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Finding your Longitude

Actually doing it!

Report of an attempt to find longitude
using a solar meridian and the time of it at Greenwich

(Page's URL: latsun-first-attempt-22704.htm)


It amused me to try. I thought it might amuse some of my readers. I wanted to help you see how you could try your hand at "the trick".

"What trick"

The trick of finding your longitude without (much) use of GPS, Google, etc.

Yes! I used GPS... to see if my result was "right".

And I used the internet to learn what time it was in Greenwich at a certain time where I was. Years ago, you would have had a very special, very expensive, very- carefully- looked- after and -adjusted clock with you for that.

I've written about the theory, and about some of the terms, used here elsewhere, in my page about latitude and longitude and the sun.


"Line of longitude"... a line going "straight" between where the axis of the earth's rotation "comes out" at the north pole to where it comes out at the south pole. (These are the "true" north and south poles, vs the "magnetic" north and south poles... the places compasses point to.)

Lines of longitude are "numbered" from "zero"... the one that passes through Greenwich, in England, according to how many degrees "around" the globe they are. So the line of longitude half way around the world from Greenwich is called "longitude 180".

"Meridian"... the line of longitude you are on.

"Solar altitude"... the height (as an angle) of the sun above the horizon at a given moment. (That's a pretty approximate definition! But it will do for here.)

"Meridian altitude"... the solar altitude at the moment when the sun is directly over the lone of longitude you are on. (The sun will be as high as it will get in the sky for that day at this time. If you wait for this "highest moment", you will learn where true south is from where you are.)

"Solar noon"... the moment when the sun will be as high as it will get in the sky that day.

"UTC time": The time according to the sun at Greenwich, in England.

What I did

I watched the sun for a few hours near the time it was highest in the sky.

I used my smartphone's GPS to get what I thought was a good value for the UTC times of the following. This of course, is a major "cheat"... but I'm new to all of this. I hope to progress to other systems that don't rely on having the UTC time.

In "the good old days", as I said before, people finding longitudes would have a clock that was showing the UTC time. Such clocks were expensive, and required considerable looking after.

From the data I'd gathered for the 5 minutes either side of solar noon, "by eye", I decided that solar noon that day (4 July 2022) occurred at 12:13:00.

To say it happened at that second is of course ridiculous. But "that second" was my best guess.

It is hard to spot "the moment" because near solar noon, the sun's altitude changes slowly.

From the data I'd gathered when the sun was at about 122 deg 40 seconds rising (11:50) and at about 122 deg 40 seconds falling (12:39), I decided that solar noon occurred at 12:16:00.

So! A "win"... my two attempts to spot when solar noon occurred were fairly close to one another. That could have been due to an error I am unaware of, but which was part of both sets of measurements. They were done with the same tool... a nice sextant that I bought as "an antique" for far below its pre-GPS cost.

Next time, I think I'll try to determine solar noon by sextant by both of the above techniques and by measuring the length of the shadow of a tall stick firmly stuck in some level ground, too, and see if all four results agree.

To check my "answer"

To check my value for when solar noon occurred, I went to SunEarthTools.com. It told me that solar noon where I was, "when I was" (4 July 22) was at 12:14:58

So if I used the average of my two determinations, I got an answer within 28 seconds of "the right" answer!! (^_^)

My longitude

Whew! When I made the notes for this page, I made a mistake in the next part, and got a not-very-good result.

Happily, as I type the notes up, I've spotted that error. Will I get a better answer this time?!

A little "gotcha".

In my first attempt at this, I said... "Solar noon at Greenwich, by definition, is at 12:00:00."

Not so! Solar noon at Greenwich will be near noon (UTC) every day... but it is subject to the same things that "mess up" any hope of simple calculations elsewhere. ("Equation of time", etc.)

Yes- our method is based on looking at how long ago solar noon was at Greenwich when it occurs at the latitude of interest.

But you cannot take it as a given that the solar noon at Greenwich occurred at 12:00:00 on a particular date.

Solar noon at Greenwich 4 July 22 was at 12:04:14. You have to look up when Greenwich had it's solar noon. I used SunEarthTools.com. I suspect there are more "do it yourself" "answers" available.

My solar noon was at 12:14:30, if I used the average of my two determinations... 10 minutes-time, 16 seconds after it happened at Greenwich.

