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One of the most frequent questions I find on Quora is something like “If it is noon at the Greenwich meridian, what time will it be at 61° E (show your work)?” or “If it is Friday at 9pm on 36 degree East, then what will be the time at 46 degree West?”. There must be about 4 or 5 a week. Why are there so many such questions? The answer is completely meaningless, since there's no mention of a latitude, nor of a time of year. And who could be interested in the answer?

My guess is that this is a frequently posed school homework assignment, as the first question suggests. This would mean that the teachers are doing their pupils a disservice by suggesting that there is an answer at all. Still, I hope this page will make it easier to answer these questions.

If it is noon at the Greenwich meridian, what time will it be at 61° E?

  1. What time is it at the origin?

    In this example, all we know is the latitudes at start at end. We need to convert the start time to UTC. What? Isn't the time at the Greenwich meridian GMT, the same thing as UTC?

    No. GMT and UTC are not the same, though they're very close, but they can be up to a second apart. For this discussion, that's not important, so we can assume that GMT is the same as UTC.

    More important, though, when people say “the time at”, they're invariably talking about local time.

    See below for a discussion of the meaning of “local time”.

    In the UK, that's GMT in the winter, but BST (UTC+1) in the summer. And further south, Spain has CET (UTC+1) in the winter and CEST (UTC+2) in the summer. So if the local time is 12:00, the UTC time is 10:00 UTC, 11:00 UTC or 12:00 UTC.

  2. What time is it at the destination?

    We need to do something similar at the destination. We only have the latitude, 61° E, so we need to go north and south and see what time zones it covers.

    • At 68° N we're in the Russia 2 time zone (UTC+3). Here the time will be 13:00, 14:00 or 15:00.
    • At 63° N we're in the Russia 3 time zone (UTC+4). Here the time will be 14:00, 15:00 or 16:00.
    • At 50° N we're in Kazakhstan, where the time zone is UTC+6. Here the local time will be 16:00, 17:00 or 18:00.
    • At 40° N we're in Turkmenistan, where the time zone is UTC+5. Here the local time will be 15:00, 16:00 or 17:00.
    • At 36° N we're in Iran, where the time zone is UTC+3:30. Iran observes daylight saving time, so here the time will be 13:30, 14:30, 15:30 or 16:30, depending on the time of year.
    • At 29.83° N we're in Afghanistan, where the time zone is UTC+4:30. Here the time will be 14:30, 15:30 or 16:30.
    • Only a kilometre or two away at 29.81° N we're in Pakistan, where the time zone is UTC+5. Here the local time will be 15:00, 16:00 or 17:00.

    So there we have it. The answer is “13:00, 13:30, 14:00, 14:30, 15:00, 15:30, 16:00, 16:30, 17:00 or 18:00”.

What did the teacher want?

I'm left with the impression that the teacher (presumably in the large plural) is ignorant of time zones. He may want to go like this:

  1. Time at Greenwich is 12 pm.
  2. The world has 24 hours spread round 360°. Therefore an hour is 360÷24 or 15°.
  3. To get the time difference, divide the longitude difference by 15. 61÷15 is 4.067 or 4 hours, 4 minutes.
  4. Therefore the time at 61° E is 4:04 pm.

The problem with this answer is that it is wrong. In almost every case above, the local time at 61° is the same as the time at 60°, where the answer would have been “4 pm”, one of the ten possibilities. If any teachers are reading this, please do your pupils a service and stop asking such unanswerable questions and expecting answers that are wrong.

If it is Friday at 9pm on 36 degree East, then what will be the time at 46 degree West?

In this case, the destination longitude mainly transverses ocean. This time I choose 46° W, 65° N, since it's probably round Greenland. And sure enough, about the only countries at this longitude are Greenland and Brazil. As far as I know, neither of them have Daylight Saving Time, and they both have a time zone offset of UTC-3:00. So the time there would be 15:00 or 16:00, still on Friday.

What time is it at the origin?

In the example I chose, the time is known at “36 degree East”. Where's that? It's somewhere in Eastern Europe or Eastern Africa. I start by using Google Maps to find where 36° E, 45° N is. In this case it's just south of Crimea, which is interesting in itself. Do you recognize the Russian annexation of Crimea? Then the time zone is EST, UTC+3:00, all year round. Otherwise the time zone is EET, UTC+2:00 in the winter or UTC+3:00 in the winter.

