## Wednesday, October 31, 2007

### STEPS FOR FINDING POLARIS

Determine the Ho and LHA of Aries.

STEP 2

The Polaris Tables are entered to find the three parts of the Polaris correction. I use the sample problem at the bottom of the table on page 275 to provide the format and I add this to my sight form. The entering argument for the tables is the LHA of Aries, 238-48.3'. The appropriate column is, therefore, last one, headed 230° - 239.

STEP 3

To find the ao part, the upper third of the table containing corrections for each integral degree of LHA from 230 to 239 is used with interpolation, if necessary to arrive at the ao correction corresponding to LHA of Aries 238° 48.3'. In this case, the tabulated ao value for LHA of Aries 238 is +1- 43.3' recording this +1- 43.3' correction on the form,

STEP 4

Now proceed to the middle third of the table, in the same column, to obtain the a1 part. The entering argument in the left margin is the tabulated latitude closest to the DR latitude, or 23 in this case. The corresponding a1 value is +0.6' which is recorded on the form.

STEP 5

The a2 part is obtained from the lower third of the table, staying in the same column, opposite the month of observation, July in this case. It is +1.0'. As a final step in finding the total correction to be applied to Ho, ao ,a1, and a2 are always added and the required - 1 °is a constantin this example, applying these corrections to Ho yields the desired latitude line, 24 19.5'N.

STEP 6

Staying in the last column, enter the Azimuth part of the table with your DR latitude 23" and extract the true azimuth of Polaris, in this case, 000.3° T. Then find the gyro error and deviation.

### COMPUTING LATITUDE BY POLARIS USING THE NAUTICAL ALMANAC

**COMPUTING LATITUDE BY POLARIS USING THE NAUTICAL ALMANAC**

Sample Problem #1

In 29 July 1981, your 1930 zone time DR position LAT 24-16.8'N LONG 164-26.0'E. At that time you observe Polaris with a sextant altitude (hs) of 23-46.8' and bearing 000.3° pgc 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. At the time of the observation the helmsman noted that he was heading 224 pgc and 244° psc. The variation 20W. What is your latitude by Polaris? And what is the deviation for that heading?

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

Answer B

What is the deviation for that heading?

A 0.0°

B 1.5°W

C 3.0 W

D 4.5°W

Answer A

To see the work form go to

**"COMPLETE SOLUTION POLARIS # 1"**

### LATITUDE AND AZIMUTH BY POLARIS

**LATITUDE and AZIMUTH BY POLARIS**

1. Determine your latitude by Polaris

2. Using Polaris to check the deviation or gyro error of the compass

**LATITUDE BY POLARIS**

A second magnitude star called Polaris (north star) provides a reference for measurement in the Northem Hemisphere. Polaris has no counterpart in the Southern Hemisphere. Polaris may be located in the northern sky between the constellation Ursa Major (big dipper) and Cassiopeia. The two stars in the bowl of the dipper at the greatest distance from the handle, point toward the North Star.

Polaris travels in a diurnal circle of small radius around the celestial north pole. This causes a special circumstance in celestial navigation. If you think of the four arguments in celestial navigation, Ho, Lat, Dec, and LHA. Polaris has some constants that make it a special case in celestial navigation. The declination of Polaris is 90° North, and as long as your are in the northern hemisphere, your LHA will be 0°. Therefore, there is only 2 arguments left - Ho and Latitude. For Polaris, the Nautical Almanac has a special (Polaris) table at the end of the white pages.

You can determine your latitude in the Northern Hemisphere by observing the Hs of Polaris, at a known time. From the time, and the DR or estimated longitude, compute the LHA of Aries 1. Correct Hs to Ho, and using the LHA T, approximate latitude, and date, determine corrections from Poiaris tables ao, a1, and a2. Add total correction to Ho, and subtract 1 degree to obtain latitude. An good example is given in the table in the Nautical Almanac.

### PLOTTING A PLANET ON STAR FINDER

If no star appears on the star base at the observed altitude and azimuth, perhaps a planet has been observed. Because their apparent positions relative to the stars change, planets are not shown on the star base. They may be plotted easily, however, by using the special red template mentioned earlier.

STEP 1

Example, For the 17th of March 1981 extract the sidereal hour angle (SHA) of the planets from the daily page of the Nautical Almanac (Located on the left-hand daily page in the bottom right hand corner). Round off to the nearest whole degree. Find the body's right ascension (RA) by use of the formula RA = 360 - SHA of the planet.

STEP 2

Find the declination of each planet using the 8hours of GMT on the 17th Round off to nearest whole degree .

STEP 3

To plot the Planets, we will plot Venus first, then the others. Place the special RED template over the star base. Just like the blue template north to north. Align the arrow on the template with the graduation at the edge of the star base so that the arrow corresponds to the Venus'

RA - 353°. The template has an open slot with declination graduations along one side. Plot the planet at its declination. measuring from the zero mark toward the center if both the pole and declination have the same name (north or south). or away from the center if they have contrary names. In this case. go 5° south and put an X or dot and label it with Venus.

STEP 4

Next Mars, aline the arrow on Mar's RA of 10 degree. Then in the open slot measure off the declination 1 degree S. put an X or dot and label it with Mars.

STEP 5

Now do the same for Jupiter. aline the arrow on Jupiter's RA of 187°. Then in the open slot measure off the declination 1 degree S, put an "x" or dot and label it with Jupiter.

STEP 6

Last, Saturn, aline the arrow on Saturn's RA of 188 degree. Then in the open slot measure off the declination 0° S, put an "x" or dot and label it with Saturn.

