Questions about Celestial Navigation

Question

Can someone please help? I did poorly in math at school, have gotten through life with basic arithmetic, but have always been fascinated by celestial navigation. In the navy many years ago I was involved in navigation and especially liked celestial.

I am now trying to learn HOW we were able to fix our position on the Atlantic or Caribbean by using a sextant, accurate time, and several publications.

I have a decent grasp of some aspects of nav astronomy but have hit a wall regarding LHA, GHA, and SHA. For example, it's important to know GHA of Aries in any sight reduction but how can Aries have a GHA if it is located on the Greenwich Celestial Meridian?

I understand that SHA and declination are celestial equivalents of latitude and longitude but I can't seem to wrap my brain around the other two hour angles.

Any help is greatly appreciated!

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• LHA: Local Hour Angle
• GHA: Greenwich Hour Angle
• SHA: Sidereal Hour Angle

Answer 1

GHA = Greenwich Hour Angle, but not Greenwich Celestial Meridian—actually, there’s no such thing. I suppose you meant the Celestial Prime Meridian (or 0° of celestial longitude). GHA is the angle in degrees between the Greenwich meridian and the object being considered—in other words, as seen from Greenwich (UK), it’s the angle between the “south” and the object, measured on the celestial equator.

LHA = Local Hour Angle. It’s the angle in degrees between the local meridian and the object being considered. It’s basically the same thing as GHA, but as seen from the observer’s location.

SHA = Sidereal Hour Angle. It’s the angle in degrees between 0° of celestial longitude (the “first point of Aries,” although now located in Pisces and [very] slowly approaching Aquarius). It’s similar to the right ascension, which is measured in hours of time instead of degrees.

GHA and LHA are related in a very simple way: $ \text{GHA} = \text{LHA} - \lambda $, where $ \lambda $ is the observer’s longitude.

I hope this clears things a bit. If not, well, I’ll be happy to provide further explanation.

Answer 2

You can do it all with arithmetic: no algebra or trig. The Navy publications you saw are designed that way.

Starting with the Nautical Almanac: there are different treatments for the stars and for the Sun, Moon and planets. The stars are more or less fixed on the imaginary celestial sphere. They don't move in relation to one another. The Sun, Moon and planets do, so their use in celestial navigation is a little more complicated. The positions of the stars are specified in relation to the First Point of Aries (equivalent to the Prime Meridian) and a Celestial Equator (equivalent to Earth's equator.) That gives a way of locating each of the stars with just two numbers: sidereal hour angle (like west longitude) and declination (like latitude). Since they're in fixed positions on the celestial sphere while the Earth is rotating there must be a reference that tells where the first point of Aries is in relation to the Prime Meridian. That's why Aries has a column with the Sun, Moon and planets giving its GHA, its angular distance from the prime meridian, and the stars are located with respect to it.

With just the information in the daily tables and the time you can calculate the point on the Earth a star is directly above: its GP. The longitude of the GP is equal to the star's SHA, plus Aries' GHA. GP's latitude is equal to star's declination.

Using a sextant you can measure its altitude. Then your distance from the star's GP is 90 degrees minus that altitude. For example, if its altitude is 40 degrees, you're 50 degrees away from its GP. Each degree of arc is 60 nautical miles. So, if you had a globe and a compass you could draw a 3000 nautical mile radius circle on the globe and know your ship was somewhere on that circle at the time of the sight. If you have two star sights, the two positions where the circles intersect are two possible locations. With three sights there would only be one intersection for all three.

Drawing circles on a globe is nowhere near good enough for fixing position, but it's a good way to visualize the problem, and how it's solved. The other publications have tables for more accurate solutions. If I didn't make it clear enough above: the first Point of Aries only passes the Greenwich meridian about once a day as the Earth rotates inside the conceptual celestial sphere. It's distance is given by the GHA in the Aries column of the daily tables.

I'm surprised you saw the Air Almanac used on board ships. It was (is?) used on aircraft, and they necessarily have less accurate sextants - bubble sextants. They measure altitude with respect to a bubble like you'd see on a carpenter's spirit level, because much of the time the horizon isn't visible, and when it is, the dip correction depends on the aircraft's altitude which isn't as well-known as, say, the navigator's eye above sea level on the ship's O-5 level.