Why do days seem to shorten so abruptly in the autumn?

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Offline syhprum

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I am always impressed how rapidly both the length of the daylight hours and the height of the mid day Sun changes at this time of year.
Is it something to do with sines and cosines ?
« Last Edit: 31/10/2008 23:22:57 by chris »
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Offline Don_1

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Re: Why do days seem to shorten so abruptly in the autumn?
« Reply #1 on: 31/10/2008 15:39:58 »
No it's more to do with signs and Cohens.
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Offline LeeE

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Re: Why do days seem to shorten so abruptly in the autumn?
« Reply #2 on: 31/10/2008 15:53:57 »
Should be easy enough to get the data and plot it to find out:)
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Offline JP

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Re: Why do days seem to shorten so abruptly in the autumn?
« Reply #3 on: 31/10/2008 16:31:15 »
Apparently there is a formula:
http://en.wikipedia.org/wiki/Sunset_equation
and it does involve trigonometric functions, as you'd intuitively expect for a rotating sphere.

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lyner

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Re: Why do days seem to shorten so abruptly in the autumn?
« Reply #4 on: 31/10/2008 19:22:21 »
Spherical Trigonometry is a bit hard but, yes - it does involve trig. Then there is the Equation of Time - Google it.

I was wandering in a park in Geneva, once, and there was a brass plaque with the curve on it up on the wall.

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Offline Pumblechook

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Re: Why do days seem to shorten so abruptly in the autumn?
« Reply #5 on: 31/10/2008 23:05:37 »
Rate of change of sunset is different to that of sunrise for most of the year.

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Offline techmind

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Why do days seem to shorten so abruptly in the autumn?
« Reply #6 on: 01/11/2008 12:08:41 »
Surely to a first approximation, the length of a day in London is roughly:

 length (hours) = 12 - 4.17 x cos(2xPI x day/365)

where "day" is the number of days from the shortest day (21 Dec).

(the factor 4.17 gives a shortest day of 7hr 50mins, the factor would get bigger as you go further north)

I've no doubt this is a bit of a simplification, and will break down as you get too close to the arctic circle...

However it will be apparent that near the spring and autumn equinox the cosine function is passing through zero, where it has its steepest gradient, so the rate-of-change of length-of-day will be maximum.
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lyner

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Why do days seem to shorten so abruptly in the autumn?
« Reply #7 on: 01/11/2008 16:02:43 »
There is an added factor. The Earth's orbit is not a perfect circle. This means that it's angular speed changes. The result is that the Sun is not overhead at the same clock time every day. Sometimes it leads and sometimes it lags. In autumn the effect happens to be that the nights start even earlier than the simple cosine formula would predict.
This time difference is called the equation of time and follows another approximate cos curve.


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Offline Soul Surfer

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Why do days seem to shorten so abruptly in the autumn?
« Reply #8 on: 01/11/2008 16:50:12 »
The position of the sun follows an approximately sinusoidal curve which is how a particle moving evenly round a circle moves when projected in time now consider a square inscribed in a circle ( a bit like the naked scientists in our logo ) the bits at the top and bottom repreesent summer and winter  when the sun does not move very much but in spring and autumn most of the movement of the sun in altitude at noon happens
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Offline Pumblechook

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Why do days seem to shorten so abruptly in the autumn?
« Reply #9 on: 01/11/2008 16:54:46 »
Noon at Greenwich shifts either side of 12:00 GMT by up to 15 minutes I think depending on the time of year. 

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Offline RD

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Why do days seem to shorten so abruptly in the autumn?
« Reply #10 on: 01/11/2008 17:50:53 »
Here is a Waldram sunpath chart for London, horizontal axis is horizon,
outer (largest) arc is midsummer, the inner (smallest) arc is midwinter...