STEP 7

Notice that Jupiter and Saturn are almost on top of each other. Then remove the red template, and place your blue template on. Aline to LHA Aries 260 degrees. The planet's approximate altitude and azimuth may now be read from the star base in the same manner as stars. Periodically. the positions of planets must be re-plotted as time passes.

### RUDE STAR FINDER ( PART 3 )

On 17 March 1981, your 0520 OR position is LA T 27- 23.0' N, LONG 39° 42.0' W. At this time you observe an unidentified star bearing 270° T with an observed altitude of 46° 30.2', The chronometer reads 08h 22m 15s, and is 01 m 45s fast. What star did you observe?

A. Altair

B. Alkaid

C. Arcturus

D. Deneb

STEP 1

Using GMT, and Greenwich date of observation, enter Nautical Almanac and record tabulated hourly value of GHA ( ARIES ).

STEP 2

Turn to the yellow pages of the Nautical Almanac, and find the "20 minute page," enter with "30-seconds." Then under the "ARIES" column find the increase in the GHA (1') since the last tabulated (hourly) value, flence 5° 08.3'. This is your M&S correction and enter this in your format.

BODY ?

DATE 17 MAR. 1981

DR LAT 27-23.0 N

DR LONG 39-42.0 W

Hs

IE

Hs

Dip

Ha

ALT Corr

Ho 46-30.2

ZT 0520

ZD +3

GMT 17th 0820

CT 08h 22m 15s

CE 1m 45s fast

CCT 17th 08h 20m 30s

GHA (Aries) 294-48.6

M&S (Aries) 5-08.3

SHA

V

GHA (Aries) 299-56.9

DR LONG - 39-42.0 W

LHA (Aries) 260-14.9

TAB DEC

d corr

DEC

STEP 3

Add the GHA (ARIES) and M&S to get the GHA (ARIES).

STEP 4

Bring down your DR longitude and enter it in your form. The rule is:

LHA (ARIES) = GHA (ARIES) + EAST LONGITUDE - LHA (ARIES) = GHA (ARIES) - WEST LONGITUDE .

So, we subtract our DR longitude to get the LHA (ARIES).

STEP 5

To use the star finder, select the blue template nearest your DR latitude, hence, 25°N and place it on the northern side of the white star finder. You should have the north side of the blue template matched up with the north side of the white star finder,

Remember to ensure that the proper side of the template is UP, hence, north to north , south to south.

STEP 6

Rotate the blue template until the 0° to 180 arrow on the template is over the LHA of 260 degrees on the base plate. The stars or planets that are available to you at that time, will be under the grid system of your blue template.

STEP 7

Locate the bearing of 270 T on the inner edge of the grid.

STEP 8

Using the Ho as the approximate altitude 46 degrees go up from the bearing of 270 degrees

to altitude of 46 degrees and you will find the unknown star "ARCTURUS".

After identifying the star, you would have to work out the sight by starting over again on your form.

### RUDE STAR FINDER ( PART 2 )

The familiar stars and constellations are not always visible from where you may happen to be. 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.

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 stars and planets available for observation at morning or evening twilight for a fix.

To use the star finder, first determine GHA of Aries (1") for your time of observation from the Nautical Almanac, Next, determine LHA of Aries (1") by subtracting your longitude from GHA

of Aries if in west longitude or by adding GHA of Aries to your longitude if it'! 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, hence, north to north -- south to south. Rotate the blue template until the 00 to 1800 arrow on the template is over the LHA 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. Moreover, 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 eagerly scanning the heavens, his sextant at hand. He is undoubtedly 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 the uses of the star finder comes into play. 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.

First, we will look at an unknown star, using a problem for an example.

### RUDE STAR FINDER PART 1

STAR IDENTIFICATION

As a navigator, you might be asked to obtain a fix from two or more stars. You may wonder how anyone except an astronomer can distinguish one star from the other. Actually, only a few of the multitudes 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, states 57 principal stars as well as tables for finding latitude by the North Star (Polaris).

Relative brightness of stars is called their magnitude; 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.

Man's imagination has given fanciful names to various groups of the brighter stars. The stars of each of these groups are said to form a constellation. Constellations are named according to objects they are thought to resemble in outline. Orion, the hunter, with his belt and sword, is a good example.

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 ,when ever the group is visible in the sky. The constellation familiarly called the Big Dipper (from a striking resemblance to a dipper with a handle) is known to astronomers as Ursa Major or Great Bear. Its resemblance to a bear puts considerable strain on the imagination, but the

## Tuesday, October 30, 2007

### CELESTIAL FORM WITH DEFINITIONS

**BODY NAME OF THE BODY**

**DATE LOCAL DATE**

**DR LAT. FOR THE TIME OF SIGHT**

**DR LONG. FOR THE TIME OF SIGHT**

**Hs SEXTANT ALTITUDE ( READING AT TIME OF THE SIGHT )**

**IE INDEX ERROR + or - "on the arc or off the arc"**

**Hs SEXTANT ALTITUDE**

**Dip HEIGHT OF EYE CORRECTION**

**Ha APPARENT ALTITUDE**

**ALT. CORR. ALTITUDE CORRECTION**

**Ho OBSERVED ALTITUDE**

**ZT ZONE TIME OF THE SIGHT**

**ZD ZONE DESCRIPTION**

**GMT GREENWICH MEAN TIME & DATE**

**CT CHRONOMETER TIME**

**CE CHRONOMETER ERROR**

**CCT CORRECTED CHRONOMETER TIME**

**GHA GREENWICH HOUR ANGLE**

**M & S MINUTES & SECOND CORRECTION ( INCREMENTS & CORRECTIONS )**

**SHA SIDERAL HOUR ANGLE ( FOR STARS ONLY )**

**V " V " CORRECTION ( FOR PLANETS ONLY )**

**GHA GREENWICH HOUR ANGLE**

**A LONG + or - ASSUMED / DR LONGITUDE**

**LHA LOCAL HOUR ANGLE**

**TAB DEC TAB DECLINATION**

**d corr " D " CORRECTION**

**DEC DECLINATION**

### BASIC CELESTIAL NAVIGATION FORM

DATE

DR LAT

DR LONG

Hs

IE

Hs

Dip

Ha

ALT. CORR

Ho

ZT

ZD

GMT

CT

CE

CCT

GHA

M&S ( Increments and Corrections )

