We can do it accurately, to any precision you care to pay for. Since n-body gravitation is a chaotic system, getting more precise predictions requires more prec

We can do it accurately, to any precision you care to pay for. Since n-body gravitation is a chaotic system, getting more precise predictions requires more precise measurements of the current state of the solar system. When it’s not possible to measure things more precisely, we instead run many simulations with small random perturbations in the current state, then classify the simulations to get probabilities.