I pointed out that planets and asteroids would not use gravitationally selective two body problems or mathematical cheats when traversing the solar system. You don't have a working model that can exist without these cheats.

This is not how planetary systems are modeled Tom. Where are you getting this bullshit? (rhetorical - no need to answer)

For everyone else:

Assuming a simple system (no relativistic effects) for a particular slice (or point) in time

**all** forces on

**all** bodies are calculated using UG, then using a=F/m the change in velocities of

**all** objects are calculated from which their positions at the next time slice are

**all** computed. By definition of it being a single point in time, all calculations for each time slice are .. simultaneous. There are no "gravitationally selective two body problems" or whatever the fuck that is supposed to mean. The time is then incremented and the process is repeated. Just a few simple Newtonian formulas are required - no differential equations and no analytic integrations to solve and no "cheats". The whole process of the simulation

**is** a piecewise numerical integration.

Where relativistic effects come into play, you need to use the appropriate corrections, but even without them you can model our solar system to arbitrary accuracy by making the time slices smaller. Of course the perihelion of Mercury will be out by .0012 degrees after a decade of time slices, but everything else will be just fine. If you want that 0.0012 degrees in Mercury's orbit corrected you'll have to account for the relativistic effects but other than that the simulation is done the same way..