SHA

V

GHA

A LONG

LHA

TAB DEC

d corr

DEC

Problem 3:

On the 15 October 1981, your vessel's 0325 ZT DR position is LAT 26"51.0'N, LONG 138°117.0, you take a celestial sight of the star Canopus. The chronometer time of the sight is OOh 25m 36s. The chronometer error is OOm 20s slow. Compute the GHA, Dec., and LHA of Canopus

BODY CANOPUS

DATE 15 Oct. 1981

DR LAT 26-51.0 N

DRLONG 138-17.0 W

Hs

IE

Hs

Dip

Ha

ALT CORR

Ho

ZT 15th 0325

ZD +9

GMT 15th 1225

CT 00h 25m 36s

CE + 00m 20s slow

CCT 15th 12h 25m 56s

GHA (Aries) 203-55.8

M&S (Aries) 6-30.1

SHA (Star) 264-06.7

V ---------

GHA (Star) 114-34.3

DR LONG + 138-17.0 W

LHA 336-15.6

TAB DEC ----------

d corr ----------

DEC S 52-40.9

STEP 1

Using GMT, and Greenwich date of observation, enter Nautical Almanac and record tabulated hourly value of GHA (Aries).

STEP 2

On the same daily page find the SHA and DEC. of Canopus and enter them in your format. Since, there is no "d" correction, the DEC is entered on the bottom declination line.

STEP 3

Turn to the yellow pages of the Nautical ~lm?~, and find the "25 minute page," enter with "56-seconds." Then under the "ARIES" column find the increase in the GHA (Aries) since the last tabulated (hourly) value, hence 6" 30.1.' This is your M&S correction and enter this in your format.

STEP 4

Add the GHA Aries, M&S, and SHA to get the GHA of the STAR.

STEP 5

Bring down your DR longitude and enter it in your form. The rule is:

LHA = GHA + EAST LONGITUDE - LHA = GHA - WEST LONGITUDE

So, we subtract our DR longitude to get the LHA of Canopus.

### FINDING GHA,DEC,AND LHA OF A PLANET

sun, except you have one more correction. The "V' correction is found the same way as the (d)correction". It appears at the bottom of the GHA sub-column for planets. Lets look at problem 2

PROBLEM 2

On the 11 December 1981, your vessel's 1816 ZT DR position is LAT 26°30.0'N, LONG 140-35.0'E, you take a celestial sight of the Venus. The chronometer time of the sight is 9h 14m 52s.

The chronometer error is 01m 02s slow. Compute the GHA, Dec., and LHA of Venus

STEP 1

Using GMT, and Greenwich date of observation, enter the Nautical Almanac and record tabulated hourly value of GHA and TAB DEC. in your form.

BODY Venus

DATE 11 December 1981

LAT 26-30.0N

LONG 140-35.0E

Hs

IE

Hs

DIP

Ha

Alt. Corr.

Ho

ZT 11th 1816

ZD -9

GMT 11th 0916

CT 9h 14m 52s

CE 01m 02s slow

CCT 11th 9h 15m 54s

GHA (Aries) 270-35.6

M&S (Aries) 3-58.5

SHA --------

V (0.8) + 0.2

GHA 274-34.3

DR LONG + 140-35.0E

LHA 55-09.3

TAB DEC S 21-47.4

d corr (0.6) +/- 0.2

DEC S 21-47.2

STEP 2

At the foot of each GHA sub-column for the PLANETS, a number is found. This number is the "v" correction. In this case "v = 0.8." Record this in your form. The "V" correction is always plus (+) for GHA except in the case of the inferior planet Venus, which has an orbit inside the earth's orbit. Its apparent motion westward, as compared with the sun's motion, shows that Venus has a numerically lesser, relative speed. When its correction should be subtracted, the letter "V" will be prefixed by a minus sign. The purpose of the "V correction is to interpolation and to keep tabulated values at a minimum, and makes possible the use of the GHA value for minutes and seconds as tabulated for the sun.

STEP 3

Record the "d" correction for the declination

STEP 4

Turn to the yellow pages of the Nautical 8.lInanac, and find the "15 minute page," enter with "54-seconds." Then under the Sun and Planets column find the increase in the Venus' GHA since the last tabulated (hourly) value, 3" 58.5.' is your M&S corre,ction and enter this in your form.

While on the 15-minute page under the "v" or"d" correction column, find the "v" 0.8 on the left hand side. This is equal to 0.2', enter this in your form and in this case it is added. At the same time, find your "d" 0 .. 6 :: 0.2. enter this in your format. This will be the declination (dec) of the Venus at the time of sight.

