The Altitude Intercept Method

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How to Determine the GHA and Declination of the Moon (Example and Solution)

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Celestial Navigation (Almanacs and Coordinates)

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Calculate GHA, Dec, and LHA of a Planet

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Determining the GHA and Declination of a Planet

The use of the Nautical Almanac to find the GHA and declination of a navigational planet differs somewhat from the procedure for a star, because both the GHA and declination for the navigational planets are tabulated in the Almanac for each whole hour of GMT. These tabulations are necessitated by the fact that the planets, being relatively close to earth in the solar system, seem to move across the unchanging patterns of the stars from one hour to the next.

Suppose that the planet Venus was observed at watch time 04-03-36 and its observed altitude was determined to be 16° 38.6'. The DR position at the time of the sight was L 34° 17.0'S, Long. 163° 09.1'E.

The Nautical Almanac is first entered to compute the GHA of Venus for the time of the observation. The tabulated value of the GHA of Venus for the whole hour of GMT immediately preceding the observation is recorded on your form. In addition, the "v" value at the bottom of the column containing the Venus tabulations is noted and recorded on the form alongside the tabulated GHA. This "v" value represents the average irregularity in the rate of increase of the GHA of Venus from one hour to the next over the three-day period covered by the daily page, as a result of the motion of the planet in its orbit.

Because the rate of increase of the GHA is not constant, a v correction derived from this v value must be applied to the tabulated GHA of the planet, in addition to the GHA increment. The v correction, like the GHA increment, is taken from the appropriate "Increments and Corrections" table in the back of the Almanac.

I should mentioned that all bodies in the solar system are characterized by this irregular rate of increase of GHA. A "v" correction is applied to the GHA increments of all the navigational planets and the moon; the "v" correction for the sun is so small that it is ignored when using the Nautical Almanac. The "v" corrections for Mars, Jupiter, Saturn, and the moon are always positive, at certain times of the year, the Venus "v" correction can be negative.

Returning to the example at hand, a GHA increment for 4 minutes 12 seconds is found from the 4-minute "Increments and Corrections" table and entered on the sight form. To find the "v" correction, the columns in the appropriate table with the headings "v" or "d" correction are used (the d correction is explained below.

The left side of each column contains "v" or "d" values, and the right side, the corresponding "v" or "d" correction. In this case, a "v" correction of +0.1' corresponding to a "v" value of + 1.1 is obtained. The tabulated GHA, GHA increment, and "v" correction are all summed to yield the GHA of Venus of 117° 51.6'.

To find the declination of Venus for the time of the observation the tabulated declination for the whole hour of GMT preceding the sight is first extracted and entered on the form as the tabulated declination (Tab. Dec.). Just as the GHA of a body in the solar system is continually changing from one hour to the next, the declination of these bodies is also changing. In contrast to the irregular rate of change of GHA, however, the rate of change in declination is nearly constant. The "d" value appearing at the bottom of the Venus column represents the average hourly rate of change of its declination over the three-day period covered by the daily page. A "d" correction (actually analogous to the GHA increment) derived from this d value is found from the appropriate "Increments and Corrections" table and applied to the tabulated declination to form the true declination of Venus at the time of the observation. The sign of the d value and hence the sign of the d correction is positive if the trend of the tabulated declination is increasing. If the tabulated declination is decreasing, the sign is negative. In this case, a "d" correction of 0.0 is obtained from the 4-minute table, using a d value of .1 as entering argument in the "v or d correction" column. The true declination of Venus at GMT 17-04-12 is S 13° 16.1'.
The use of the Nautical Almanac for Venus is now complete.

Celestial Coordinates and the Nautical Almanac

Imagine a clear plastic balloon covering the earth's surface. On it we shall trace the equator, the poles and the Greenwich meridian. Now, if we expand this balloon until it imaginarily touches the Sky, a view from inside this balloon shows these tracings against the sphere of stars. There is now a celestial equator directly above the earth's equator, a celestial north and south pole directly above the corresponding earth poles, and a celestial Green­wich meridian directly above the earth's prime meridian. A celestial body's coordinates can be defined exactly as ones on the earth except now we are using the expanded tracings. Sky coordinates are named differently. Sky latitude is called declination (Dec.) and is labeled north or south depending toward which pole the body is from the equator. Sky longitude is called Greenwich Hour Angle (GHA) and differs from earth longitude in that it is measured always westward from the Greenwich meridian, 0° to 360°.

