Question:Relationshi between clock time & longitude/lati

F

Ferg

New member
Calling Dr. Bob

I noticed that the days are now getting longer by ~1 minute/day, and wondered why clocks and longitude/latitude both use minutes and seconds. I’m @ 38 degrees north, and we’re slightly longer than one minute I’m guessing that at the equator, it’s exactly one minute

Am I correct in thinking they’re related?
 
Ferg, google "Greenwich Mean Time" to start your research.

I remember reading about one of the early explorers and how he discovered that keeping a clock set to GMT was a way to assist him to pinpoint his position. Greenwich is located on the prime meridian.

Definitely a correlation between them, I'm just not the best one to explain it.

Calling Dr. Bob,,
 
Yes they are related. No, can't remember all the details, but it takes a very accurite "watch" and a bunch of brain busting math to work out where you are on the planet if you are using that method. :roll: Those early navigators were astronomers and mathmaticians, or they were lost or lucky. :( 8) 8)

Harvey
SleepyC :moon
 
Great observations
The return of length of day has more to do with the Earths position and tilt in its orbit around the sun
At the winter Solstice, the sun is 23.5 degrees South of the Equator. So our days in the North are short. As we come toward Spring, everyday sees the Sun appear to move North until Summer Solstice it reaches 23.5 degrees North of the Equator I’m reminded of Sir Francis Chichesters great circumnavigation in 1967 as he wrote of “racing the sun” as he crossed 23degrees South on the passage North.
Our days lengthen as a function of Earth orbit and our tilt more than our latitude
GMT and local time give us our Longitude East and West of Greenwich England
The Earth rotates 360 degrees every 24 hours so each hour is a 15 degrees slice. The development of an accurate timepiece revolutionized navigation as it could be kept on GMT and sextant sights would give lines of position based against a dead reckoning
My home in Nanaimo is therefore GMT plus 8 hours or 123 degrees West.
49 degrees North latitude means short days in winter and long days in summer. In the tropics the length of night and day basically stay the same year round as the tilt of the Earth affects the Equator region the least.
It’s a fascinating subject to learn celestial navigation and I see I’ve forgottten much. Dr Bob can add I trust.
When one plots and fiddles with a sextant and tables at sea it makes a person thankful for GPS!
 
https://www.youtube.com/watch?v=Y00SLWPy0mg

Unless you are using "time" to establish the geographic position of a passing celestial body in the practice of celestial navigation, they have nothing in common. Establishing the geographic position of three celestial body's within a short time using a sextant provides the base for calculating a "fix" of ones position at sea or in the air.
 
On our recent trip to Hawaii I was practicing my celestial navigation quite a bit.
It's a fun hobby for me, but I wouldn't want my life to depend on it as did the sailors of old time. I have such respect for them!

I admit I cheat a bit. Although I use an old-time sextant for measuring the altitude of the sun, once I have my numbers and my GMT time I use modern software (Starpilot) on my phone to do the actual calculations of my position.
Once in awhile I use my calculator just to exercise my brain but normally I don't. They say you can get your position within 1 nm (one minute is one mile)
but I average between 3-5 nm of my actual position.

I guess I am a bit geeky as my wife lays in the sun and I am beside her measuring it! LOL
 
Ferg":1mp88qpb said:
. . .wondered why clocks and longitude/latitude both use minutes and seconds.
Click to expand...

I'm getting old, but here's what I remember:

They are related in that both come to us from on an ancient counting and measuring system using the number 60 as a base.

A minute of longitude is 1/60th of a degree of an arc of a circle, which is 360 degrees around. A second of longitude is 1/60th of a minute of longitude. These are measures of a how far around a circle you've gone, i.e., they represent a portion of an arc of longitude or latitude around the earth. All of the "great circles" around the earth (the lines of longitude plus the equator) are roughly the same length. Therefore, a minute or second of a degree of one of these circles will always be about the same length anywhere on the earth. Parallels of latitude, on the other hand, get shorter and shorter as they approach the poles, and, correspondingly so do the distances measured by a degree, minute, or second on one of these lines. All circles have exactly 360 degrees, but they can be any length.

Hours, minutes, and seconds on a clock, of course, are measures of time, not distance. But people long ago saw that if they had an accurate clock set to solar time at a fixed known position (the prime meridian at Greenwich, England), and if they could take an accurate reading of the sun's position in their current location, then they would be able to calculate their current east-west position. For instance, if your clock says it's 1:00 pm in Greenwich, but the sun is at it's highest point (i.e. noon) where you are, then you know you are 15 degrees (1/24th of 360 degrees) to the west of Greenwich. This relationship, one hour of solar time = 15 degrees of arc, remains the same as you move over the globe, but the distance represented in miles (or kilometers, etc,) that this one hour of time and 15 degrees of arc measures will change as you move away from the equator.

There are many interesting books (and a pretty good movie) about the mad race to develop a reliable clock. See, e.g., "Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time."
 