STEP 5

Add the GHA, M&S, and "v" correction to get the GHA TOTAL; subtract the "d" correction to find the declination of Venus

STEP 6

Bring down your DR longitude and enter it in

your form. The rule is:

LHA = GHA + EAST LONGITUDE LHA = GHA - WEST LONGITUDE So, we ADD our DR longitude to get the LHA of Venus

### FINDING GHA AND DECLINATION OF THE SUN

Problem 1:

On the 26 February, 1981, your vessel's 1615ZT DR position is LAT 25-14.0S LONG 57-22.0'W, you take a celestial sight of the sun. The chronometer time of the sight is 8h 13m 19s. The chronometer error is 01m 46s slow. Compute the GHA, Dec., and LHA

BODY Sun

DATE 26 February 1981

DR LAT 25-14.0S

DR LONG 57-22.0W

Hs

IE

Hs

Dip

Ha

ALTCORR

Ho

ZT 26th 1615

ZD +4

GMT 26th 2015

CT 8h 13m 19s

CE + 01m 46s slow

CCT 26th 20h 15m 05s

GHA 116-47.0'

M&S 3-46.3'

SHA - - - - - - - - --

V -- - ~ - - - - - -

GHA (SUN) 120-33.3'

DR/LONG - 57- 22.0'W

LHA 63 - 11.3'

TAB DEC S 8-31.0'

d corr (0.9) +/- 0.2

DEC S 8030.8'

STEP 1

Using GMT, and Greenwich date of observation, enter the Nautical Almanac and record tabulated hourly value of GHA and TAB DEC. in your format

STEP 2

At the foot of each declination sub-column, which applies to the sun, a number is found which is used for interpolation for any left over minutes of GMT. This number is called the "d", in this case "d 0.9" This is the average over the three day period that the declination changes per hour of GMT. The "d" is recorded on the D CORR line off to the side. This is a correction, as with any correction, it is either a + or - . If the declination increasing (getting larger), then it is a plus ( + ) correction, if the declination is decreasing, then it is a minus ( - ) correction.

Step 3

Turn to the yellow pages of the Nautical Almanac, and find the "15 minute page," enter with "5-seconds." Then under the Sun and Planets column find the increase in the sun's GHA since the last tabulated (hourly) value, hence 3° 46.3' is your M&S correction and enter this in your format. Always add the GHA and "m & s "tabulated value together to get the total GHA

Step 4

While on the 15-minute page under the "v" or "d" correctioncotumn, find the "d" 0.9 on the left hand side. This is equal to 0.2', enter this in your format and in this case subtract. This will be, the declination (dec) of the sun aUhe time of sight.

Step 5

Bring down your DR longitude and enter it in your form. The rule is:

LHA = GHA + EAST LONGITUDE ,LHA = GHA - WEST LONGITUDE So, we subtract our DR longitude to get the 'LHA

### FINDING ( Ho ) OF PLANETS

During evening twilight on 28 December 1981, the sextant altitude (Hs) of the planet Venus was 29°43.2'. The height of eye was 40 feet, and the index error was 2.0' on the arc. What was the observed altitude (Ho)?

BODY Venus

DATE 28 December 1981

DR LAT ---------

DR lONG ---------

Hs 29°43.2'

IE - 2.0' on

Hs 29° 41.2'

Dip (40 ft) - 6.1'

Ha 29° 35.1'

ALT CORR - 1.0'

Ho 29° 34.1

STEP 1

Record the given information in your format.

STEP 2

Apply your IE, in this case it is on the arc, so we subtract it.

STEP 3

Using the DIP Table on the inside cover of the Nautical Almanac, enter with your height of eye 40 feet = - 6.1'. Dip correction is always a minus correction

STEP 4

On page A2 "Altitude Correction Tables 100 - 900 Sun, Stars, Planets" under the STARS AND PLANETS section. Enter with your Ha and find the Al T Correction [ -1.7' ]. Venus & Mars have an additional correction. Under Venus on December 28 with an Ha of 290 = + 0.7'. You take net result and use that as your Al T corr. Main corr - 1.7 Additional Corr. + 0.7 Net Corr. - 1.0

### FINDING ( Ho ) OF STARS

You observe the star Antares at a sextant ititude (Hs) of 38°18.7' on 28 February 1981. The index error is 2.4' on the arc. he height of eye is 40 feet (12.2 meters). What is the observed altitude ( Ho )?

BODY Antares

DATE 28 February 1981

DRLAT ----------

DRLONG - - - - - -

Hs 38°18.7'

IE - 2.4 on

Hs 38° 16.3'

Dip (40 ft) - 6.1'

Ha 38° 10.2'

ALT CORR - 1.2'

Ho 38° 09.0'

STEP 1

Record the given information in your format.

STEP 2

Apply your IE, in this case it is on the are, so we subtract it.

STEP3

Using the DIP Table on the inside cover of the Nautical Almanac, enter with your height of eye 40 feet = - 6.1'. Dip correction is always a minus correction

STEP4

On page A2 "Altitude Correction Tables 10° - 90° Sun, Stars, Planets" under the STARS AND PLANETS section. Enter with your Ha and find the AL T Correction. Altitude corrections for "stars and planets" are minus (-) corrections

### SUN LOWER AND UPPER LIMB

You observe the lower limb of the Sun at a sextant altitude (Hs) of 42°44.0' on 22 June 1981. The index error is 0.8' off the arc. The height of eye is 70 feet (21.3 meters). What is the observed altitude (Ho)?

BODY Sun lower limb

DATE 22 June 1981

DR LAT

DR LONG

Hs 42° 44.0'

IE + 0.8' off

Hs 42° 44.8'

Dip (70 ft) - 8.1'

Ha 42° 36.7'

ALTCORR + 15.0'

Ho 42° 51.7'

STEP 1

Record the given information in your format.

STEP 2

Apply your IE, in this case it is off the arc, so we add it.

