[vhffm]

It is a shortcoming of the integrator (Euler), not in the calculation of the force (as you suspected).

See [1]. Especially slides 11 and 12 may be of interest.

[1] http://www.astro.sunysb.edu/phy277/lect30.pdf

As a sidenote, there are better integration schemes, but all of them will have some error because we discretize the system.

[junku901]

Wow that is really interesting. Thanks. By the way, if there are always some error in all systems, then what kind of systems are used by NASA or other space exploration institutes?

[vhffm]

I'm not in the business of space mission engineering, so I don't know details. Sorry.

But in general, you can control the error and make a trade-off between computing time and accuracy. You would select a timescale over which you want the error to be below some value, and then only consider the simulation valid until then.