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From: Dr J R Stockton on 21 Jan 2010 15:52
In sci.astro message <z9-dnapK7sqJ48jWnZ2dnUVZ7rGdnZ2d(a)bt.com>, Tue, 19
Jan 2010 09:40:35, Mike Dworetsky <platinum198(a)pants.btinternet.com>
posted:
>
>
>Equation of Time describes the varying difference between apparent noon
>and mean noon (or clock noon) caused by the Earth's axial inclination
>and orbital eccentricity. The Sun transits earlier or later than noon
>as read by a clock. The length of the day is unaffected.

Only approximately.

The length of the solar day must be a constant plus the derivative of
the equation of time, giving an overall variation of a fraction of a
minute.

--
(c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <URL:http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.
From: Mike Dworetsky on 22 Jan 2010 02:25
Dr J R Stockton wrote:
> In sci.astro message <z9-dnapK7sqJ48jWnZ2dnUVZ7rGdnZ2d(a)bt.com>, Tue,
> 19 Jan 2010 09:40:35, Mike Dworetsky
> <platinum198(a)pants.btinternet.com> posted:
>>
>>
>> Equation of Time describes the varying difference between apparent
>> noon and mean noon (or clock noon) caused by the Earth's axial
>> inclination and orbital eccentricity. The Sun transits earlier or
>> later than noon as read by a clock. The length of the day is
>> unaffected.
>
> Only approximately.
>
> The length of the solar day must be a constant plus the derivative of
> the equation of time, giving an overall variation of a fraction of a
> minute.

True, but usually this is no more than a few seconds a day, and I didn't
want to get into a long explanation. Also, there are other factors that can
change the length such as atmospheric conditions, and they cannot be
predicted by calculation in advance. There are good reasons why the
Almanacs only give sunrise and sunset to one-minute precision.

(I was at the Observatory on La Palma some years ago when one of the
astronomers was actually doing a comparison of Almanac Office predictions of
local sunset vs observations, and the variations were of order +/- 30 sec.
Definition used was upper limb on the horizon.)

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

From: Dr J R Stockton on 23 Jan 2010 17:17
In sci.astro message <ROSdnQRcudR9z8TWnZ2dnUVZ8oudnZ2d(a)bt.com>, Fri, 22
Jan 2010 07:25:17, Mike Dworetsky <platinum198(a)pants.btinternet.com>
posted:
>Dr J R Stockton wrote:
>> In sci.astro message <z9-dnapK7sqJ48jWnZ2dnUVZ7rGdnZ2d(a)bt.com>, Tue,
>> 19 Jan 2010 09:40:35, Mike Dworetsky
>> <platinum198(a)pants.btinternet.com> posted:
>>>
>>>
>>> Equation of Time describes the varying difference between apparent
>>> noon and mean noon (or clock noon) caused by the Earth's axial
>>> inclination and orbital eccentricity. The Sun transits earlier or
>>> later than noon as read by a clock. The length of the day is
>>> unaffected.
>>
>> Only approximately.
>>
>> The length of the solar day must be a constant plus the derivative of
>> the equation of time, giving an overall variation of a fraction of a
>> minute.
>
>True, but usually this is no more than a few seconds a day, and I
>didn't want to get into a long explanation. Also, there are other
>factors that can change the length such as atmospheric conditions, and
>they cannot be predicted by calculation in advance. There are good
>reasons why the Almanacs only give sunrise and sunset to one-minute
>precision.


I assume the atmospheric effects are almost entirely on the deflection
of the sunlight, and only slightly on the actual rotation of the Earth.

It should be possible to predict local noon much more exactly.

No chance recently of making any such observations here.

--
(c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05.
Web <URL:http://www.merlyn.demon.co.uk/> - w. FAQish topics, links, acronyms
PAS EXE etc : <URL:http://www.merlyn.demon.co.uk/programs/> - see 00index.htm
Dates - miscdate.htm estrdate.htm js-dates.htm pas-time.htm critdate.htm etc.
From: tadchem on 23 Jan 2010 19:14
On Jan 19, 4:40 am, "Mike Dworetsky"
<platinum...(a)pants.btinternet.com> wrote:
> tadchem wrote:
> > On Jan 14, 8:16 am, The 1919 Eclipse <eclipse-1...(a)sbcglobal.net>
> > wrote:
> >> What's the equation for the length of day, as a function of latitude
> >> and calendar date?
>
> You would have to look up the variation of solar declination over the course
> of a year.  Any formula for this would involve orbital eccentricity and
> axial tilt, and take leap years into account.
>
> Given the declination (N or S of the celestial equator) from an almanac or
> formula, the hour angle H of rising or setting at some latitude (N +; S -)
> is
>
> cos H = -tan (lat) tan (dec)
>
> If cos H comes out with absolute value greater than unity, the sun is
> circumpolar and either doesn't rise or doesn't set, depending on
> circumstances.  Convert answer from radians to hours and multiply by two for
> total length of a day.
>
> The above does not take into account horizontal refraction.  This typically
> lengthens the day by 8 minutes or more.  Does the OP need this refinement?
>
>
>
> > The length of day also varies with the date:
> >http://en.wikipedia.org/wiki/Equation_of_time
>
> > Tom Davidson
> > Richmond, VA
>
> Equation of Time describes the varying difference between apparent noon and
> mean noon (or clock noon) caused by the Earth's axial inclination and
> orbital eccentricity.  The Sun transits earlier or later than noon as read
> by a clock.  The length of the day is unaffected.
>

It is *precisely* the difference between "apparent noon" and "mean
noon" (as defined by the "mean solar day" of exactly 24 hours) that
defines the variation in the length of day, as the OP literally
requested. This is where the analemma fits into the calculations.

It is possible that the OP was *actually* concerned with the variation
in the length of the daylight hours, as this would be very dependent
on the latitude and the orientation of the earth's axis relative to
the sun, its exact degree of tilt, the eccentricity of earth's orbit,
the longitude of perihelion, and other orbital elements. The humidity
of the air towards the sun at sunrise and sunset would also affect the
refractive index of the air, and thus the refraction of the apparent
sun.

This latter effect alone has been shown to influence the times of
sunset and sunrise by several minutes.

Tom Davidson
Richmond, VA
From: Steve Willner on 29 Jan 2010 16:33
In article <3MWJdTL7V3WLFwwc(a)invalid.uk.co.demon.merlyn.invalid>,
Dr J R Stockton <reply1003(a)merlyn.demon.co.uk> writes:
>I assume the atmospheric effects are almost entirely on the deflection
>of the sunlight, and only slightly on the actual rotation of the Earth.

That's correct. The orientation of the Earth in space is defined by
"UT1"(and to a much smaller extent by polar motion and precession/
nutation). UT1 is _predicted_ to some amazing accuracy (I think it's
microseconds but could be wrong.) and known after the fact much
better than that. Details are no doubt given at

http://www.iers.org

but I don't find them in an instant and don't have patience to search
the site more diligently. Measurements come from VLBI monitoring of
a network of quasars.

As Mike mentioned, visible sunrise and sunset times are sensitive to
local atmospheric conditions (mainly density, which depends on
pressure and humidity) along the line of sight to the horizon.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swillner(a)cfa.harvard.edu
Cambridge, MA 02138 USA
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