STEP3

Using the DIP Table on the inside cover of the Nautical Almanac, enter with your height of eye 70 feet = - 8.1'. Dip correction is always a minus correction.

STEP4

On page A2 "Altitude Correction Tables 1 OQ - 90° Sun, Stars, Planets" under the Sun -- April - September --(because our problem is in June). Enter with your Ha and find the AL T Corr under the Lower Limb column. Lower limb are always + corrections and upper limbs are - corrections.

Example 2 Sun Upper Limb

You observe the upper limb of the Sun at a sextant altitude (Hs) of 22°34.0' on 2 October 1981. The index error is 1.8' on the arc. The height of eye is 30 feet. What is the observed altitude (Ho)?

Body Sun upper limb

DATE 2 October 1981

DR LAT - - - - - - - - - -

DR LONG ---------------

Hs 22° 34.0'

IE - 1.8' on

Hs 22°32.2'

Dip (30 ft) - 5.3'

Ha 22° 26.9'

ALTCORR - 18.3'

Ho 22° 08.6'

STEP 1

Record the given information in your format.

STEP 2

Apply your IE, in this case it is on the arc, so we subtract it.

STEP 3

Using the DIP Table on the inside cover of the Nautical Almanac, enter with your height of eye 30 feet = - 5.3'. Dip correction is always a minus correction

STEP 4

On page A2 "Altitude Correction Tables 10° - 90° Sun, Stars, Planets" under the Sun --- October - March --(because our problem is in October). Enter with your Ha and find the ALT Corr under the Upper Limb column. Remember that Lower limb are always + corrections and upper limbs are - corrections.

### MOONRISE AND MOONSET ( PAGE 3 )

6. Determine the difference between your DR latitude and the tabulated latitude nearest yours. Convert the difference into degrees to the nearest whole degree.

DR LAT 23S

TAB LAT 20S

DIFF. 3 Degrees

7. Determine the latitude time correction by multiplying the difference by the ratio in step 6 and rounding it to the nearest minute.

1.4 min x 3 degrees = 4.2 or 4 min

1.1 min x 3 degrees = 3.3 or 3 min

8. Apply the latitude correction to the tabulated latitude time value. This is the time of moonrise at the standard meridian at that latitude if the Nautical Almanac tabulated twilight for every whole degree of latitude.

20S 0058 - 0018

- 4m - 3m

23S 0054 - 0015

9. Find the time difference between the dates.

30th 0054

29th 0015

diff 39 min

10. Now enter Table II for Longitude - {Tables for Interpolating Sunrise Moonrise, Etc. } page xxxii at the back ·of the Nautical Almanac for the longitude correction. Enter with your DR Long approx. 160° E and difference of 39 minutes and you get a correction of 18 minutes. This time is subtracted for east Long and added if in west Long.

0054

-18

0036

11. Determine the difference between your DR lonitude and the standard meridian.

STD MER. 165-00.0E

DR LONG 159-46.3E

DIFF. 5-13.7

5 Degrees = 20 min

13.7 = 0m 55s =21min

12. Convert the arc ( degrees and minutes ) into time ( hours and minutes ). Use either the arc to time table in the Nautical Almanac or the arc to time formulas.

13. Apply the difference of the time to obtain the exact time of moonrise.

MR at STD MER 0036

+ 21

ZT of MOONRISE 0057

### MOONRISE AND MOONSET ( PAGE 2 )

With the given information in the following. problem, determine the zone time of moonrise.

At 2100 zone time, on the 30 January 1981, your DR position is LAT22° 26.0'S, LONG 158° 50.1'E. You are steering a course of 115 T at a speed of 15.5 knots. What is the zone time of moonrise?

A.0015 B.0036 C.0057 D.0134

Procedure Follow these steps to calculate the zone time of moonrise.

1. Enter "The Nautical Almanac" and locate

the page that correspond to the date you are using.

2.

Using a universal plotting sheet determine the DR position (latitude & longitude) of your

ship at the approximate time of moonrise [ 00 58 ].

Lat. 22° 52.2'S Long. 159° 46.3'E

Select the proper section.

IF you need ... THEN use the ...

moonrise upper section.

moonset lower section.

JAN 1981

30 29

Lat. MR MR

3.

Go down the latitude column and locate the tabulated latitudes that bracket your DR latitude and extract the latitudes and moonrise on the 30th and 29th since it is in

for the day preceding, if east longitude. Using the daily difference between the times for the nearest tabular latitude, and the longitude, enter Table II of the Almanac "Tables for Interpolating Sunrise, Sunset, etc." and take out the correction. Apply this correction to the LMT of moonrise or moonset at the Greenwich meridian on the given date to find the LMT at the position of the observer. The sign to be given the correction is such as to make the corrected time fall between the times for the two dates between which interpolation is being made. This is nearly always positive (+) in west longitude and negative (-) in east longitude. Convert the corrected LMT to ZT.

With the given information in the following. problem, determine the zone time of moonrise.

At 2100 zone time, on the 30 January 1981, your DR position is LAT22° 26.0'S, LONG 158° 50.1'E. You are steering a course of 1150 T at a speed of 15.5 knots. What is the zone time of moonrise?

A.0015 B.0036 C.0057 D.0134

Procedure Follow these steps to calculate the zone time of moonrise.

STEPS

1. Enter "The Nautical Almanac" and locate

the page that correspond to the date you are using.

2.

Using a universal plotting sheet determine the DR position (latitude & longitude) of your

ship at the approximate time of moonrise [ 00 58 ].

Lat. 22° 52.2'S Long. 159° 46.3'E

Select the proper section.

