Re: Analemma

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.

An analemma has 2 components, a vertical displacement due to the angle
between the equator and the ecliptic, and a horizontal displacement due
to the elliptical nature of the earth's orbit that gives rise to the
difference between solar time and mean solar time.

You do need to read up on the topic "Equation of time"....

The horizontal displacement is due to two causes:
1. The elliptical shape of the Earth's orbit, as you correctly point out
2. The inclination of the Earth's axis - an effect you missed.

The first (ellipticity) effect, combined with the vertical
displacement, would only cause an oval figure of the analemma.

The second (inclination) effect, combined with the vertical
displacement, would cause a symmetrical 8-shaped figure of the
analemma.

The two effects combined will cause an unsymmetrical 8-shaped figure
of the analemma - but only if the inclination is sufficiently large
compared to the ellipticity. In the case of e.g. Mars, the
ellipticity of the orbit is much larger - and as a result, the
analemma will become an oval, not an 8-shaped figure.

And if the Earth had been most distant from the Sun near an
equinox rather than near a solstice, the two loops would be of
equal size although somewhat asymmetrical.

Checkout http://www.analemma.com for more info

Did you check out http://www.analemma.com ? To judge from your
response you didn't, or if you did, you glanced over it too
quickly. Pay a more thorough visit to that site!

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