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greenwich meantime naviagation

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Astro Navigation Demystified
Navigate Without GPS

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Converting GMT to GHA

Greenwich Mean Time (GMT) is the local mean time anywhere on the meridian of Greenwich. In other words it is the Local Hour Angle of the Mean Sun on the meridian of Greenwich.

Since the Greenwich meridian is used as the base meridian from which the longitude of all places on Earth are identified, it provides the link between the LMT of a place and the LMT at Greenwich (or GMT).

Example. In the diagram below, imagine that we are looking down on the North Pole.

GMT white

P represents the North Pole

G represents the position of Greenwich on the Earth’s surface.

GP represents part of the Greenwich Meridian (0o).

MP represents part of the meridian of longitude 45oW and M is a point on that meridian.

AP represents part of the meridian of longitude 30o E and A is a point on that

meridian.

The meridian of the Mean Sun, for a very brief instant, coincides with the meridian 45oW. and so, at that instant, the Local Mean Time at point M is noon.

At the same instant, the Local Hour Angle of the Mean Sun at Greenwich is 45o. Therefore, the LMT at Greenwich must be 3p.m. since the time difference for 45o is 3 hours and Greenwich is to the East of M.

It follows that the Greenwich Mean Time must also be 3p.m. (since GMT is equal to the LMT at Greenwich).

The LMT at point A must be 2 hours after GMT (since the time difference for 30o is 2 hours and A is to the East of Greenwich).

Therefore, the LMT at point A must be 5p.m.

Greenwich Hour Angle (GHA). The angle between two meridians of Longitude can be expressed as an hour angle. The hour angle between the Greenwich Meridian and the meridian of a celestial body is known as the Greenwich Hour Angle.

The Local Hour Angle between an observer’s position and the geographical position of a celestial body can be found by combining the observer’s longitude with the GHA.

In the diagram below , O represents the longitude of an observer;

X represents the meridian of a celestial body;

G represents the Greenwich Meridian.

diag 5 nonumBecause in this case, the observer’s longitude is east and because LHA is measured westwards from the observer’s meridian to the meridian of the celestial body, LHA is equal to the longitude plus the GHA.

For a fuller explanation of GHA and LHA click here

Converting GMT to GHA.

Because GMT is measured westwards from the reciprocal of Greenwich (i.e. 180o) and GHA is measured westwards from the Greenwich meridian (i.e. 0o) we convert GMT to GHA as follows: If GMT, when converted to arc, is less than 180o then add 180o; if GMT is greater than 180o then subtract 180o). Examples:

Example 1. Convert 0840 GMT to GHA.

Step 1. Convert GMT to arc.

8h = 8 x 15 = 120o 0’ 0”

40m = 40 ÷ 4 = 10o 0’ 0”

= 130o 0’ 0”

Step 2. Convert to GHA.

GHA =130o 0’ 0” + 180o 0’ 0” = 310o 0’ 0”

Example 2. Convert 1530 GMT to GHA.

Step 1. Convert GMT to arc.

15h = 15 x 15 = 225o 0’ 0”

30m = 30 ÷ 4 = 7o 30’ 0”

= 232o 30’ 0”

Step 2. Convert to GHA.

GHA = 232o 30’ 0” – 180o 0’ 0” = 52o 30’ 0”

Note. Because GHA relates to apparent solar time and GMT relates to mean solar time, we must take the equation of time (EOT) into account when converting GMT to GHA. Therefore the next example includes a calculation for EOT.

Example 3. Convert 0415 GMT to GHA. E0T = +1 m

Equation of Time = mean solar time – apparent solar time

∴ apparent solar time = mean solar time – equation of time

∴ GHA = GMT – EOT.

Step 1. Convert 0415 GMT to arc.

4h = 4 x 15 = 60o 0’ 0”

15m = 15 ÷ 4 = 3o 45’ 0”

= 63o 45’ 0”

– EOT – 1’ 0” (correction for EOT)

= 63o 44’ 0”

Step 2. Convert to GHA.

GHA =63o 44’ 0” + 180o 0’ 0’’ = 243o 44’ 0”

Latitude & Longitude & GreenWich MeanTime Navigation

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How do I determine my longitude and latitude without any technology?
You can do it with:
A quadrant,
A Sundial
A Watch

The first part is the easiest – latitude
At sea, in the middle of nowhere, to find out your latitude, you find Polaris.
Polaris is a star that is exactly aligned with the axis of the Earth toward the north. No matter where you are in the northern hemisphere this star is toward the North.

Polaris is in the axis of the Planet Earth

And therefore always at the same place in the sky, regardless of earth rotation.

Now, given the location of Polaris, if you are navigating in the northern hemisphere, it will be above your head if you are at the north pole (90°) and right on the horizon (0°) if you are on the equator, any position. You then use a quadrant to measure as accurately as possible the position of Polaris above the horizon, and this is you Latitude.
If you are in the southern hemisphere your could use Sigma Octantis instead but it is much more difficult and not as accurate.
If this is during the day you can find out using the sun. Now this is more difficult. But the sun at 12:00 on 20th March / September(equinox) will be right above your head on the equator and will be at the horizon on the north pole. You use your quadrant again to measure the angle and your latitude is 90- your results….
Now to measure your longitude. Well sorry but you cannot do it without a great piece of technology. It took about 60 years to be created from the moment the British government offered £20 000 to whomever could make it.
This my friend, is a watch. Not a simple one, oh no. A watch that gives Greenwich time for months without running fast or slow EVEN ON A BOAT. Because of course the mechanism of any watch from the 18 century would struggle with the movements of a boat.
The principle is easy, once we have defined that the line going through Greenwich observatory is the mark 0 (which in itself wasn’t that simple as Paris was claiming it as well). Your longitude is the time difference between Greenwich and your position (between 0 and 24 hours) translate into degrees (0 – 360).

So what you need is to know the time wherever your are and then the time in London.
If you think the former is the most difficult … think again.
With a sundial, it is fairly straightforward to know the time.
To know the time in Greenwich, however you need to have embarked a watch showing the time there and that hasn’t been impacted by the movement of the boat at sea.
So now that you have the time difference between your place and Greenwich you know how far you went.

Mahalo

SIGNATURE:
Clifford "RAY" Hackett www.rayis.me RESUME: www.rayis.me/resume

I founded www.adapt.org in 1980 it now has over 50 million members.
$500 of material=World’s fastest hydrofoil sailboat. http://sunrun.biz

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Mahalo

SIGNATURE:
Clifford "RAY" Hackett www.rayis.me RESUME: www.rayis.me/resume

I founded www.adapt.org in 1980 it now has over 50 million members.
$500 of material=World’s fastest hydrofoil sailboat. http://sunrun.biz