47 ASTRO NOTES 47
Astro Navigation
Subjects covered:
Definitions, Celestial sphere
Time
Using the Nautical Almanac
Sunrise / sunset / moonrise / moonset – exercises
Amplitude
Sextant, errors
Altitudes, Zenith Distances
Exercises for various heavenly bodies
Meridian Passage to find latitude
Latitude by Polaris
PZX triangle, LHA
Marc St Hilaire, ABC tables, Azimuths – exercises
Sun Run Sun – exercise
Star sights by Sight Reduction Table
The Celestial Sphere
Imagine standing on the earth looking up at the inside of a hollow concentric sphere whose axis runs through the Earth’s poles.
All the stars and other celestial bodies are imagined to be projected on the concave interior of this sphere. A line drawn from the common centre of the earth and celestial sphere to a star would pass through the surface of the earth at the Geographical Position of the star.
It is convenient to imagine the earth as stationary and the celestial sphere rotating around us on the common axis, carrying all the heavenly bodies with it.
The stars would all move together, and if we lay on our backs in the open on a summer’s night we would get the impression of the heavens all rolling together from east to west.
If we watched the sky long enough we would see the planets are not always in the same place relative to the stars, and the sun too appears to move across the surface of the celestial sphere.
There are two components to the sun’s apparent motion:
1. The earth is spinning on its axis every day, so the celestial sphere too appears to rotate in the opposite direction, causing all the bodies to rise and set.
2. The earth is travelling in an elliptical orbit round the sun every year, resulting in changes to the sun’s declination and changing the length of each day
Siderial Hour Angle (Star)
The SHA of a star is the angle subtended at the celestial pole between the meridian passing through the First Point of Aries ^ and the star’s meridian.
But what is this “Aries”? Think of it as being the Hollywood equivalent of the Greenwich Meridian, the Prime Meridian for the Stars!
The earth rotates on its axis, and the interval of time elapsed between two successive transits of a heavenly body over the same meridian, is called a day.
There are 3 astronomical days:
· Sidereal day.
· Solar day.
· Lunar day.
The lunar day is longer than the solar day and the solar is longer than the sidereal day.
The sun is used for time measurement, however the interval between two successive transits are not equal therefore we have to make allowances for this fact, as follows.
We say that the TRUE SUN, registers APPARENT SOLAR TIME.
But we do not have watches that can keep pace with this apparent time so we use
the MEAN SUN which is imaginary and conceived to move along the equinoctial at a uniform rate equal to the average rate of the True Sun on the ecliptic and is called MEAN TIME
Equation of Time is the difference between Apparent and Mean time and is tabulated daily in the Nautical Almanac.
Lets look at how longitude affects time.
• GMT or UT is the datum.
• The sun rises in the East and sets in the West so all locations to the east of us have already had sunrise so our time is behind theirs.
• All locations to the West have not yet had sunrise so their time is behind ours.
• The mean sun travels at a rate of 15˚ per hour.
• So LMT of sunrise, sunset and meridian passage at any longitude, is as stated in the nautical Almanac, the GMT changes at the rate of 15˚ per hour.
• Therefore GMT at any longitude = LMT ± (Long)
15
• If your longitude is 060˚ West and time is 0754 GMT what is your LMT?
• If your Longitude is 150˚ East and the time is 0600 on December 14th what is the GMT.
• GMT 0754
Long 0401
LMT 0353
• LMT 0600 14th = 3000 13th
Long E 1000
GMT 2000 13th.
CHRONOMETER
For any sight other than a meridian altitude, it is essential to know the exact time. (On the equator an error of 1 second results in a position error up to 0.25 miles).
For astronomical navigation we use Greenwich Mean Time or UT. This ascertained from UTC (Coordinated Universal Time), derived from atomic clocks, which is kept very close to UT. The difference is kept at less than 0.9 sec by means of occasional Leap Seconds in UTC.
Aboard ship the time is maintained by a very accurate type of clock called a Chronometer, which may be driven by traditional clockwork or modern quartz crystal.
1) Traditional. This is a spring driven clock with a precision-made mechanism designed to maintain a steady rate. It is mounted in gimbals in a glass topped box to protect it as much as possible from ship’s motion and rapid changes in temperature. Any jarring or violent motion can damage bearings and pivots, while temperature changes cause a variation in rate, despite built-in compensation.
