NavList:

The ultimate, absolute source of Solar System ephemeris data is the work of NASA/JPL's numerical integration team. They do it right: model the physical forces (almost entirely gravitation) from one second to the next, calculating the net acceleration of each body then using that to update the velocity and then the position. Repeat...

The output of those integrations are used by all ephemeris authorities including the modern "Nautical Almanac". They were also formerly used to generate the analytic models, which we find in computation manuals like the slim "Astronomical Formulae for Calculators" and the later (fatter!) "Astronomical Algorthms" by Jean Meeus, which were the only real option for home computation through the end of the twentieth century. 

Today we can access the output of the JPL integrations directly. You can download their model data directly --some hard work in the details. The easiest way to get the data is via the JPL Horizons web app. Below (attached) is output for the planet Mars every six hours for the year 2026. Between tabulated values, linear interpolation is sufficient. You decide how closely you tabulate the values so that linear interpolation satisfies your accuracy requirements. If this sounds like you would end up with large data files, don't worry... there are many ways to compress the data. And don't worry, the days when mere megabytes mattered are far behind us...

You can use the data you generate from JPL Horizons to check your implementation of an analytical model (Meeus etc.), or you can leap into the 21st century and simply use the data and linear interpolation as your primary ephemeris engine. That's how all my apps work, though there are certainly "use cases" for analytical models. Reminder for my web apps: try my USNO Clone and my Nautical Almanac Data. They and my GPS Anti Spoof apps all use this sort of simple implementation of the exceedingly accurate, gold-standard JPL numerical integrations of the Solar System.

You could also ask an A.I. how to generate ephemeris/almanac data for the Sun, Moon, and planets. They will all tell you to apply analytical models (in other words "Meeus" formulae) perhaps produced by some standard Python module. That's because the A.I. language models consume the internet and then generate a consensus from that. In fields with little new development, old code and old solutions dominate. It's still the 1990s for ChatGPT! ...at least for ephemeris calculations.

Beyond the available JPL data, you will also need some standard computations and datasets for things like delta-T, Sidereal Time (that's LHA Aries for us), coordinate transformations, and so on. The true orientation of the Earth is the singular element here that cannot be computed from known physical laws. We cannot see inside the Earth, and its absolute orientation in longitude (and less so in latitude) must be observed and to a limited extent it can be extrapolated for some few years into the future. Ultimately, this is the limit on almanac data. We can predict where the planets will be on the celestial sphere (relative to each other) for centuries into the future, but we cannot predict exactly what time it will be when each of those planets will cross some specific local observer's meridian.

And what about stars? This is a harder nut to crack. Celestial navigation's requirements for stellar coordinates are somewhat unique in the modern world. We need coordinates "of date" with precession, nutation, aberration, and proper motion all included to produce positions that correspond to real observations of the sky. For the most part, these are calculated at each date from standard Hipparcos coordinates from the 57+1 "official" navigation stars (widely available, even on Wikipedia). I have not found a comprehensive source --with good "provenance"-- for stellar positions "of date"... You can calculate test cases, but that's not necessarily reliable.

You mentioned putting your lines of position and a fix on a "Mercator grid". It's not really "Mercator". The only grid required is "locally conformal" or 'longitude space scaled by cos(latitude) at the center of the grid. For the fix itself, be sure to review the least squares fix calculation in the back of the Nautical Almanac (included since the late 1980s! :) ) since that provides the true fix for any number of LOPs.

Hope that helps. ...helps anyone interested in creating their own apps for celestial navigation. I'm happy to discuss any of the details, so far as I am able.

Frank Reed