IF you need ... THEN use the ...

moonrise upper section.

moonset lower section.

JAN 1981

30 29

Lat. MR MR

3.

Go down the latitude column and locate the tabulated latitudes that bracket your DR latitude and extract the latitudes and moonrise on the 30th and 29th since it is in east longitude. If it was west longitude, we would have used the 31st data. 4.Determine the difference between tabulated latitudes and the time values .

S 20° 0058 - 0018

S 30 0044 - 0007

S 10 14m - 11m

5.

Determine the ratio of change in time for each degree of change of latitude by dividing the latitude difference into the time difference.

14 min / 10° = 1.4 min

11 min / 10° = 1.1 min

### MOONRISE AND MOONSET ( PAGE 1 )

Time of rising and setting of the moon is important, if there is a need to work at night it would be nice to know if there will be moonlight; when it will be light and how long. Times of moonrise and moonset are listed in the Nautical Almanac. These times can be computed from the Nautical Almanac for any point on the earth. The listed times in the Almanac, however, are LMT of moonrise and moonset at the Greenwich meridian.

Finding Time of Moonrise· and Moonset

Finding the time of moonrise and moonset is similar to finding the time of sunrise and sunset with one difference. Since these moon phenomena occur later from one day to the next and at variable rates of change, which are rather large (on the average about 51 minutes a day), there could be a considerable error from using time corrected only for latitude and zone time. The arguments for determining the time of moonrise and moonset are the observer's longitude and the differences in times on the two Greenwich dates (tabulated latitudes) that straddle the local date. For purposes of navigation, however, you would be sufficiently accurate to interpolate between consecutive moonrise or moonset at the Greenwich meridian. Since apparent motion of the moon is westward. relative to an observer on the earth;

INTERPOLATION IN WEST LONGITUDE IS BETWEEN THE PHENOMENON ON THE GIVEN DATE AND THE FOLLOWING ONE.

NAUTICAL ALMANAC SOLUTION

For the given date, enter the daily-page table for latitude, and extract the LMT for the tabulated latitude next smaller than the observer's latitude, (unless this is an exact tabulated value). Apply a correction from Table I of the Nautical Almanac "Tables for Interpolating Sunrise, Moonrise, etc." to interpolate for latitude, determining the sign of correction by inspection. Repeat this procedure for the date following the given date. if in west longitude; or

## Monday, October 29, 2007

### MORNING AND EVENING TWILIGHT

**REMEMBER**

**IF DR LONGITUDE IS TO THE RIGHT ( EAST ) OF THE STANDARD MERIDIAN THEN SUBTRACT THE TIME.**

**IF DR LONITUDE IS TO THE LEFT ( EAST ) OF THE STANDARD MERIDIAN THEN ADD THE TIME.**

**MORNING OR EVENING TWILIGHT**

**Twilight is that period before sunrise when darkness is giving way to daylight,and that period after sunset when daylight is giving way to darkness. In celestial navigation,**

**morning and evening twilight are usually the most important periods of the day. Ordinarily,these are the only times during which you can fix your positions byRemember:IF DR longitude is ...to the right (EAST) of the STD. MeridianTHEN ...subtract the time.to the left (WEST) of the STD. meridianadd the time.MORNING or EVENING TWILIGHTTwilight is that period before sunrise when darkness is giving way to daylight, and that period after sunset when daylight is giving way to darkness. In celestial navigation, morning and evening twilight are usually the most important periods of the day. Ordinarily, these are the only times during which you can Fix your position by obtaining nearly simultaneous lines of position from celestial observations. At nautical twilight, the sun is 12° below the celestial horizon. At the darker period of civil twilight, the center of the sun is 6° below the celestial horizon, and during good weather, bright stars are easily distinguished, and the horizon is sharp and clear. This is approximately the mid-time of the period during which the experienced navigator makes twilight observations. In order for the navigator's eyes to adjust to the darkness, the navigator usually wants to get on the bridge 20 or 30 minutes prior to civil twilight. The Nautical Almanac lists data for obtaining nautical twilight as well as civil twilight for three day intervals.With the given information in the following problem, determine the zone time of morning civil twilight.At 0400 zone time, on the 24 June 1981, your DR position is LAT 23° 10.0'N, LONG85° 33.0'W. You are steering a course of 295 T at a speed of 10.0 knots. What is the zone time of civil twilight?**

**A.0433 B.0450 C.0517 D.0458 **

**Procedure Follow these steps to calculate the zone time of civil twilight.Step Action1. Enter ''The Nautical Almanac" and locatethe page that correspond to the date you are using.2. Using a universal plotting sheet determinethe DR position (latitude & longitude) of your ship at the approximate time of sunrise [ 04 58 ].3. Select the proper section.IF you need AM twilight then use the upper sectionIF you need PM twilight then use the lower section4. Go down the latitude column and locate the tabulated latitudes that bracket your DR latitude and extract the latitude and sunrise data. **

**JUNE 24 1981**

**LAT. CIVIL**

**N 30 0433**

**N 20 0458**

**5. Determine the difference between tabulated latitudes and the time values. **

**N 30 0433**

**N 20 0458**

**10 25 min**

**6. Determine the ratio of change in time for each degree of change of latitude by dividing the latitude difference into the time difference.**

**25 min / 10 degree's = 2.5 min**

**7. Determine the difference between your DR latitude and the tabulated latitude nearest yours. Convert the difference into degrees to the nearest whole degree.**

**DR LAT N 23**

**TAB LAT N 20**

**DIFF. 3 degrees**

**8. Determine the latitude time correction by multiplying the difference by the ratio in step 6 and rounding it to the nearest minute.**