Two day chronometers should be wound at the same time every day, 8 day chronometers should be wound at the same time on the same day every week.
2) Quartz Crystal. Most common these days. Generally requires a new battery every 6 months or 12 months, and may have a battery level indicator. Usually a backup battery keeps the mechanism going while the battery is changed. A note of battery renewal dates should be kept with the chronometer.
Normally a glass-topped padded locker with internal lighting is built in to the chart table, where the chronometer can be read without being exposed to draughts. Resist the temptation to use the locker for stowing odds and ends such as spare keys, and be sure to keep any magnets well away.
Details of stations transmitting time signals are given in ALRS Vol 2. The well known BBC “pips” are easily available worldwide on BBC World Service, but are not intended for precise use. The error, however, is within 0.4 seconds of UTC. The time is indicated by the start of the 6th (long) pip.
_ _ _ _ _ _____
55 56 57 58 59 00 seconds.
Other stations use different systems.
Do NOT get time signals from a digital radio as there is a delay processing the signal.
Chronometer Error
The chronometer is checked against radio time signals every day, and the difference “error” is logged in the Chronometer Rate Book. The daily change in error is averaged over several days and this is logged as the “rate”. If no time signal has been obtained for several days, the exact time is found by applying the daily rate to the last known error.
Example:
Date GMT Chron Error Daily Rate
11 Nov 10 00 10 01 05 1m 05s Fast
19 Nov 10 00 10 01 11 1m 11s Fast 0.75s gaining
If no more time signals were obtained, find the time of sight on 24 Nov at 1600.
Accumulated rate 19th/1000-24th/1600 (5.25 days) = 5.25 x 0.75 = 3.9375 ≈ 4 sec gain.
Error at 19th 1000 1 m 11s Fast
Accumulated rate to 24th 1600 4s Gain
Error at 24th 1600 1m 15s Fast
Chronometer 15 57 36
Error - 1 15 F
GMT at time of sight 15 56 21
No attempt should be made to reset the chronometer. It must be allowed to run undisturbed, and the error applied to the time shown.
If a chronometer requires repair or cleaning, the gimbals should be clamped and the chronometer packed with the greatest care.
Traditionally more than one chronometer was carried, in order for comparisons to be made, but this is less common now time signals are readily available, and in an emergency a good quality quartz crystal watch will do.
Reading the Chronometer
If an assistant is available, when you are taking the sight shout “Stand by”. At the precise moment the heavenly body is touching the horizon in your sextant telescope, shout “Stop”.
The assistant notes the second hand reading, then the minute, finally the hour, then asks you for the sextant reading.
If no assistant is available you must start a stop watch at the instant of the sight then compare stop watch with chronometer to calculate time. Some sextants are provided with stop watch brackets fixed to the handle.
Be very careful to calculate the correct GMT time and date, especially if in a position far away from the Greenwich meridian. Does this chronometer read 03h 04m 49s or 15h04m 49s?
THE NAUTICAL ALMANAC
This is published annually by the Hydrographic Office as NP 314-09 (for year 2009), the last two numbers denoting the year. An identical version is published simultaneously by the US Nautical Almanac Office in Washington.
The almanac provides data on the Sun, Moon, 4 Planets, and major stars enabling us to find their positions in the Celestial Sphere to within 0.1’ of arc.
Additional tables are provided to correct sextant readings, find rising and setting times etc.
Clear instructions are provided on page 254. It is important that the tables are used precisely as described, as allowances have already been made for interpolation and rounding off.
Certain tables are arranged as Critical Tables. In these an interval of apparent altitude, say, corresponds to a single value. No interpolation is required. At a critical entry the upper of two values is taken.
For instance, if App Alt is between 11 01 and 11 15, the correction is +11.5’. If App Alt is 11 00, the correction is 11.4’
.
NAUTICAL TABLES
Ships are required to carry nautical tables to assist in mathematical calculations.
While the availability of cheap calculators makes computation of complex formulae easy, there are disadvantages:
Ø It is still necessary to remember the formulae
Ø Calculators are easily damaged
Ø It is easy to enter the wrong number but still get a convincing answer.
The most common tables are those published by Nories or Burtons, and are basically ready-reckoners in which the common navigation problems have been worked out for a wide rsange of values.
With practice they are very easy to use and in many cases give quicker results than calculators.
Sunrise and Sunset
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