I can't believe the doctor hasn't responded to his beeping pager yet. Or maybe the answering service hasn't reached him yet. (I'm showing my age now! I wonder if doctors still use those. My Dad was a surgeon so I remember them well. Lol)
 
You are going to have to use that very accurate stop watch, and there are going to be certain atmospheric variations as to the very precise increase length of day: Fortunately the US Navy has done off of this for us:here, you have to put in your state and city. It will not be exactly one minute. But half of the year it is increasing and half of the year it is decreasing--365.25 days a year..!

Great information above. More modern measurements find that the earth is not a precise sphere, and the initial "measurements" were slightly off...but getting a 3 position fix within 3 to 4 miles is good on anyone's boat! Certainly better than I could usually get on a sailboat...then all of that math! Each year has an almanac, and there are a number of different tables to help you do the trig. All of these are available on the internet and an $11 Casio calculator will do the math if you are patient. Site reduction tables 249 (air) are also on the internet.

The advent of calculators which both did the math and contained all of the tables, as well as nautical almanac were a huge advance. Now a phone app does it all. Of course ... GPS will give you a very precise time signal..but if you have GPS--then you don't need celestial..Some of our modern watches are extremely precise--better than the best chronometers of 70 years ago. I even have a solar powered watch which determines the length of each day of the year at a given latitude...

The latitude is measured in degrees minutes and seconds. A minute is a nautical mile, works there, and pretty close on the equator (which is zero degrees) But as you go North or South of the equator the distance of a degree decreases with the distance form the equator, or higher latitude:

1° longitude = cosine (latitude) * length of degree (miles) at equator.

Each degree of latitude is approximately 69 miles (111 kilometers) apart.
At the equator, the distance is 68.703 miles (110.567 kilometers).
At the Tropic of Cancer and Tropic of Capricorn (23.5° north and south), the distance is 68.94 miles (110.948 kilometers).
At each of the poles, the distance is 69.407 miles (111.699 kilometers).

A degree of longitude is widest at the equator with a distance of 69.172 miles (111.321 kilometers).
The distance gradually shrinks to zero as they meet at the poles.
At 40° north or south*, the distance between a degree of longitude is 53 miles (85 kilometers).

A book I lugged around for many years is: Bowditch, "The American Practical Navigator".

For those who might be interested, it is a really great book about many parts of navigation and seamanship:

Since it is a U S Government publication: the 2002 most recent edition is here. it is on the internet, or you can order your own edition for about $25 from Barnes and Noble. The first edition was published in 1802! Nathaniel Bowditch was a genius.

It also clarifies the various projections of charts and maps, as well as explaining the chart datum: Some of the US charts are still based on NAD 27, most on NAD 83--(North American Datum 1927 convention or North American Datum 1983 convention). Most of our GPS should be set to NAD 83.
 
An interesting fact about celestial navigation is that one can determine one's latitude without a clock (e.g., doing a sun sight at its zenith); but you need accurate time to determine longitude.

That's the source of the such terms as "sailing down your westing"; that is, before accurate chronometers, ships would use dead reckoning, or coastal navigation, to reach their desired latitude, then "sail down latitude" since they could remain on course using noon sights (no time required). They would pick a latitude that contained no dangers until they more or less bumped into their destination since they could not know, except very roughly, where they were east-west on that latitude.

Accurate chronometers allowed sights of heavenly bodies other than noon sights, and also the determination of longitude.
 
Also one has to mention in the Northern Hemisphere the angle of Polaris (North Star from the horizon) is approximately equal to latitude.

Even though the chronometer was developed in the 1767, the shortage and very high cost allowed continuation of another method: Lunar Distance (navigational)

This method was used (practically about 1755) to calculate Longitude prior to an accurate and affordable chronometer. Measuring the difference from the local noon time, from the calculated prime (Greenwich)meridian time (today called Universal coordinated Time; UTC,) would give longitude. Lunar distance: The angular distance from a celestial body (Sun, Planet or star) to the moon. Even with those early tables, the math was time consuming, and one had to bring forward by dead reckoning the noon to position to a moon site/star position. (on some occasions the noon sight and moon site can be close together.) Dead reckoning is compromised by currents, the amount of leeway, and accuracy of speed measurement (chip log), and compass course steered.

Lunar distance was improved with better tables in 1767 and published in the Nautical Almanac (British) from that time on. The calculations with the more modern tables were reduced from 4 hours to about 30 minutes (and in some cases to as little as 10 minutes.) This method was used up until about 1905. It is still taught in some navigation courses. It was useful until very accurate and relatively inexpensive chronometers were available..

In 1905 the first radio time signals were transmitted world wide--and ships could now check their chronometer against the Prime Time (UTC), instead of checking with telegraphic time or "ball drops" from the Naval Observatory before starting a voyage.

I know of several other C Brats who have gone during their sailing life times, from celestial and RDF/depth finder, navigation to Loran A, Loran C, Omega, (1973) Sat Nav (1983) and true GPS (1989).
 
Besides the lunar distance method, I believe one could also determine longitude using the moons of Jupiter. Both methods were pretty awkward, time consuming, and not as accurate as when done with a chronometer (1-2 nm error vs 15 nm or more). Of course both lunar and Jupiter methods also depended on those 2 celestial bodies being above the horizon.

