Re: length of day

Schlyter,I am still laughing at your really stupid attempt to sound
profound in the Equation iof Time matter and unless this participant
wants to actually go chase your particular rainbows you have conjured
up ,he is wasting his time.You are just another mathematician trying to
bluff and bluster your way with material that is exquisite to an
astronomer but senseless to a mathematician who cannot handle the
principle therefore ,to astronomers you just look ridiculous whatever
non astronomers might think.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------


http://groups.google.co.uk/group/sci.astro/browse_frm/thread/80c436407f12fb2f/9aab6af404f6dc31?q=paul+schlyter+oriel36&rnum=1&hl=en#9aab6af404f6dc31


In article <273f8e06.0307231821.2b1f9...@­posting.google.com>,




- Hide quoted text -
- Show quoted text -

Oriel36 <geraldkelle...@xxxxxxxxxxx> wrote:
> pau...@xxxxxxx (Paul Schlyter) wrote in message
<news:bflfhd$a8l$1@xxxxxxxxxxxxxx>...
>> In article <1058914045.1973...@xxxxxxxxxx­ara.net>,
>> George Dishman <geo...@xxxxxxxxxxxxxxxxx> wrote:

>>> The Equation of Time tells you the difference between the effect
>>> of a circular and an elliptical orbit.


>> No it doesn't!


>> The Equation of Time contains two conponents:


>> 1. The component due to the Earth's elliptical orbit:
>> 1 cycle/year


> That is correct,it is the difference betwen axial and elliptical
> rotation via Kepler's second law,it is a property of the Earth's
> rotation and not the Sun's observed motion.


>> 2. The component due to the 23.4 degree tilt of the Earth's axis:
>> 2 cycles/year


> You did not read Maskelyne who correctly points out that Equatorial
> orientation does not affect the apparent motion of the Sun for it is
> neither accelerated or retarded against axial rotation,



Of course the apparent motion itself of the Sun (i.e. the orbital
motion of the Earth) is unaffected by the tilt of the Earth's axis.

But it's not quite that simple: the selected coordinate system
matters too. And if we use the RA/Decl coordinate system, that
system will be dependent on the axial tilt of the Earth.


To clarify matters, let's consider two simplified cases:


1. Earth's orbit is a perfect circle, and the axial tilt is exactly
zero degrees. In this case the Sun will always appear at the
celestial equator, moving uniformly at 360/365.2422 degrees per day.
The equation of time will always be zero.


2. Earth's orbit is a perfect circle, and the axial tilt is exactly
90 degrees. The north and south polar circles will reside at the
equator, and the Tropic of Cancer will reside at the North Pole and
the Tropic of Capricorn at the South Pole. The Sun will move along
RA=0h and RA=12h. Starting at the December solstice, the Sun's RA
will be 0h while it appears to move straight northward at
360/365.2422 degrees/day, while the Equation of Time increases by
4*360/365.2422 minutes per day. This continues until the June
solstice, when something dramatic happens: the Sun's RA suddenly
jumps from 0h to 12h, and the Equation of Time also suddenly jumps
12h (we can say it increases by 12h or decreases by 12h, it doesn't
matter which). Now the Sun's RA will he 12h while it appears to move
straight southward at 360/365.2422 degrees/day, while the Equation of
Time still increases by 4*360/365.2422 minutes per day. At the
December solstice the Sun's RA suddenly changes from 12h to 0h,
and there's another sudden change in the Equation of Time by 12h.


Now compare the two cases: the Sun's apparent motion (= the Earth's
orbital motion) is exactly the same in both cases. But we flipped
the coordinate system (RA/Decl) by 90 degrees, and this caused some
dramatic changes in the way the Equation of Time behaved.


Now, even if the tilt is larger than 0 degrees but less than 90
degrees, there will be some effect on the Equation of Time from
this. Not because the apparent motion of the Sun changes (it
doesn't, as you correctly pointed out), but because our
coordinate system changed.


--
------------------------------­------------------------------­----
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/

.