Hello John,
You're pretty unbelievable too ;) Here (I hope) are some answers
to some of your questions.
1) The obliquity effect is responsible for the figure-eight shape. It's
shaped this way because the obliquity value in the course of one year
has four zeros, i.e., two maximums and two minimums. The eccentricity
effect results in an elliptical shape, it does not "cross-over" on
itself (form a figure-eight) because it has only two zeros, i.e., one
maximum and one minimum.
The following URL illustrates the graphs of the two components over the
course of a year and how they combine to result in the EoT. Remember
that the EoT is the summed difference of the apparent solar day length
and mean solar day length. You can see this directly be tracking the
solar day length at various dates in Graph A and see how they effect
"the total" below in Graph B. For example, when the day length value in
Graph A goes through zero the EoT value in Graph B is at a maximum, this
makes sense, yes?
ftp://ftp.gcstudio.com/pub/sundial/sday_eot.gif
The following URL illustrates the shape of each of the two components as
well as the final result when the two are combined, i.e., the Analemma
itself.
ftp://ftp.gcstudio.com/pub/sundial/analemma.gif
2) The magnitudes of each of these two effects AND the phase in which
they are related to one another determines the final shape. It's
possible where one effect alone can dominate. In the case of Mercury,
eccentricity alone determines the shape. For example, in the solar day
and EoT graph (first URL above) visualize what would occur if you were
to slide the eccentricity values around the fixed obliquity values, this
would change how they combine, right? Something similar is actually
occurring, i.e., the longitude of perihelion and the vernal equinox are
moving relative to one another at almost an arc-min per year! Also, the
magnitudes of obliquity and eccentricity change in time as well but on a
much slower scale.
In summary:
1) Obliquity (if it exists) causes the figure-eight
2) Eccentricity (if it exists - and Kepler seemed to think so) distorts
the shape of the figure eight.
3) The distortion is created when the two are combined. This in turn
depends on each of their relative magnitudes and how they are related to
one another, i.e., their phase to one another.
4) Remember that in the physical sense these two effect are modulating
the apparent right ascension of the Sun, i.e., the EoT = RA(apparent) -
RA(mean). THIS IS SUPER IMPORTANT!!!
5) Consider how the values operate on a daily basis and then realize
that it is their summation that lead to the EoT.
Finally, Mars has a high eccentricity value, third highest in
the solar system (Earth has the third lowest) and a moderate obliquity
value (very close to our own). Eccentricity is dominate, i.e., no
figure-eight.
-Luke
John Carmichael wrote:
>
> You guys are unbelieveable! I've had the martian analemma & EOT question
> for a long time but never asked it for fear that you'd think I was a bit
> crazy. I thought who would even go to the trouble to calculate it since
> there's not a big market for sundials on Mars. I'm delighted that someone
> else has had the same question and even has a picture of one!
>
> Understanding why analemma and EOT curves take the shape that they do is a
> question that we have all struggled with. In fact, is is in the top ten of
> the FAQs that I recieved. I've always thought that if you compare the
> factors which determine the curve for two different planets, then it would
> be a lot easier to see how each factor affects the curve's shape.
>
> Now I know the shape of the EOT curve is determined by the earth's axis
> inclination and the eccentricity of its orbit. Which of these two factors
> cause the two big humps and the two small humps of the curve?
>
> The analemma's shape is simply the EOT values plotted against the solar
> declination. Right? Which of these factors causes the figure eight? Why is
> one lobe bigger than the other? Why is the analemma slightly off center
> vertically? Why doesn't Mars also have a figure eight analemma?
>
> I'm sure there are many people who'd like answers to these questions myself
> included. I have my own theories but I'm not sure that they are correct.
>
> Thanks for dealing with my flood of questions this week.
>
> John Carmichael
> Tucson Arizona
>
> is>Hello,
> >
> > The March '82 Sky&Tel article, "The Analemmas of the Planets", is an
> >interesting piece, I scanned a portion of my copy and posted the image
> >of the Martian Analemma at the following URL.
> >
> >ftp://ftp.gcstudio.com/pub/sundial/marseot.jpg
> >
> > As Robert mentions it has a teardrop shape, this I believe is due to
> >the fact that the eccentricity component currently dominates over the
> >figure-eight shape of the planet's obliquity component. If I'm not
> >mistaken, I believe Earth's Analemma had such a shape (teardrop) some
> >95,000 years ago.
> >
> > BTW, the article also illustrates a "human" Analemmatic Dial with an
> >Analemma implemented for EoT correction, the dial is in Tucson Arizona
> >at the Flandrau Planetarium.
> >
> >Best,
> >
> >Luke
> >
> >
> >R.H. van Gent wrote:
> >>
> >> John Carmichael wrote:
> >>
> >> > I usually don't write two different letters to the list on the same
> day, but
> >> > could'nt resist the following question in view of today's landing on
> >> > Mars.
> >> >
> >> > What would the martian analemma and Equation of Time look like?
> >>
> >> Martian and other non-terrestrial analemmas were discussed in:
> >>
> >> David A. Harvey, "The Analemmas of the Planets", Sky &
> >> Telescope, vol. 63 (1982), 237-239.
> >>
> >> The Martian analemma is rather simple compared with the terrestrial case
> >> and
> >> resembles an asymmetrical droplet.
> >>
> >> Even more boring are the elliptical analemmas of Mercury, Venus and
> >> Jupiter.
> >>
> >> 8-shaped analemmas such as the terrestrial case are found on Saturn,
> >> Uranus,
> >> Neptune and Pluto. That of Saturn barely manages to form an 8 and those of
> >> Uranus and Pluto exhibit large north-south spans of 164 and even 180
> >> degrees.
> >>
> >> These calculations were based on the planetary rotation parameters as
> they were
> >> known at that time and can probably be improved somewhat for the outermost
> >> planets as better determinations have become available.
> >>
> >> Also have a look at:
> >>
> >> http://www.analemma.com/
> >>
> >> ================================================================
> >> * Robert H. van Gent * Tel/Fax: 00-31-30-2720269 *
> >> * Zaagmolenkade 50 * E-mail: [EMAIL PROTECTED] *
> >> * 3515 AE Utrecht * Home page (under construction): *
> >> * The Netherlands * http://www.fys.ruu.nl/~vgent/ *
> >> ================================================================
> >
> >
