And do you need a chronometer or some other means of knowing the time in a different part of the world? Is it just a case of using the stars to determine the precise time where you are, or are there other methods?
I’d use one of these to determine where I was…especially at sea, but not limited to the sea. I’ve got an old brass one it’s tough to use but it works.
Very easy provided you know the time with accuracy. The Earth rotates once every 23.9345 hours (approx) or, what is the same, 15.041º / hour. If you observe a star crossing your meridian at a certain time and you know at what time it crosses the zero meridian (information which you can get from the almanac) the time difference can be converted directly into longitude by a simple division.
At sea observing meridian crossings is not practical and other more complex methods are used which involve measuring the altitude of the celestial body over the horizon and then “reducing” the sight. There are several methods but the most common is the St Hillaire method invented by a Frenchman of that name. It involves assuming you are in a certain position and calculating the error which, in turn, tells you how far off you were in your assumption. It is not something which can be explained in a simple post but there are books out there about it. I did a Celestial Navigation thread some time ago but (not surprisingly) it did not raise much interest.
Short of using GPS, you must know the correct local time to determine longitude from the stars.
At the beginning of my career as a navigator, I was trained to acquire headings from the sun and moon and to use sight reduction tables to get a “fix” using stars and planets. This was many years ago, and I’d never be able to do it today without a few hours of brushing up. From what little I do recall, there are a few entering arguments, (like the time, your latitude (using your estimated position) and the elevation you got from sighting the object with a sextant) which you use to enter different sight reduction tables to extract numbers. There’s a long worksheet we would use to eventually come up with (IIRC) the geographic position of where the targeted celestial body falls on the earth, plus a line of bearing from that position. Get two or three positions and respective lines of bearing, and where they all cross is where you hopefully are.
Once you got the hang of it, the method I used was fairly reliable. But the learning process was extremely painful and long, and it would take anywhere from 5-10 minutes to get a few lines of bearing. If you’re on a slow-moving ship, that’s ok. If you’re on a plane, like I was, the position you came up with, by the time you came up with it, could be up to 60 miles off. We consider an accurate “fix” to be within a couple of miles. So basically it would tell you where you were and not really where you are.
Well, there is a non-answer if I ever saw one. the question is " How do you determine longitude from the stars?" and I don’t see how your post answers that.
Furthermore, your post is wrong. You need to know Universal Time (UT, GMT for practical purposes), not local time. If you know Local Legal time and the hours difference with UT you can calculate UT. Local solar time would be useless.
flyboy88, I assume you learnt sight reduction using HO249 tables (for air navigation). Most people who are taught navigation concentrate on the mechanics of the process, not the concepts, so it is easy to forget the steps and even make mistakes. OTOH, I studied astronav just for the heck of it and I studied the concepts and foundations in depth and I feel it is like swimming or riding a bicycle: once you have learnt it you will never forget it. I studied and became profficient in several sight reduction methods and I am sure I could be ready to reduce sights efficiently in no time.
Interestingly, Philosphr your location only gives your latitude, which is appropriate as you link me to a bit about sextants. However a sextant on its own is little use to me, as my question is about longitude
Thanks for the other answers. I perhaps should have mentioned that I was wondering about how the longitudes of fixed points on land were determined with scientific accuracy when the first really scientific surveys were being done.
For example I’m just reading about how in the 19th century the longitude of Madras was determined so as to place the great triangulation of India in the world context. Apparently it would take many years of observations to do this, but I don’t think the book (“The Great Arc” by John Keay) says which method was used. I have a feeling though that they would not have regarded chronometers as accurate enough at that time, since they got a figure for Madras relative to Greenwich that was supposedly accurate to seconds of a degree.
I was wondering why it takes so many years to compute, and also which variables are used; it’s just a hunch, but I suspect these surveyors would have wanted to make all the relevant observations themselves and not rely on someone else’s tables. Flyboy do you know anything about how these tables you used were made?
It would have interested me.
I often take readings on land for practice (using an artificial horizon), but my results are always 5-40 miles off. I’ve checked and rechecked my math. My sextant seems to work fine. So does my watch. I don’t get what I’m doing wrong.
