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From: Androcles on 30 Jan 2010 09:19

"tadchem" <tadchem(a)comcast.net> wrote in message
news:a4a3753b-ec24-4f2c-9297-644021bdea8a(a)o28g2000yqh.googlegroups.com...
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
===================================================
http://www.androcles01.pwp.blueyonder.co.uk/Analemmae/Analemmae.htm





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