The beauty of a noon sun sight is that one needs nothing but a sextant to figure latitude. The calculation is trivial (one subtracts the sextant reading from 90°). Lunar and Jupiter based methods require someone else, somewhere else, and somewhen else to have produced the tables that these non-sun sights require.
 
I am a huge fan of modern navigational equipment. GPS is ridiculously accurate, dependable, and easy to use. We carp and complain about relatively minute discrepancies in charts, and out-of-place or missing navigational aids, and hiccups with electronics, but I mean, really. . .

People used to set off in wooden boats - with nothing but sails and oars to propel them - into waters where more than the occasional channel marker was missing from charts. Whole continents were missing. If they had charts.

I'm going to go re-read the account of Shackelton's 1916 crossing from Antarctica's Elephant Island 800 miles to South Georgia Island in a boat the size of a C-dory.
 
The moons of Jupiter was never used as a practical navigation method, because of the magnitude of magnification required for a telescopic sextant or octant. It is possible that some well stabilized modern ship could use that method...but highly unlikely...

The Lunar method could be used any night the moon is visible, with select stars. Also using the Sun during the day, if the moon is visible. Taking a number of sights, and plotting them, will give higher accuracy, but never to the extent of a chronometer noon sight. The Lunar method was used for extensive survey work of the world's coasts for early charts. (I think I used some of those era charts at one time! Some of the charts I first used had depth soundings which followed the tracks of sailing ships as they tacked and worked their way up the Western coasts of the Americas.) Also the Lunar method established the need for the Sextant, whereas before the octant was the navigational instrument of choice.
 
Uh, I thought that was a one arm alarm clock. For navigation he used lunars, which don't require a chronometer.

In his trips story he sort of gives a running account of his alarm clock. I always wondered how he found his way and if you read real carefully, he tells you.

Boris
 
I wrote this perl script years ago, showing how daylight time changes in a sine curve. I found the equations somewhere on the internet:

#!/usr/bin/perl
# -----------------------------------------------------------------------
# Description: Calculates the hours of daylight, given a latitude and date.
# Syntax: daylight [yyyymmdd] [latitude]
# where -
# yyyymmdd is the date, which may be entered in any of the shortened
# forms dd, mmdd, or yymmdd. Any parts that are omitted use the
# current localtime as defaults.
# latitude is either the angle in degrees North of the equator, or
# the name of a limited list of cities (see $lat below). If omitted,
# the default is the latitude of Appleton, Wisconsin, 44.25 degrees.
# Uses an equation derived from David Toomey.
# -----------------------------------------------------------------------
# Changelog:
# 20001226 Smitty created.
# -----------------------------------------------------------------------
use POSIX;
use Math::Trig;

$lat{"Appleton"}=44.25;
$lat{"Atlanta"}=33.65;
$lat{"Chicago"}=41.78;
$lat{"Honolulu"}=21.33;
$lat{"Madison"}=43.13;
$lat{"Miami"}=25.8;
$lat{"San Antonio"}=29.53;

($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst)=localtime(time);
if($datein=shift) {
if ($datein=~/^\d{1,2}$/) { # dd
($yyyy,$mm,$dd)=(1900+$year,$mon+1,$datein);
} elsif($datein=~/^(\d{1,2})(\d{2})$/) { # mmdd
($yyyy,$mm,$dd)=(1900+$year,$1,$2);
} elsif($datein=~/^(\d{2,4})(\d{2})(\d{2})$/) { # [yy]yymmdd
($yyyy,$mm,$dd)=($1,$2,$3);
$yyyy+=2000 if($yyyy<100);
} else {
die("ERROR: invalid date format = $datein\n");
}
} else {
($yyyy,$mm,$dd)=(1900+$year,$mon+1,$mday);
}
$numpat='^\d+\.{0,1}\d*$';
$latitude="Appleton" unless($latitude=shift); # Default.
$latitude=$lat{$latitude} unless($latitude=~/$numpat/);
die("ERROR: Bad latitude\n") unless($latitude=~/$numpat/);
($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst)=localtime(
mktime(0, 0, 0, $dd, $mm-1, $yyyy-1900));

# Following equation derived from that of David Toomey.
$p = asin(.39795*cos(.2163108 + 2*atan(.9671396*tan(.00860*($yday-185)))));
$daylight = 24 - (24/pi)*acos(
(sin(0.8333*pi/180) + sin($latitude*pi/180)*sin($p)) /
(cos($latitude*pi/180)*cos($p)));

$hours=int($daylight);
$minutes=int(($daylight-$hours)*60.0);
$seconds=sprintf("%2d",($daylight-$hours)*3600-$minutes*60);
$mm='0'.$mm if(length($mm)<2);
$dd='0'.$dd if(length($dd)<2);
print("yyyymmdd=$yyyy$mm$dd latitude=$latitude daylight=".
"$hours hours, $minutes minutes, $seconds seconds.\n");
 
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