By establishing the GHA and Dec of a celestial body for a particular instant of time, we have found the corresponding latitude and longitude of the geographical position of that body. Since the Sun, Moon and planets change their GHA and Dec constantly as they seem to move through the sky, these coordinates are listed in the Nautical Almanac for each hour of each day of the year with additional corrections in the yellow pages in the back of the Almanac for each minute and second of the hour. Listing the positions of these six bodies for each hour of the year is not a particularly space consuming process. Parts of two pages will cover a three day period as you can see by using the daily pages of the Nautical Almanac. However, there are fifty-seven navigational stars that may be easily observed during twilights and many more fainter stars which might also be picked up during this period. Therefore, to conserve space for these stars which in effect are stationary with respect to the celestial sphere, we can use another type of longitude called Sidereal Hour Angle (SHA). This is also an angular measurement along the equator but the starting point is not the Greenwich meridian.

Another arbitrary point has been chosen as the basis for SHA called the vernal equinox. Also called the first point of Aries, it is the position the Sun occupies on the first day of spring when the Sun changes from a southern declination to a northern one. At this transition point, the Sun is on the equator. The vernal equinox is designated by the sign for Aries. We can then establish a permanent longitude of stars with respect to the celestial sphere and are only left with the problem of relating this longitude to the Greenwich meridian which changes its position on the sphere as the earth rotates. To solve this problem, we need to find the GHA of the vernal equinox. Add to this the SHA of the star and you have the GHA of the star.

In southern latitudes, the celestial equator will cross the northern section of the meridian.
The vernal equinox can be roughly positioned on the equator by finding the constellation of Pegasus (if it is visible at the time you observe), taking the left side of the square as one unit of length and proceeding down from the lower left star in the square one more unit. The vernal equinox will be slightly to the right of where you arrived.

Our sight reduction forms are fairly self explanatory as to where to enter GRA, Dec, and SHA. We go into the Nautical Almanac with Greenwich time and date and pick out the value for the hour of GMT. In the case of a star, GHA is chosen out of the Aries column. At the bottom of the planets and Sun column and in separate columns of their own in the Moon section we find a small-type number designated "v" or "d" (the Sun has no "v" and the stars have no "v" or "d"). The "v" is an extra correction for additional longitude move­ment of the celestial body and the "d" is an extra correction for additional declination movement of the body. Planets, Sun and Moon move on their own in orbits around the Sun and earth and this change of position in the sky is accounted for in the "v" and "d" corrections. The "v" correction will always be positive except in the case of Venus where it may be negative. In this case, the "v" will be marked with a negative sign. The "d" correction can be either positive or negative depending on the trend of the declination. Look at the declination column of the body in question at the time in question and see if it is increasing or decreasing. This will establish the sign, increasing being positive, decreasing being negative.

These "v" and "d" numbers are only reference numbers for the celestial body's movement in one hour. If we took a sextant sight at thirty minutes after the hour, the actual correction would be 30/60 or 1/2 of the reference numbers. To save our doing the arithmetic, we enter the yellow pages in the back of the Nautical Almanac with the minute and second of our sight, pullout a value for the earth's movement in columns entitled Sun-Planets, Aries and Moon, and then go the the right hand side of the minute box and find the "v" or "d" values. The corresponding number to these values is the correction factor, to be added or subtracted as the sign of the "v" or "d".

Celestial Coordinates

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Celestial Navigation (Time)

The sextant and an accurate timepiece are the only two major instruments needed by the celestial navigator. In 1135, Englishman John Harrison developed the first chronometer that could be taken on board ship amidst the temperature changes and motion and yet tell extremely accurate time. By the end of the eighteenth century, such instruments were being constructed with more reason­able size, weight and price. By the early twentieth century, time ball signals activated by telegraph and low power audible signals in major ports enabled the navigator to check the accuracy of his chronometer. Now, accurate and inexpensive quartz chronometers as well as radio time signals make the establishment of time an easy task.

Time and longitude are directly related. Without time, longitude by normal methods cannot be established correctly. Considering the earth to be encircled by 360° of longitude with a rotation of 24 hours of time, we find

that one zone or hour of time corresponds to 15° of longitude, in other words, one hour of rotation of the earth corresponds to 15° angle of rotation of the earth. Reducing this even further, one second of time corresponds to one quarter of a minute of longitude, equal to one quarter of a mile (roughly) at the equa­tor, less of a distance as latitude increases. An error of time, is a error of longitude

A system of time zones has been established worldwide, most zones being one hour or 15° wide. In some cases the actual boundaries vary to coincide with state borders or island groupings. Everyone within the zone keeps the same time called zone time or ZT. The centers of each zone have longitudes evenly divisible by fifteen such as 0°, 15°, 30°, 45°, etc. The edges of the zones extend 7 1/2 to each side of the center. Therefore, the zone whose center is 60° would include longitudes from 52 1/2 degree's to 67 1/2 degree's.

