# Algorithmic methods or techniques to find conjunctions in high N state vector ensembles?

Suppose I wanted to answer the question Will Starman/Roadster pass particularly close to any asteroids in the next few years? or try to predict satellite conjunctions around Earth (e.g. Celestrak's SOCRATES), and I had ephemerides, TLEs, or interpolatable tables of state vectors.

I could propagate those in small time steps, calculate all $$N$$ positions and all $$N(N-1)/2$$ distances and search for any below a distance $$d_{conj}$$, but that might not be the most efficient way to do this.

Question: What are the algorithmic methods or techniques to do this kind of search more efficiently? Assume the propagators return a six-vector (position and velocity). I need an explanation or authoritative reference, not just a name-drop.

This question is distinct from Algorithmic methods or techniques to find conjunctions in high N Keplerian element ensembles? because it specifically asks about methods that operate on State vectors (either tabulated or propagated on demand) which may include n-body effects (e.g. the Sun moves, Jupiter does its thing, etc.)

• I have decided to re-ask this question based on this advice. I expect it to fly this time, rather than "conjunct" (collide) with its sibling question. – uhoh Dec 29 '18 at 6:21