Tuesday, February 10, 2009

The Nautical Almanac, Pub. 229 and Longitude

The Nautical Almanac is published annually by the Naval Observatory in the United States and Her Majesty's Stationery Office in the United Kingdom. It provides the navigator with the declination and Greenwich hour angle of all the celestial bodies normally used in navigation for an entire year. In order to find these coordinates, the exact Greenwich mean time (GMT) of the observation must be known. The Almanac contains the information needed for solution of navigation problems in addition to the Greenwich hour angles and declinations of celestial bodies.
The 1981 edition is used by the Coast Guard in all license exam questions requiring information from the Almanac. Each pair of pages covers a three day period.

The left hand daily pages provide:
1. The GHA of the hour circle of the first point of Aries for each hour of GMT.
2. The GHA's and declinations of the planets Venus, Mars, Jupiter, and Saturn for each hour of GMT.
3. The sidereal hour angles (SHA) and declinations of the 57 navigational stars. The SHA's and declinations change only slightly from one three day period to the next, they are only listed once for each three-day period rather than for each hour of GMT.
4. A tabulation of the local mean time of meridian passage and sidereal hour angle (SHA) of the planets is in the lower right corner of the page. This information is used in star identification.
The right-hand daily pages provide:
1. The GHA and declination of the sun for each hour of GMT.
2. The GHA and declination of the moon for each hour of GMT.
3. Local mean times of sunrise, sunset, twilight, moonrise, and moonset.
4. The mean times of the sun's meridian passage, moon's meridian passage, and the equation of time are in the lower right corner.

In order to obtain accuracy the exact value of the GMT of the observation to the nearest second must be used. The daily pages provide coordinates for whole hours, and the increments and corrections pages provide corrections for minutes and seconds of GMT, which must be added to the GHA and declination values given for a body in the "daily pages".

In the increments and corrections section, the table is entered with minutes and seconds of GMT. Included in the Almanac is a table for each minute from zero to 60, and each minute's table has a line for zero through 60 seconds. Reading each line from left to right are the GHA corrections for that number of minutes and seconds for the sun and planets, Aries, and the moon. The portion of the table to the right labeled "v" or "d" Corr" (correction) provides corrections for declination and for "excess of motion". Standard sight forms cannot be taken in the testing room for use in license exams. Using standard forms in learning how to solve celestial problems is recommended.

Finding your Location
Step 1: You can express your position by Latitude and Longitude.
Step 2: Chartmakers or geographers use an imaginary grid to locate a place on a map. This grid is made up of intersecting lines of latitude and longitude.
Step 3: Lines of latitude run east and west around the globe. The latitude is measured in degrees north and south from the Equator. Lines of longitude that run north and south from North pole to the South pole are measured in degrees east and west from the Prime Meridian.
Step 4: Prime Meridian runs through Greenwich, England. It is the planet’s Home Base.
Step 5: You can find the longitude of your location with an accurate sense of time. Before you can do any longitude calculations, you must convert your local zone time, as shown on your watch, to GMT (Greenwich Mean Time, the clock time at Greenwich).
Step 6: The local zone time is the local clock time which is the mean solar time of central meridian of your local time zone.

In several places in the world, hundreds of different times were adopted, each one corresponding to its own meridian. To simplify this situation, the Earth surface was divided into 24 time zones, each one delimited by two meridian forming a hour angle of 1 hour at the poles. The mean solar time of the central meridian of each time zone was assigned by convention to all places belonging to the time zone.

Three Basic Ideas to find Longitude:
1. The first of these ideas is the relationship between time and the rotation of the Earth. It takes an average time of 24 hours for the Earth to rotate 360 degrees. If you divide the number degrees in a circle by the number of hours in a day, you will find that the Earth turns 15 degrees every hour. 360° / 24 hours = 15° per hour. You can take this a step further and say that the Earth turns one degree in four minutes. 1 hour = 60 minutes / 15° = 4 minutes per degree.
2. The second idea is that you have to be careful about the difference between the events and time. Events like sunrise in the east always happen before the same event in the west. But time as shown on eastern clocks is later than on western clocks at the same instant. Local time earlier, position is westward. Local time later, position is eastward.
3. The third and last idea needed for longitude is the applying of Equation of Time.