From just a little thought, and a lot of arithmetic, you should be able to work out the following, which I simply fetched from a page at astrolabesailing.com

The ground position of the sun moves westward at the following rate:

    360º in each day
    15º every hour
    1º every four minutes (of time)
    15 minutes (of arc) each minute (of time)
    1 minute (of arc every 4 seconds (of time)

As I said, my noon had been 10 minutes-time, 16 seconds-time after Greenwich time.

10 minutes-time 16 seconds-time= 10.27 minutes-time
15 minutes-arc * 10.27 minutes-arc/minute-time= 154.05 minutes-arc
                    =2 degrees, 34.05 minutes-arc

... so my longitude "should" have been the one called "2 deg, 34.05 minutes-arc (west)".

(When I made the mistake of assuming solar noon at Greenwich had occurred at 12:00:00, the calculated longitude was 3 deg, 37.5 minutes (west).)

From my smartphone's GPS, I learned that the "right answer", the answer my efforts should deliver, was 2 degrees, 40.80 seconds.

At the latitude involved (about 50) that disagrees with my value by only about 5 miles! Not bad for someone with no training on a first try! (Thank you, nhc.noaa.gov/gccalc.shtml for cooridnates to distances, and directionsmag.com for degrees and minutes to degrees and a decimal fraction.

(On my "Greenwich solar noon was 12:00:00" attempt, the GPS longitude disagreed with my value by about 40 miles. I said "A little disappointing, I admit... but I cling to the thought that there might just be an error in my arithmetic somewhere!" I clung to that thought... and worried about "where might I have made an error?" The "where" struck me in in the middle of an evensong where the men and boys were singing beautifully. (First Service, Thomas Weelkes))

And I had fun with this, and look forward to trying again. And trying to master the "tricks" that will allow me to do this without the help of the internet for the UTC time. I hope this introduction to it all will enable and encourage ***you*** to have a go, and that you, too, find it fun if you do.

I'd like to stress....

Yes! I used the internet to find out when solar noon was, in UTC, at Greenwich. I believe, but have yet to confirm, that there were simple, inexpensive alternatives "in the olden days".

I also used the internet for knowing the UTC time as I watched the sun's progress in the sky. There were alternatives "in the olden days"... but they weren't inexpensive.

But my other uses of the internet were only to get "good" values to check my answers against.

My most serious "cheat" was using the rather lovely sextant that I was able to buy. I could never have made a copy of that.

But I could have measured the sun's altitude by a method that I could have managed. (The stick-shadow method.) All I would have needed for that would be a good ruler and a way to make something level... a story for another time, or for solving for yourself. Doing it yourself is much more fun than reading how someone else did it.

Details, details...

Since writing this page, another "nuisance" that we need to factor in has come to my attention...

If you are "cheating" by using "GPS time" for when your local solar noon occured, you need to know that GPS time and UTC time are NOT the same!

This matters, because the data in the Nautical Almanac... or in our "hobbyist" world, fetched from the internet... about times in Greenwich may well be given as UTC times. In July 2022, GPS and UTC differ by about 18 seconds. And yes, 18 seconds matters here! Yikes. (I'll say more about all of that, too, when I take this page to a "second edition". Sorry I can't do it now.)

I learned about this when a kind friend who knows about these things sent me somehting I've edited slightly, but was quite like...

Did you know that GPS does not actually use UTC? GPS time
"started" on 1/1/1980, at the time that UTC time was THEN. But
GPS time has since diverged from UTC time by 18 seconds. This
is because GPS time does not add leap seconds. So to set your
clocks from a raw GPS signal you need to know the current leap
second adjustment. I'm not sure, but I think the GPS system
transmits the current leap second adjustment
in it's data channel.

Leap seconds is also an interesting topic when discussing NTP.
There are different ways an NTP implementation will adjust
a leap second. Some just add or remove a second at midnight
but this can introduce horrible unexpected bugs. Other
implementations speed up or slow down hours before to slowly
get there. What's interesting is when we're approaching a leap
second event NTP servers on the internet can and do diverge,
potentially introducing more strange bugs.

A Google search tells me...

"NTP is short for Network Time Protocol. And that NTP an internet protocol used to synchronize with computer clock time sources in a network. It belongs to and is one of the oldest parts of the TCP/IP suite. The term NTP applies to both the protocol and the client-server programs that run on computers."

I assume it was THIS "NTP" that my friend was referring to.

There ARE situations and systems where disagreements over "the time" of "only" a second DO matter! Even if... especially if!... they "only" occur for short periods at infrequent itervals.

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