So, what you say is that the precision of the next position is tied to the interval length between two timestamps? The smaller your interval, the more precise you approach reality. Digitally you can calculate this position to an exact precision, from T=0 to T=1, but with an analogue timelapse you can go to infinitely small intervals, T=0 to T=0.000..01, and since infinitely small is not reachable, you never know precisely where you end up. Makes sense.
This is actually the explanation of the theory of chaos
The theory of chaos and the 3 bodies problem are strictly related items but they are not exactly the same stuff
Put it this way
You have 3 bodies , the only forces involved are the gravitational forces
It is quite easy to write the differential equation, giving the position of the 3 bodies at a certain time T
Despite a common misconception these are deterministic problems
Given the initial configuration, there is one and one only possible configuration at time T
The point is that in most cases these equations can not be solved
As you know there is not a general method to solve differential equations
You can however try to guess the type of solution
Are the solutions closed ( such as a circle) or open ( such as a parabole) functions ?
In the former case the system is stable
After a initial transiction period the 3 bodies sooner or later will alwayes pass through the same points in the space
In the latter case it is not
Henry Poincare , at the beginning of tlast century found the solution using topology methods a branch of math which was his own creature
The solution of the differential equation can be open functions thus the system may not be stable
The link to the theory of chaose and the quoted claim is the following
Even very small differences in the initial parameters can make a "closed" solution turn into an "open" one
This was shock
Scientists gave for granted that a deterministic system is also predictable ( see the famous Laplace claim...)
From the 3 bodies problem the theory of chaos got started
