Quick Question

What's the equation for the length of day, as a function of latitude
and calendar date?

The 1919 Eclipse wrote:
What's the equation for the length of day, as a function of latitude
and calendar date?

You can calculate the local times of sunrise and sunset
for a given date, then take the difference between the two.

Keep in mind that there are different definitions for
sunrise and sunset for different disciplines.

Take a look at this:

http://williams.best.vwh.net/sunrise..._algorithm.htm

On 1/14/10 7:16 AM, The 1919 Eclipse wrote:

What's the equation for the length of day, as a function of latitude
and calendar date?

There's an app for that.
http://emeraldsequoia.com/h/

On Jan 14, 8:16*am, The 1919 Eclipse
wrote:
What's the equation for the length of day, as a function of latitude
and calendar date?

The length of day also varies with the date:
http://en.wikipedia.org/wiki/Equation_of_time

Tom Davidson
Richmond, VA

tadchem wrote:
On Jan 14, 8:16 am, The 1919 Eclipse
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.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

In sci.astro message , Tue, 19
Jan 2010 09:40:35, Mike Dworetsky
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. 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.

Dr J R Stockton wrote:
In sci.astro message , Tue,
19 Jan 2010 09:40:35, Mike Dworetsky
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)

In sci.astro message , Fri, 22
Jan 2010 07:25:17, Mike Dworetsky
posted:
Dr J R Stockton wrote:
In sci.astro message , Tue,
19 Jan 2010 09:40:35, Mike Dworetsky
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. 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.

On Jan 19, 4:40*am, "Mike Dworetsky"
wrote:
tadchem wrote:
On Jan 14, 8:16 am, The 1919 Eclipse
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