My email to Paul Schlyter and his reply, posted with permission:
On http://www.stjarnhimlen.se/comp/tutorial.html you note that
Mercury's ascending node is given as:
N = 48.3313_deg + 3.24587E-5_deg * d
According to https://ssd.jpl.nasa.gov/txt/p_elem_t1.txt Mercury's
ascending node precesses in the negative direction.
As Where to get rate of change for calculating ephemeris from JPL Horizons notes, NASA's
value matches the negative of your value almost exactly.
Are you using a different sign convention here, or is this an error?
It's neither - instead I use a somewhat different reference system.
I use the "epoch of the day" instead of the fixed epoch of, say,
J2000.0. So add the rate of precession to the negative rate of change
you found at NASA's site, and you should get my rate of change.
Since I use the "epoch of the day", the positions I get are suitable
to compute e.g. the rise, transit, and set times for the planets. Of
course they are also good for computing the positions of several
planets relative to one another. But if you need the positions to plot
on a star map drawn for some fixed epoch, you need to apply a
correction for precession to these positions.
Yes, it can be confusing to distinguish those different astronomical
coordinate systems from one another. But that's a consequence of
living on the planet Earth which orbits the Sun, rotates, and wobbles.