**3 degrees x 2.5 min = 7.5 min or 8 min**

**9. Apply the latitude correction to the tabulated latitude time value. This is the time of twilight at the standard meridian at that latitude.**

**N 20 0458**

**- 8**

**N 23 0450**

**10. DR ahead using this time to get a more accurate DR postion.**

**Twilight at STD MER 0450**

**DR time 0400**

**50 min**

**50 min x 10 kts = 8.3 mi**

**DR postion at 0450 is LAT. 23-13.2N , LONG. 85-40.9W**

**11. Determine what standard meridian is closest to your DR position.**

**STD MER 90-00.0W**

**12. Determine the difference between your DR longitude and the standard meridian.**

**STD MER 90-00.0W**

**DR LONG. 85-40.9W**

**DIFF. 4-19.1**

**13. Convert the arc ( degrees and minutes ) into time ( hours and minutes ) . use either the arc to time table in the Nautical Almanac or the arc to time formulas.**

**4 degrees = 16m 00s**

**19.1 = 1m 16s**

**17m 16s =17 min**

**14. Apply the difference of time to obtain the exact time sunrise.**

**SR at STD MER 0450**

**- 17**

**ZT of twilight 0433**

**REMEMBER - IF DR LONGITUDE IS TO THE RIGHT ( EAST ) OF STD MERIDIAN THEN SUBTRACT THE TIME.**

**IF IT IS TO THE LEFT ( WEST ) OF THE STD MERIDIAN THEN ADD THE TIME**

### SUNRISE, MOONRISE, TWILIGHT

**We**

**use the following phenomena with the apparent motion of the sun and the moon:**

SUNRISE - The instant the upper limb of the sun appears on the visible horizon.

MOONRISE - The instant the upper limb of the moon appears on the visable horizon.

SUNSET - The instant the upper limb of the sun disappears beyond the visable horizon.

MOONSET - The instant the upper limb of the moon disappears beyond the visable horizon.

TWILIGHT - The period of semi- darkness occurring just before sunrise ( morning twilight )

or just after sunset ( evening twilight ).

The navigator uses morning and evening twilight for star observations because during twilight the darkness makes the stars visible,but permits enough light to define the horizon. Both conditions are necessary if an accurate sextant altitude (hs) is to be obtained. There are four stages of twilight,based upon the position of the sun with respect to the horizon. They are:

ASTRONOMICAL TWILIGHT - The sun is 18 degree's below the horizon. Too dark for observations.

NAUTICAL TWILIGHT - The sun is 12 degree's below the horizon. Favorable for observations.

Recorded in Nautical Almanac.

OBSERVATIONAL TWILIGHT - The sun is 10 degree's below the horizon. Best for observations.

CIVIL TWILIGHT - The sun is 6 degree's below the horizon. Too light for observations. Also recorded in the Nautical Almanac.

SUNRISE - The instant the upper limb of the sun appears on the visible horizon.

MOONRISE - The instant the upper limb of the moon appears on the visable horizon.

SUNSET - The instant the upper limb of the sun disappears beyond the visable horizon.

MOONSET - The instant the upper limb of the moon disappears beyond the visable horizon.

TWILIGHT - The period of semi- darkness occurring just before sunrise ( morning twilight )

or just after sunset ( evening twilight ).

The navigator uses morning and evening twilight for star observations because during twilight the darkness makes the stars visible,but permits enough light to define the horizon. Both conditions are necessary if an accurate sextant altitude (hs) is to be obtained. There are four stages of twilight,based upon the position of the sun with respect to the horizon. They are:

ASTRONOMICAL TWILIGHT - The sun is 18 degree's below the horizon. Too dark for observations.

NAUTICAL TWILIGHT - The sun is 12 degree's below the horizon. Favorable for observations.

Recorded in Nautical Almanac.

OBSERVATIONAL TWILIGHT - The sun is 10 degree's below the horizon. Best for observations.

CIVIL TWILIGHT - The sun is 6 degree's below the horizon. Too light for observations. Also recorded in the Nautical Almanac.

**SUNRISE AND SUNSET**

**It is necessary to know the times of sunrise and sunset because it allows the navigator to take a amplitude ( bearing ) of the sun to help check his deviation or gyro error of the compass.**

**Twilight is of importance because during these periods of time the navigator will be taking sights.**

**You will need to know how to determine the most best time for taking sights. Basically,all three times depend on the observer's position with respect to latitude,longitude,and the location ( east or west ) of the nearest standard time meridian. Remember that the times shown for rising and setting of the sun and the moon,and twilight in ALL publications are standard times. If that zone is keeping Daylight Saving Time ( DST ) it must be accounted for after the final time is figured.**

**With the given information in the following problem,determine the zone time of sunrise.**

**At 0400 zone time on 24 June 1981, your DR position is LAT 23-10.0N, LONG 85-33.0W. You are steering a course of 295 T at a speed of 10.0 knots. What is the zone time of sunrise?**

**Use the NAUTICAL ALMANAC 1981**

**A. 0452**

**B. 0458**

**C. 0504**

**D. 0510**

**Procedure - Follow these steps to calculate the zone time of SUNRISE.**

**1. Enter "The Nautical Almanac" and locate the page that corresponds to the date you are using.**

**2. Using a universal plotting sheet determine the DR postion ( latitude & longitude ) of your ship at the approximate time of sunrise ( 0522 ).**

**3. Make sure you are in the proper section ( top section for sunrise ).**

**4. Go down the latitude column and locate the tabulated latitudes that bracket your DR latitude and extract the latitude and sunrise data.**