[attachment=5110]

http://www.learn.londonmet.ac.uk/packages/clear/visual/daylight/analysis/hand/sunpath_diagram.html

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Offline techmind

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Why do days seem to shorten so abruptly in the autumn?
« Reply #11 on: 01/11/2008 17:52:26 »
Maybe we've gone on a bit of a tangent with diversions in the equation of time:
 http://en.wikipedia.org/wiki/Equation_of_time

But is the "equation of time" (as in the Wikipedia article) the same for all places on the earth?
"It has been said that the primary function of schools is to impart enough facts to make children stop asking questions. Some, with whom the schools do not succeed, become scientists." - Schmidt-Nielsen "Memoirs of a curious scientist"

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Offline techmind

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Why do days seem to shorten so abruptly in the autumn?
« Reply #12 on: 01/11/2008 17:59:52 »
Here is a Waldram sunpath chart for London, horizontal axis is horizon, outer (largest) arc is midsummer, the inner (smallest) arc is midwinter...

That's an interesting diagram, but I'm not too keen on the non-linear vertical scale. You're making me feeling very sunlight-deprived. Are you trying to sell foreign holidays? [;)]

For this country, I prefer http://www.learn.londonmet.ac.uk/packages/clear/visual/daylight/analysis/hand/images/sunpath_diagram/london_orthographic1.png
"It has been said that the primary function of schools is to impart enough facts to make children stop asking questions. Some, with whom the schools do not succeed, become scientists." - Schmidt-Nielsen "Memoirs of a curious scientist"

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Offline syhprum

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Why do days seem to shorten so abruptly in the autumn?
« Reply #13 on: 01/11/2008 19:10:23 »
I checked my sundial at noon UTC and found it was 18'42" fast.
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blakestyger

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Why do days seem to shorten so abruptly in the autumn?
« Reply #14 on: 01/11/2008 19:51:38 »
No it's more to do with signs and Cohens.

You mean Tesco are responsible?

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lyner

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Why do days seem to shorten so abruptly in the autumn?
« Reply #15 on: 01/11/2008 21:51:54 »

But is the "equation of time" (as in the Wikipedia article) the same for all places on the earth?
I think it must be because there is only one table in nautical Almanacks and the Ephemeris tables apply everywhere in the World.
Yes, it must be because it only refers to the angle of rotation of the Earth relative to the angle in its orbit.

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lyner

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Why do days seem to shorten so abruptly in the autumn?
« Reply #16 on: 02/11/2008 21:03:51 »
I checked my sundial at noon UTC and found it was 18'42" fast.
It could only be correct if you lived on the meridian and when the equation of time correction happens to be zero. Check it every week and plot a graph over the year; it could be interesting.
When they relied on the Sun for time, the trains had to go faster coming back from Cornwall than when going there if they wanted to keep to the timetables.

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Offline Soul Surfer

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Why do days seem to shorten so abruptly in the autumn?
« Reply #17 on: 02/11/2008 22:24:58 »
Some years ago I created a live equation of time graph on my office wall by marking the position of the shadow of a corner of my office window on the adjacent wall with coloured dots you put in a planner chart at a fixed time in the afternoon whenever I could do it.  You need to have a watch that you are confident is showing the correct time within a few seconds to do it neatly.  It created an interesting topic of conversation.  Most people were quite suprised when I told them it proved that the earth's orbit was not a perfect circle and that sundials only showed the correct time four times a year.  The graph is an uneven figure of eight with the winter lobe bigger than the summer lobe because the earth is nearest the sun near midwinter.
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lyner

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Why do days seem to shorten so abruptly in the autumn?
« Reply #18 on: 03/11/2008 18:53:37 »
Lucky to have a south facing office. Clearly a management lackey.

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lyner

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Why do days seem to shorten so abruptly in the autumn?
« Reply #19 on: 03/11/2008 18:54:01 »
Or perhaps the boss.

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Offline Soul Surfer

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Why do days seem to shorten so abruptly in the autumn?
« Reply #20 on: 03/11/2008 19:00:42 »
LOL!!   

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Offline Bored chemist

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Why do days seem to shorten so abruptly in the autumn?
« Reply #21 on: 03/11/2008 19:18:51 »
Couldn't be anything to do with them messing up the clocks could it?
http://en.wikipedia.org/wiki/Daylight_saving_time
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