For purposes of celestial navigation, zone time must be converted to Greenwich Mean Time, time kept at the zone whose center is 0° or the Prime Meridian. This is done by means of the Zone Description or ZD, a number obtained by dividing your longitude by 15 and rounding the answer off to the nearest whole number.

If the longitude is west, the ZD is positive. If the longitude is east, the ZD is negative. For example, if your longitude were 50° W, dividing by 15 would give 3.33. Rounding to the nearest whole number would give 3 as a ZD. It would be a +3 since longitude is west. This means that GMT is three hours later than your zone time. If your longitude were 129° E, dividing by 15 would give 8.6. Rounding to the nearest whole number would give 9, a negative ZD since longitude is east. If addition or subtrac­tion of the ZD to your ZT puts your GMT over 24h or less than OOh, a date change must be made. For example, if zone time is 1500 on 3 April, ZD is +11, this makes a GMT of 0200 on 4 April. If ZT is 0400 on 7 November, ZD is -7, this makes a GMT of 2100 on 6 November. In the cases where daylight time is used instead of standard time, a negative one hour (-l hour) is applied to the ZD to get GMT.

Watch error or WE is the error that your timekeeper varies from true zone time. For instance, if your chronometer is 10 seconds slow, the error should be added to the time indicated to give true zone time. A fast error should be subtracted from the chronometer reading to give true zone time. A chronometer doesn't necessarily have to tell the exact time. If its rate of loss or gain, say one second per day, is consistent then the known error can be applied to get true zone time. In the absence of a chronometer, a stopwatch can be used that is set to a radio time signal. In this case, the time the stopwatch is started is added to the stopwatch reading at the time of sextant sight to obtain true zone time. The watch time or WT is the time read on your timepiece to the nearest second at the time your sextant sight is taken. Below is a example

WATCH TIME (W.T.) IS THE READING OF YOUR WATCH AT THE INSTANT YOU MAKE THE SEXTANT READING. THE WATCH IS SET TO THE STANDARD TIME OF THE TIME ZONE THE BOAT IS IN.

ZONE TIME (Z.T.) IS THE CORRECT TIME OF THE ZONE YOU'RE IN.

WATCH ERROR (W.E.) IS THE AMOUNT OF TIME THE WATCH IS SLOW (S) OR FAST (F). IF THE WATCH IS SLOW, YOU ADD THE ERROR. IF IT'S FAST, SUBTRACT.

1.WATCH TIME OF SIGHT WAS 0812 AND 15 SECONDS. WATCH ERROR WAS 12 SECONDS (F).

W.T. 08h-12m-15s

W.E. -12s (F)

Z.T. 08h-12m-03s

Celestial Navigation (Index Error)

Even a perfect sextant can develop index error (I.E.),which may change everyday.The index and horizon mirrors getting slightly out of adjustment cause this error. You check for this each time you use the sextant by lining up the actual horizon with the reflected image of the horizon.

Rather than continually adjusting the mirrors of your sextant, it is easier to apply an index correction (I.C.) to compensate for index error. Suppose your sextant was reading 1.5' too high (on the arc) when it should have read zero. In order to bring it back to zero you must subtract that amount. Your index correction (I.C.) would be -1.5'.
If your sextant was 2.2' "off the arc". Too low, your (I.C.) would be +.2.2
Coast Guard problems will give you either the "index error" or the index correction, so make sure you keep them straight. Here are some practice problems:

1. Your sextant reading is 31-28.6 index error is 2.5 on the arc. What is the corrected reading?
Answer: because an index error on the arc is too high, the number must be subtracted:

Hs 31- 28.6
I.C. -2.5
Hs 31- 26.1

2. Your sextant is reading 26-13.8'. Index correction is -1.2' what is the corrected reading?
Answer: An index correction is applied directly by following the + or - sign.

Hs 26- 13.8'
I.C. -1.2
Hs 26- 12.6

3. Your sextant reading is 45-29.6, I.E. is 1.8' off the arc.
Answer - if the index error is "off," you add it.

Hs 45 -29.6
I.C. +1.8
Hs 45 -31.4

4. Your sextant reading is 12- 05.4'. I.C. is +2.1,
Answer: Follow the plus or minus sign when working with I.C. (Index correction).

HS 12- 05.4
I.C. + 2.1
Hs 12- 07.5

Here are some more for practice.
1. Sextant reading: 32-49.8' 1.8 off the arc corrected: 32-51.6

2. Sextant reading: 18-52 .7 1.9 off the arc corrected: 18-54.6

3. Sextant reading: 58-22.0 2.7 on the arc corrected: 58-19.3

Sextant Errors And Adjustments

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°.

horizon split.

