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Re: (meteorobs) algorithm for Solar Coordinates (including sun's true longitude)

Okay, so I'm figuring this out.  Correction of errors appreciated.  (Gary
Kronk are you still reading this list?)

>Just so I understand, the original question was: "At what UT time & date in a
>given year can the Earth be found at a given solar longitude, i.e., a
>particular fixed point relative to the stars in its annual orbit?"
>
>And the flip question, of course: "What is Earth's solar longitude at a
>particular UT time/date in a particular year?"

Yes Lew, as I see it, these are the two basic problems to be solved.  The
second one, given a date compute the solar longitude, is the "easier" of
the two.  It can be done from formulas in Meeus.  Unless I find something
better, I'm planning on solving the first question, given a solar longitude
compute the date, by successive approximation.

>Now how do you convert from the Sun's RA/Dec position at a given time, to our
>solar longitude? Or is the point of Jerry&Judy's post that we first calculate
>the Sun's ecliptical longitude *in our sky*, and then we - what? -
>subtract 180
>degrees to get Earth's ecliptical longitude as seen from the Sun?? Sorry
>about
>the dumb "coordinates" question here! :)

There are no dumb questions!  I've been struggling with these very
questions since this thread started.  Now I think I've got some answers and
I'd like you all to do a sanity check for me.

The first thing to do is to define "Solar Longitude".  From "Meteor
Showers: A Descriptive Catalog", by Gary W. Kronk [Kronk88]:

    (lowercase lambda):  Solar longitude (degrees). This is measured in
degrees and represents the location of an object along the plane of the
solar system as viewed from the sun. It is used to predict when Earth will
encounter a meteor stream. [p. xv-xvi]

and from the same reference:

    Solar Longitude: The longitude of the sun as given in geocentric
coordinates. The evaluation of meteor data strongly relies on this figure
rather than a conventional date. [p. 274]

And from Gary Kronk's web site, specifically the glossary page,
http://medicine.wustldot edu/~kronkg/glossary.html :

    Solar Longitude: This is an angular measurement that specifies the
location of Earth in its orbit around the sun. More precisely, it is the
longitude of the sun as given in geocentric coordinates. The evaluation of
meteor data strongly relies on this figure rather than a conventional date.

Overkill, well maybe, but I feel like I have a precise definition of Solar
Longitude, to restate, Solar Longitude is the angle along the ECLIPTIC from
the vernal equinox to the position of the Earth, which is equal to the
geocentric ecliptic longitude of the sun.  So just using RA won't work
because it's in a different coordinate system, even though RA and Solar
Longitude are both 0 degrees at the same time (and possibly 90, 180, and
270, too).  The reference plane for RA/Dec is the equator.

We can compute Solar Longitude two ways, 1) Compute the RA/Dec of the Sun,
then do a coordinate conversion from one spherical coordinate system to
another, namely ecliptical longitude/latitude, or 2) Compute the ecliptical
longitude directly, from formulas found in Meeus or some other reference.

As it turns out, ecliptical longitude/latitude are usually computed as an
intermediate step to determining the RA/Dec.  In the example given by
Jerry&Judy, the solar longitude is the value S= 199.90987 deg when the
RA=198.38082 deg.  Close, but this would be a difference of about a day and
a half.

The sun's position in geocentric ecliptical coordinates is equal to the
angle along the orbit.  No plus (or minus) 180 degrees needed.  According
to Meeus, VSOP87 computes heliocentric longitudes (L) which, according to
him, do require S=L+180 deg.

Enough for today.  Each time I read a section in Astronomical Algorithms I
learn a little more.  Right now my head is spinning a little.

Gregg Lobdell
gml@halcyon.com
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