Re: Analemma


"Paul Schlyter" <pausch@xxxxxxx> wrote in message
news:fimhvh$2ege$1@xxxxxxxxxxxxxxxxx
: In article <V7w3j.139804$7_4.62186@xxxxxxxxxxxxxxxxxxxxxxxxx>,
: Androcles <Engineer@xxxxxxxxxxxxxxxxxx> wrote:
: >
: >"Paul Schlyter" <pausch@xxxxxxx> wrote in message
: >news:fils50$24eo$1@xxxxxxxxxxxxxxxxx
: >: In article <5r6bt2F124vsqU1@xxxxxxxxxxxxxxxxxx>,
: >: OG <owen@xxxxxxxxxxxxxxxxxxx> wrote:
: >:
: >: > "Paul Schlyter" <pausch@xxxxxxx> wrote in message
: >: > news:fijiti$1715$1@xxxxxxxxxxxxxxxxx
: >: >> In article
: >: >> <4c3fe0dc-31c3-4dbe-9cac-eae4f05e7e5f@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
: >: >> <perseus@xxxxxxxxxx> wrote:
: >: >>>Is it true that the uppermost loop of the Sun's Analemma is ALWAYS
: >: >>>bigger than the bottom loop, and if so can anyone tell me why?
: >: >>
: >: >> Only from the northern hemisphere is the uppermost loop bigger. As
: >: >> seen from the souther hemisphere, the lowermost loop is bigger.
: >: >>
: >: >> The uppermost loop is where the Sun resides during summer. And
: >: >> the biggest loop is where the Sun resides when the Earth is most
: >: >> distant from the Sun. If the Earth's orbit had been a perfect
: >: >> circle, the two loops would be of equal size, and symmetrical.
: >: >
: >: > Surely it would be a straight up and down.
: >:
: >: Only if the Earth's axis wasn't inclined at all, in which case there
: >: wouldn't even be any "up-and-down" motion but the analemma would
: >: collapse into a point. But as soon as the Earth's axis is inclined,
: >: the analemma will become an 8-shaped figure, not just a straight
: >: up-and-down motion as you believe.
: >
: >
: >Err... the "upper" and "lower" extents correspond to summer and
: >winter solstice and are a result of Earth's tilt.
:
: Of course .... however the Earth's tilt *also* causes the "sideways"
: motion in the analemma, yielding a symmetrical 8-shape of the analemma.
: However, the ellipticity of the Earth's orbit disturbs this symmetry,
: and the result is our real, asymmetric 8-shaped analemma.

If we imagine a tilt of 90 degrees and a circular orbit then
the Arctic and Antarctic circles coincide with the equator,
the analemma is a vertical line from directly overhead to
a point beneath our feet which we cannot observe below the
horizon.
If we imagine a tilt of 0 degrees and a circular orbit then
the arctic and Antarctic circles shrink to points and coincide
with the poles, the analemma is a point, no change in
zenith.
If our clocks kept sidereal time then the analemma would
be an East-West circle, but because we choose to use
solar time with noon defined as the sun at zenith it
would artificially shrink to a point. We are deliberately
not considering the position of the sun in the zodiac
for our analemma. Hence the East-West component is
an artefact, the difference between solar and sidereal time,
the 365-day and 366-day years, and not the tilt at all.

I do agree that the orbital eccentricity is responsible for
the lack of symmetry, but I cannot agree that the E-W
component is a function of tilt as you suggest.


.

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