**LAT. SUNRISE**

**N 30 0500**

**N 20 0522**

**5. Determine the difference between tabulated latitudes and the time values.**

**N 30 0500**

**N 20 0522**

**________________**

**10 22 min**

**6. Determine the ratio of change in time for each degree of change of latitude by dividing the latitude difference into the time difference.**

**22min / 10 = 2.2min**

**7. Determine the difference between your DR latitude and the tabulated latitude nearest yours.**

**Convert the difference into degree's to the nearest whole degree.**

**DR LAT 23N**

**TAB LAT 20N**

**DIFF. 3**

**8. Determine the latitude time correction by multiplying the difference by the ratio in step 6 and**

**rounding it to the nearest minute.**

**3 degree's x 2.2 min = 6.6 min = 7 min**

**9. Apply the latitude correction to the tabulated latitude time value. This is the time of sunrise at the standard meridian at that latitude.**

**20N 0522**

**- 7 min**

**23N 0515**

**10. DR ahead using this time to get a more accurate DR postion.**

**SR at STD MER 0515**

**DR time 0400**

**DIFF 1:15**

**1:15 X 10 kts = 12.5 mi**

**DR postion at 0515 is LAT 23-14.9N, LONG. 85-44.4W**

**11. Determine what standard meridian is closest to your DR postion.**

**STD MER. 90-00.0W**

**12. Determine the difference between your DR longitude and the standard meridian.**

**Convert the arc ( degrees and minutes ) into time ( hours and minutes ). Use either the arc to time table in the Nautical Almanic or the arc to time formula**

**STD MER 90-00.0W**

**DR LONG. 85-44.4W**

**DIFF 4-15.6**

**4 Degree's = 16m 00s**

**15.6 = 1m 02s**

**17m 02s = 17min.**

**13. Apply the difference of time to obtain the exact time of sunrise.**

**SR at STD MER 0515**

**- 17**

**ZT of SUNRISE 0458**

### CALCULATING FIRST ESTIMATE LAN (Example)

**Example: Your ships 0700 DR position on 24 January 1981 is LAT 22-25.0N**

**LONG 46-10.0W. Your vessel is on course 110 T at a speed of 12.0 knots. Your job**

**is to determine zone time of LAN.**

**STEP**

**1: DATE 24 JAN 1981**

**STEP 2: MER. PASS. 1212**

**STEP 3: DR LONG 45-11.5W**

**STEP 4: STD MERIDIAN 45-00.0W**

**STEP 5: d (arc) 0-11.5**

**STEP 6: d long. time + 0m 46s**

**STEP 7: ZT LAN ( 1st Est. ) 12h 12m 46s = 1213**

### CALCULATING FIRST ESTIMATE OF LAN

**Step 1 Enter the date.**

Step 2 Go to " THE NAUTICAL ALMANAC " and use the time of meridian passage for 24

January 1981.

Step 3 Set up universal plotting sheet

Plot 0700 DR position and DR ahead to 1212

Example: 1212 - 0700 =

5h 12m at 12 knots = 62.4 miles

Step 4 Enter your DR longitude for the time of meridian passage you used from the almanac

( 1212 ).

Step 5 Enter the nearest standard meridian.

Step 6 Calculate the difference in arc between the standard meridian and your DR longitude.

Step 7 Convert the arc in step 5 into using the " Conversion of Arc to Time " from the Nautical

Almanac.

Step 8 Now apply the time correction to the time of meridian passage from the almanac.

Because we are west of our standard meridian,we must add the difference. By applying

this correction you will have the time of LAN at the meridian for your DR position. This is

called the first estimate of LAN.

Note: if your clocks are set to daylight savings time ( DST ) add one hour to your zone

time or use the standard meridian that your clocks are set to.

Step 2 Go to " THE NAUTICAL ALMANAC " and use the time of meridian passage for 24

January 1981.

Step 3 Set up universal plotting sheet

Plot 0700 DR position and DR ahead to 1212

Example: 1212 - 0700 =

5h 12m at 12 knots = 62.4 miles

Step 4 Enter your DR longitude for the time of meridian passage you used from the almanac

( 1212 ).

Step 5 Enter the nearest standard meridian.

Step 6 Calculate the difference in arc between the standard meridian and your DR longitude.

Step 7 Convert the arc in step 5 into using the " Conversion of Arc to Time " from the Nautical

Almanac.

Step 8 Now apply the time correction to the time of meridian passage from the almanac.

Because we are west of our standard meridian,we must add the difference. By applying

this correction you will have the time of LAN at the meridian for your DR position. This is

called the first estimate of LAN.

Note: if your clocks are set to daylight savings time ( DST ) add one hour to your zone

time or use the standard meridian that your clocks are set to.

## Saturday, October 27, 2007

### ZONE TIME OF LOCAL APPARENT NOON ( LAN )

**Local apparent noon (LAN) is a sight taken on the Sun at the instant it transits an observer's meridian. At that time, the Sun is at its highest altitude. The purpose of observing the Sun at LAN is that it allows you to establish your latitude.**

**ZONE TIME OF LAN**

**The purpose of determining watch time of LAN is to arrive on the bridge within a few minutes of the time you should take your sight. Since zone time of LAN is based on your dead reckoning (DR) longitude, the exact moment it transits over your meridian will seldom be precisely calculated, but you should be able to figure it real close.**

**The Greenwich Mean Time of meridian passage, or GMT Mer. Pass, is found on the lower right daily pages of the "Nautical Almanac" just below the sunset table. This is also the time that the Sun will be over any standard meridian, no matter what zone you maybe in. Be sure that you use the page for the right date.**