Re: How to calculate point of intersection of ecliptic with horizon?

Hello, Trencavel! Your question prompted me to ask one of
the friendly astronomy-software experts who inhabit the Net!
His name is Elwood C Downey, and he's the author of the much
used 'xephem' charting program for UNIX workstations. He has
given permission for you to peruse the codebase of 'xephem'
for your solution. You can obtain xephem's C source at:
    http://iraf.noao.edu/~ecdowney/xephem.html

Here are the details from Elwood's response...

From: EC Downey
Subject: Re: Algorithm for ecliptic azimuth?

>How to calculate point of intersection of ecliptic with horizon?

I am overqualified in the sense that all I know is how to do it very
accurately, and am not sure off hand what simplifying assumptions might
be applied. In any case, I can't imagine it ever reducing to a "formula"
in the high-school math sense!

The only thing I can think to recommend is to string together some of the
functions from xephem, and even here it is a general conversion from
ecliptic to horizon coordinates, not one specifically answering just the
question being asked regards to the point of intersection.

But with that said, the line of reasoning to convert would proceed as
follows (all angles are in radians):

    given a month/day/year, compute the time as a modified julian date:

	cal_mjd (mn, dy, yr, &mjd);

    given an ecliptic position, lat and long, and time, mjd, convert to
    to equatorial, ra and dec:

	ecl_eq (mjd, lat, lng, &ra, &dec);

    fill in a Now struct (defined in circum.h) with location and mjd, then
    use it get local sideral time, lst, to convert ra to ha:

	now_lst (Now *np, &lst);
	ha = hrrad(lst) - ra;

    convert ha and dec to alt and az:

	hadec_aa (lat, ha, dec, &alt, &az);

All functions are part of xephem. I have not listed the functions these
call in turn but they are all there too, of course. Hope this is of some
help. Kind regards,

Elwood