on the glare surrounding the Sun until the Sun's disk is seen. Filters will be needed in front of the index mirror to protect the eye from the Sun's brightness. Also, filters may be necessary in front of the horizon glass if the Sun's sparkle on the water is too bright. A second method is useful for non-glaring objects such as the planets, stars and daytime Moon. Hold the sextant upside down in the left hand and sight through the glass toward the celestial object. Then move the index arm until the horizon appears in the mirror. The advantage in this method is that it is easier to find the celestial object by direct observing and leave the easily found horizon line for the moving mirrors. Once the object is reasonably well lined up with the horizon, the sextant is turned right side up and the final adjustments with the micrometer drum are made.

If some mathematical calculations are made ahead of time, the rough altitude of the celestial body can be figured allowing a third method to be used. This involves presetting the sextant to the prefigured altitude and then scanning the horizon with the horizon glass until the celestial body comes into the field of view of the mirror. The rough azimuth of the body can also be prefigured so that the area of scanning can be limited. For this method, the sextant would be held right side up the whole time. Some practical hints on using the sextant are in order especially if the instrument represents a considerable investment and happens to be the only sextant aboard. A lanyard attached to the sextant and to the observer saves accidental dropping of the instrument, either to be damaged on the deck or to be lost to Davy Jones Locker. Wrapping oneself around the shrouds when taking a sight over the rail saves the navigator from the same fates.

Sighting when the ship gets to the top of a wave is important to insure that the real sea horizon is used rather than the closer top of a nearby wave. The real sea horizon can vary in distance depending on the height of the observer's eye but corrections for this can be made.

Once the sextant is obtained, adjustments to the mirrors may be necessary to reduce the index correction to a minimal amount. One or two adjusting screws are located on each mirror for this purpose. Each mirror should be perpendicu­lar to the sextant frame and when the sextant is set at zero the two mirrors should be parallel to each other. Three tests are involved.

The first test is for perpendicularity of the index mirror. Hold the sextant on its side (with handle down) and with the index arm set to 35°. Place your eye close to the sextant near the index mirror so that you can see the sextant arc in the mirror (reflected) and also just to the right of the mirror (direct). If these two images are not in a straight or continuous line, the mirror is not perpendicular to the frame. Adjusting the screws will bring the images in line.

The second test is for perpendicularity of the horizon glass. Actually, the "glass" is only half glass with the right half of the frame filled with a mirror. The horizon is viewed through the glass, the reflected image of the celestial object viewed in the mirror. If this horizon glass is not perpendicu­lar to the frame, the error is referred to as side error. If a star is viewed both in the glass and in the mirror with the sextant set near zero, by adjusting the altitude, the star should pass over itself, become superimposed. If instead the reflected image of the star passes to the right of the direct image, side error exists and can be minimized by adjusting the two screws at the base of the horizon glass. Other celestial bodies may be used for this test as well as reasonably distant terrestrial objects.

The third test is for parallelism of the index mirror and horizon glass when the index arm is set exactly at zero. If at this setting the horizon or a celestial body appear higher or lower in the mirror than in the glass, the mirrors are not parallel and should be adjusted until they are. This error is called index error. This is an error in the sextant itself and can be found by setting the sextant to read exactly zero and observing the sea horizon, a distant mountain top (a reason­ably flat one), or a celestial object. At zero reading, the objects observed should appear the same height in the horizon glass and mirror.

If this is not the case, in other words, if the horizon or object in one side is above or below that in the other side, adjust the micrometer drum or the tangent screw until the objects are level with each other. Note the sextant reading. This is the amount of index correction. If the arrow is to the left of the zero or "on the arc", the I.C. is negative. If the arrow is to the right of the zero or "off the arc", the I.C. is positive. An easy way to remember this, though at first confusing, is to memorize. If it's on, it's off. If it's off, it's on. With a plastic sextant, the index correction should be ascertained for each set of sights since plastic will expand and contract with varying temperatures and will have different instrument errors. With a brass or aluminum framed instrument, the index correction should always be the same barring tampering with the mirrors or dropping the instrument.

Errors and Adjustments of the Sextant
The sextant is subject to a number of errors and adjustments. To find the true altitude of a celestial body from the observed these must be allowed and adjusted for. These are:
1. Index Error
2. Dip
3. Refraction
4. Parallax
5. Semi-diameter

Index error is an instrumental error. When looking through a sextant at the horizon the exact level will seldom be seen to be at 0°. Before you use the sextant the index error should be determined. If the error is less than 0° it should be added to whatever reading is obtained, if more subtracted.

Tip:
1. If its off, its on, ADD.
2. If its on, its off SUBTRACT.

Refraction is extracted from the Nautical Almanac. It allows for the bending of light rays as they travel through layers of varying density air.
Parallax corrections are needed if the observed body is a planet, the sun or the moon.
Semi-diameter correction is needed if the observed body is the sun or the moon. In this case either the top or bottom of the celestial object (upper or lower limb) is made to touch the horizon. To obtain the center of the body this correction is applied, from the Almanac. Once all the corrections are applied we have the true altitude. And this subtracted from 90 gives you the zenith distance. Which means you know exactly how far you are from that point on the earth which is at right angles to your observed celestial body. Remember the more sights you take the better you will get, so get lots of practice.

How to Compute the Time of Moonrise and Moonset

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How to Compute the Time of Twilight

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How to Compute the Time of Sunrise and Sunset

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How to Compute the Zone Time of Local Apparent Noon (LAN)

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