Before you use the sextant the Index error should be determined.

horizon level.

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.

Dip is an adjustment made for the height of the eye above sea level. In practice this is usually taken as 0.98 times the square root of the height of the eye in metres above sea level multiplied by 3.28.

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. From the Almanac.

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 us the zenith distance. Which means we know exactly how far we are from that point on the earth which is at right angles to our observed celestial body.

How To Use A Sextant

A sextant is not difficult to use but it takes 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 often used with the Sun but is often 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, an important step in sextant use that I skipped over quickly a couple of paragraphs ago. 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 downin 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.

Sextant Adjustment

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 perhaps 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.

Choosing a Sextant

In choosing a sextant, the biggest decision is quality versus purchase price. There are two basic "grades" to investigate, plastic and metal, with the corresponding retail price ranges varying.

The gap here is considerable the buyer should be better armed to choose the side of the gap best suited to him or her.

The plastic sextant's one advantage is price. This should be weighed against several disadvantages. First, since plastic will expand and contract with varying temperatures, the index correction (instrument error) is constantly changing. This can be partially compensated for by obtaining an index correction each time a set of sights is taken. However, the navigator may find that even between the first and last sight during a twilight series, the change can be considerable. Remember, a minute of error in sextant altitude directly corre­sponds to one nautical mile on the plot.

Secondly, plastic sextants weigh less than a pound and some varieties offer considerable wind resistance, all making it more difficult to hold the sextant vertical when sighting in breezy conditions.

Thirdly, the quality of the components is less, the filters, the mirrors, the zero to three power viewing scopes. And lastly, the life of a plastic sextant is shorter, depending on the amount of use. Filters break off, the plastic gearing wears down, the micrometer drum develops slop.

Any of the plastic sextants make excellent teaching aids where principle, not accuracy, is important. Also, as a back-up sextant, the micrometer plastic sextants can be very valuable. However, as a primary sextant when the celestial fix is important, I would strongly recommend investing in the better grade.

The advantages of a metal sextant are obvious after reading the disad­vantages involved in using a plastic sextant. Index correction is always the same unless the sextant is dropped or mirror adjustments are made. The weight (2 to 4 pounds) and open work frame reduce windage problems, the better optics and filters give guaranteed accuracy and the life of the instrument is indefi­nite as long as care is exercised in usage and storage.

The metal frame may be made of either brass or an aluminwn alloy, lightening the weight from roughly four to three pounds. The size of the frame varies too, also changing the weight. I find that the lighter sextants are easier to hold for a length of time.

The telescope power varies from three to eight power, the advantage of the higher power being mainly its ability to pick up the light of a star earlier in the twilight when the naked eye still cannot see it. The disadvantage of greater power is reduced field of view, and this becomes critical when the navigator is trying to keep the celestial body in the field while bouncing around on a small vessel. A four power scope is a good compromise:

Lighting is another option. Of course this isn't needed during the day but near the end of twilight, it is convenient to press a button or turn a switch to illuminate the arc and micrometer drwn. The battery case, wires and bulb socket arel all subject to corrosion at sea and batteries tend to wear down when most needed so often this "luxury" is questionable. The extra cost for lighting will finance an inexhaustible supply of penlight flash­lights which will clip on to clothing or store in the sextant case. Cases usually come with the sextant and are included in the price.

Second hand metal sextants are a rarity and often not much of a price bargain. Some sextants are sold as "antiques" and application of this title prices them beyond their useful value. The true antiques, the vernier sextants or octants, are nice as display items but the difficulty of reading a vernier versus a micrometer drum is a big disadvantage. Sometimes Navy surplus sextants can be found at reasonable prices. In any of these situations, instrument cleaning or mirror resilvering may be necessary but this cost will be minimal compared to the price of the instrument.

The final choice of instrument to buy comes down to how much you can afford, how essential celestial navigation is to your voyage, how comfortable the instrument is to use, and how experienced the navigator is in handling the sex­tant. Guaranteed accuracy ratings become less important when rough sea conditions and navigator inexperience prevail.

AZIMUTH BY CALCULATOR

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STEPS FOR FINDING TIME OF MOONRISE

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CELESTIAL NAVIGATION (MOON SIGHT )

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MOON (RISING AND SETTING)

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 important 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 ordinary 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:
In east longitude it is between the phenomenon on the given date and the
preceding one.

NAUTICAL ALMANAC SOLUTION
For the givin 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 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 ofthe 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.

POLARIS

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CELESTIAL NAVIGATION (POLARIS)

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AZIMUTH (LONG METHOD) #1

PELORIS FOR TAKING A SUN AZIMUTH














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