Clock time and Sun time are different by as much as 16.5 minutes. The important thing is that if you're going to compare Sun time to the chronometer's clock time, you have to change the chronometer's clock time to Sun time so that you're comparing like terms. And that's what the Equation of Time does. You can find the Equation of Time from the Nautical Almanac. By applying the Equation of Time to the chronometer's clock time, you convert Greenwich Mean Time (GMT:Clock time.) to Greenwich Apparent Time (GAT:Sun time). GAT is simply the Sun time back at Greenwich, England.

Now you can observe Local Apparent Noon and do your simple subtraction of GAT to find your longitude. It is noon at the very instant that the sun were right over your head. Local Apparent Noon is simply noon for your exact location, and sets your watch to 12:00 based on Sun Time. The time of Local Apparent Noon, recorded as 12:00 local time, is compared to the time back in Greenwich.

To solve the navigational triangle to find computed altitude (Hc) and azimuth (Zn) for a celestial sight. By comparing Hc with observed altitude (Ho), the navigator finds the altitude intercept (a). With the assumed position coordinates, azimuth, and inter­cept, a line of position can be established. There are two basic methods for solving a navigational triangle or other spherical tri­angle by sight reduction table or by mathematical solution.

A sight reduction table presents solutions of the navigational triangle for com­putation of the altitude and azimuth of a celestial body. The variable components are co-latitude, polar distance, and meridian angle "t". Their values depend on time of the observation and the observer's position. The parts of the triangle are computed co-altitude (in order to find Hc) and azimuth angle (in order to determine Zn). Mathematical solutions use the same formulas used to pre-compute the values found in the sight reduction tables. Final results, found through the correct use of either method, seldom differ by more than one-tenth minute of arc for intercept values, or one tenth degree for azimuth values.

Sight Reduction Table - Pub. 229
The Sight Reductton Table for Marine Navtgatton (Pub 229) is a form of sight reduction table which is produced by the Defense Mapping Agency. They are designed to help you in solution of navigational triangles to find computed altitude (Hc) and azimuth (Zn). There are six volumes of Publication 229, each volume covering 15 degrees of latitude. All of the problems used in USCG license exams, which may be solved with Publication 229, are in latitudes 15 degrees to 30 degrees covered by Volume II of the tables.

The entering arguments for 229 are assumed latitude, the whole degree LHA which results when assumed longitude is applied to GHA, and declination. The main part of the tables is divided in half. The first half of Volume II covers latitudes 15 degrees through 22 degrees, and the second half covers latitudes 23 through 30 degrees. The latitude which is used to enter the table may be either north or south. Each half covers LHA's from 0 degrees through 360 degrees.

There are two pages for each LHA value from 0 through 90 degrees, and 270 through 360 degrees. Left-hand pages are for situations where declination and latitude are both north or both south, they are said to have the "same name." Each "same name" page covers declinations from 0 through 90 degrees.

The adjacent right-hand pages cover "contrary name" situations (meaning the declination is north and latitude south or vice versa) for the LHA values at the top of the page, and "same name" situations when the LHA values are between 90 degrees and 270 degrees located at the bottom of the page. The dividing line between "contrary" and "same name" situations is the step-like line across the right-hand page. The step-like line across the right-hand page represents the horizon. Entry values of LHA, latitude, and declination (same or contrary) should never result in crossing this line, as this would mean the body is below the horizon.

The inside front and back covers of each 229 are an interpolation table to be used for correcting the the altitude and azimuth angle obtained in the main part of the table for the declination increment. Declination increment is the minutes and tenths of minutes part of the declination of the body. For example, if the body's declination is N 43°­23.7', the declination increment is 23.7'. In other words, declination is tabulated on each page in whole degrees, and you must interpolate between those whole degrees for your actual declination value. Declination increments 00.0 through 31.9 minutes are located inside the front cover, and declination increments 28.0 through 59.9 minutes are inside the back cover.