Shit, sorry Philosphr, in my haste to construct a smartarse reply I failed to notice the bit about the Lunar distance method. But do you really still receive copies of the necessary tables, and keep them by your trusty sextant?
They were surprisingly accurate a century before that.
The sextant method would theoretically give you an accuracy of within 600 feet, but a one second clock error would throw you off by double that amount.
At $41 per year, it’s not that difficult. And there are some reduction charts that are cheaper, and good from year to year.
Here is an excellent historical book on how it was solved:
A sextant is a useful instrument in determining latitude, even on land but, of course, there are better methods and instruments. As I said the most precise method is to measure the time difference between the local meridian crossing and the crossing of the meridian of reference. There are special meridian telescopes built for this in the meridian plane. the problem thus becomes one of knowing what the time is in the meridian of reference: i.e.: being in India and knowing what time it is in Greenwhich. The Chronometer is one instrument used for this but also the common observation of astronomic events like the occultation of the moons of Jupiter.
Flyboy used a very different method used for navigation. He used the Celestial Almanac to determine the Geographical Position (GP) of the bodies at the time of observation and simple tables of spherial triangles to resolve the spherical triangle which results with three points: the pole, the observer and the GP of the celestial body. today there is no need for these tables because a $20 calculator can do it instantly.
I have posted a schematic diagram of the basic process of sight reduction by the Marc St. Hillaire method.
tdn, the sight reduction tables are good forever and you do not need to buy new ones. It is the almanac which you need to buy new every year.
Yep, that’s what I meant to say. I just assume use of the almanac because that’s the system I’d learned. I was taught the reduction method, but I’ve long since forgotten how to do it.
Yep, that’s what I meant to say. I just assume use of the almanac because that’s the system I’d learned. I was taught the reduction method, but I’ve long since forgotten how to do it.
Two questions about the reduction method:
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Don’t you need a number or two to plug in to the equation, and that number changes each year? Where do you get it?
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Is that method only for the sun and moon, or can you use it with stars and planets?
Thanks for the answers, and sorry for furthering my smartarsedness.
I knew about the Longitude book, rodent. What I was trying to find out was whether there was a method that does not rely on chronometers; while they were good for ships at sea, I don’t think chronometers were accurate enough for scientists surveying land at the beginning of the 19th century. For example, when Lambton triangulated the south of India between 1803 and 1805, he discovered the peninsula was 40 miles narrower (east to west) than had been thought. And that’s an area which would already have been visited by many ships with chronometers. He needed to know the longitude to within inches, not tens of miles.
Let’s get the vocabulary right. You take a sight with the sextant and the process if calculating the navigational information is called “sight reduction”. Now, of the dozens of methods of sight reduction the most common and the one you probably learnt is the Marc St. Hillaire which, in turn has dozens of variants.
These methods are good for any celestial body as long as you can get the infprmation which is contained in the almanac (today you have computer programs which calculate it so there’s no need to buy the almanac). You enter the almanac with the body ID and UT and extract GHA and dec (mainly) as well as some other (not so important) data. That is the only infpormation which changes from year to year. In fact, it changes mainly for the bodies in the solar system and you could use an old almanac for the stars. Calculating the position of the stars given UT is quite trivial, it is the bodoes in the solar system which wander all over the place. in fact, the Sun’s position can also be calculated with relative ease. the moon and planets are something more complex though.
As I said, the observation of celestial events, like the occultation of the moons of Jupiter were used but chronometers were also of use. It was (is) not a matter of either/or but a matter of continuously revising and improving previous estimates and all information was taken into account and given the appropriate weight. There was no way to determine longitude with a precission of a cm though because that was beyond the precission of the instruments they had. You would need to determine the meridian passage with an precision of 1/200 second which was only possible by averaging thousands of readings and even then you weren’t too sure.
It may be worth noting that extremely precise measurement of time (Universal, not local, as Sailor has pointed out) is essential to the Global Positioning System. Of course, you don’t have to worry about it – the satellites take care of this for you.