system
Given the following post, respond as if you're commenting on Reddit:
human
Why doesn't the n-body problem make the rotation curves of disc galaxies unpredictable?

The difference between the observed and expected rotation curves of disc galaxies is explained by the presence of dark matter.

But how do we even have a predicted rotation curve for disc galaxies?

Doesn't the n-body problem mean the radial velocities of the stars in a galaxy are completely chaotic and unpredictable?
gpt
The n-body problem doesn't mean that trajectories are completely ~~chaotic and~~ unpredictable. It just means that there is no known analytical solution for 3 or more bodies. We can still do numerical simulation to an arbitrary degree of precision -- limited only by our computational resources.

The general technique is to calculate the two-body solution on every possible pair of bodies in the simulation, and sum the effects on each body for a given time-step. The number of calculations is proportional to *n^2*, so it becomes time-consuming very quickly. Various methods are used to approximate the result with less complexity.