NavList:

Time steps means it is an iterative method, you can't calculate all the positions and velocities for an arbitrary time without calculating all the intervening time steps from now until then or from a known start point until then.

How long the steps are compared to the total elapsed time considered, the relative masses and the obital periods of the other involved bodies is significant. With 350 bodies the computational load it probably pretty high and requires periodic error checks, yearly, every decade, every century, every millenia, will depend on the body.

For the navigationally important bodies they can all be treated as 2 body problems for periods of decades before errors become important, except maybe Mercury.

Re: The Three-body Problem
From: Dave Walden
Date: 2021 Oct 27, 04:37 -0700

The JPL DE430 ephemeris used for the Nautical Almanac doesn't approximate a 3 body problem.  It includes the interactions of over 350 bodies.  All the planets plus largests asteroids.  It calculates interactions based on physics and then time steps.  New versions of the DE series include all new data from ground based position obervations, spacecraft tracking data, and laser and radar ranging data.  It reflects planet shape effects, relativistic effects and others.  See for example:

https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf