Dan,
The coincidence is simply the intersection of the ecliptic and
equatorial planes. At the Vernal Equinox the two suns share a common
point which is also their origin, i.e., both solar longitude and RA =
zero. The mean sun is in essence defined by the dynamical mean sun
(moving along the ecliptic), the sun of the mean anomaly, for time
keeping purposes it runs along the equator. I don't know anything about
Newcomb, I do know that Flamsteed's contribution to the equation of
center allowed the EoT to be calculated with higher precession.
I did compile and run your program last night. I compared its results
by overlaying it onto the analemma I calculated using my solar
calculator. I must say the results looked to be in good agreement with
one another. I didn't do any real numerical comparison but visually they
look very close. I'll send you the image.
Luke
Daniel Lee Wenger wrote:
>
> Luke
>
> Your argument is very clear as usual, but it is the statement that by
> definition the mean sun
> and the dynamical mean sun coincide at the Vernal Equinox that is the key
> to the question.
>
> Where have you seen this definition of the mean sun? I have looked at all I
> can find on the web about
> Newcomb who I believe introduced the concept of the mean sun and I cannot
> find any clear statement
> that does define the mean sun. Certainly your statement does define a mean
> sun. Certainly the notion of
> an EoT that averages to zero over the year defines a mean sun. It is not
> clear to me that they are one and the same.
>
> Dan
>
> >Daniel Lee Wenger wrote:
> >>
> >> Luke
> >>
> >> Your statement that eccentricity will always be synchonous to
> >> the passage of perihelion needs, I believe, amplification. There
> >> is no a priori reason that I know of that the mean sun and the
> >> actual sun should have the same right ascension at perihelion.
> >
> >Dan,
> >
> > Ok, first let's consider three suns at work here. The first is the
> >apparent sun traveling nonuniformly along the ecliptic. The second is
> >the dynamical mean sun traveling uniformly along the ecliptic, the mean
> >anomaly sun if you like. And the third is the mean sun traveling
> >uniformly along the equator. By definition the dynamical mean sun (mean
> >anomaly sun) and the mean sun coincide at the Vernal Equinox (First
> >Point of Aries) and since both travel at uniform rates along great
> >circles (one along the ecliptic and the other along the equator) the
> >longitude of the dynamical mean sun is equal to the right ascension of
> >the mean sun. At perihelion the longitude of the dynamical mean sun has
> >to be, by definition, the same as the longitude of the apparent sun but
> >we just got done saying that the longitude of the dynamical mean sun is
> >equal to the RA of the mean sun! Therefore, since the two suns along the
> >ecliptic share the same longitude at perihelion they also share the same
> >RA which is equal to the RA of the mean sun.
> >
> > I haven't compiled or run your EoT iteration program (yet) but I hope
> >this answers your questions concerning why it works.
> >
> >
> >Luke
> >
> >
> >Daniel Lee Wenger wrote:
> >>
> >> Luke
> >>
> >> Your statement that eccentricity will always be synchonous to the passage
> >> of perihelion needs, I believe, amplification. There is no a priori
> >>reason that
> >> I know of that the mean sun and the actual sun should have the same right
> >> ascension at
> >> perihelion. The fact is that one may choose the mean sun to have the same
> >> right ascension
> >> as the sun at any time of the year. The resulting EoT of course will be
> >> different and will not
> >> average out to zero during the year. There is a point in the year such
> >> that, if the mean sun
> >> corresponds to the right ascension of the sun, the EoT will average out to
> >> zero. It just happens
> >> that this occurs very near to perihelion. My calculations show that the
> >> position is within a fraction
> >> of a degree of perihelion but is not at perihelion. There may be an
> >> argument that it should be at
> >> perihelion but I do not know that argument. The calculation that I did to
> >> find that point where the
> >> average EoT goes to zero may be round off error dependant.
> >>
> >> Can you find my error in thinking or can we agree.?
> >>
> >> Dan Wenger
> >>
> >> >Hi Bill,
> >> >
> >> > If you mean to ask why the EoT was made to be zero at a given
> >> >set of dates, I think the answer is that it wasn't. One can't
> >> >arbitrarily make the EoT zero points (four of) synchronous to a set of
> >> >dates. The EoT has two components, obliquity (the tilt of our axis
> >> >relative to the plane of our orbit) and eccentricity (the elliptical
> >> >shape of our orbit). Obliquity will always be synchronous to the four
> >> >cardinal positions of the orbit (the equinoxes and solstices),
> >> >eccentricity will always be synchronous to the passage of perihelion.
> >> >The two components however are NOT synchronous to one another, I have
> >> >explained this in some detail in earlier messages. In short, because the
> >> >two components are not synchronous to one another the EoT undergoes
> >> >variation in time. So a set of 17th century values will definitely not
> >> >be the same as those today, i.e., the shape of the analemma will be
> >> >different.
> >> >
> >> >Regards,
> >> >
> >> >Luke Coletti
> >> >
> >> >
> >> >[EMAIL PROTECTED] wrote:
> >> >>
> >> >> 4/3/00
> >> >> Does anyone know why the equation of time is indexed to zero on 9/1,
> >>12/25,
> >> >> etc.? That is to say, when the clock was originally being indexed to
> >> >>the sun
> >> >> (17th century?), why did they pick this set of dates as the zero
> >>point? Why
> >> >> not, for example, set the clock to where the analemma crosses itself,
> >>or to
> >> >> one of the solstices, or equinoxes? I'm sure there is a good reason,
> >>but I
> >> >> haven't been able to think of it. Maybe it has to do with indexing the
> >> >>clock
> >> >> to sidereal time, and not to sun time. Any takers?
> >> >>
> >> >> Bill Gottesman
> >> >> Burlington, VT
> >>
> >> Daniel Lee Wenger
> >> Santa Cruz, CA
> >> [EMAIL PROTECTED]
> >> http://wengersundial.com
> >> http://wengersundial.com/wengerfamily
>
> Daniel Lee Wenger
> Santa Cruz, CA
> [EMAIL PROTECTED]
> http://wengersundial.com
> http://wengersundial.com/wengerfamily