But this is just a guess. Let's look at the time zone map. Further north it could be in Russia. It's just far enough east not to touch the Norwegian time zone (UTC+1/UTC+2).

And further south? Also nothing of great interest, only UTC+2 or UTC+3. So the time is either 19:00 or 18:00 UTC.

The time at the destination

In this case, the destination longitude mainly transverses ocean. This time I choose 46° W, 65° N, since it's probably round Greenland. And sure enough, about the only countries at this longitude are Greenland and Brazil. As far as I know, neither of them have Daylight Saving Time, and they both have a time zone offset of UTC-3:00. So the time there would be 15:00 or 16:00.

Is this the answer that the teacher wants? Probably not. He probably wants you to take the difference in longitude, divide by 15 and treat it as a time offset, giving a time of 15:32 (or, as he might prefer it, 3:32 pm). Problem: that's just plain wrong. Everywhere in the world is in some time zone or another, and the smallest increments (in only a couple of zones) are 15 minutes.

Local time

Everybody knows what local time is, right? I thought so, anyway. In fact, there's no accurate definition. For me, it's obvious that it's the time used at a particular location, in other words as defined by your local time zone.

But it seems that some people (India again?) use in a different sense. I commented on an answer to the question “What is the longitude of a place whose local time is 11:00am when it is 9:30am at longitude 15 degrees?. He answered:

the standard Time is calculated by time zone only but local time has 4 min difference at every longitudes. And longitudes play very important roll to calculate the time. there are 24 time zones in the world and according to that question I think this the way to calculate. and only because of longitudes time can be calculated. Greenwich Prime Meridian is the base line to divide the world into eastern hemisphere and western hemisphere and this is the longitude only.

That's not correct, of course. But clearly it's being taught. It seems that some people (India again?) use the term “local time” to mean mean solar time, also known as local mean time, an obsolete method used to even out the effects of eccentricities in the earth's orbit before the advent of time zones. There's no basis for this assumption: local time is the time that you will see on clocks in any specific location, and it's defined by the time zone.

This definition does serve one purpose, though: if I'm correct, it explains these nonsensical questions, at least when “local time” is specified.

It's probably worth summarizing the different forms of time:

Solar time       Time based on the position of the sun in the sky
Equation of time       Description of the time shifts caused by the eccentricity of the earth's orbit
Mean solar time       Solar time corrected for the eccentricity of earth's orbit
Local mean time       Solar time at a particular location
Standard time       Time defined by a time zone
Local time       The time used at a specific location, usually standard time
Coordinated Universal Time (UTC)       Time standard for time zones
Greenwich Mean Time (GMT)       UK Civil time in winter, close to UTC
Time zone       A geographical area with the same standard time and legislation

For the purposes of time calculations, only time zone, UTC and local time are of interest.

What's missing here is the definition of local time. Search for definition local time and I get:

There are two conflicting versions here: one is the official time based on the time zone, the other is the mean solar time. Looking at the references, the ones I would rely on would be https://www.collinsdictionary.com/ and https://en.oxforddictionaries.com/. The reference at http://www.dictionary.com/ dates itself: it's nearly 200 years out of date, before time zones came into existence.

Or so I thought. It seems that all three of these links actually define the term both ways, though the https://en.oxforddictionaries.com/ quote refers to solar time rather than mean solar time.

As usual, the Oxford English Dictionary clarifies:

local time n. (originally) time at a particular place reckoned from the instant of transit of the mean sun over the meridian at that place (which defines noon); (now more usually, and sometimes as a postmodifier) time as reckoned in the time zone containing the observer or the specified place;

So the meaning changed with the advent of time zones, as one would expect. The quotations show the last use of the old meaning in 1865:

1865 Catholic World Apr. 127/1 Railway time is gradually beating local time.

And the first clear reference to the new meaning is:

1968 H. Franklin Crash i. 9 Our estimated time of arrival at Cairo is 17.45 local time, 15.45 G.M.T.

Unfortunately things aren't that clear-cut. https://keydifferences.com/difference-between-local-time-and-standard-time.html goes into great detail explaining (implicitly) that local time is mean solar time. Interestingly, the author's name looks Indian.

In any case, the term “local time” has been made ambiguous enough that it's best not to use it without clarification.


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