6 added 3 characters in body edited Feb 8 at 1:25 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vectorlarge ensembles of state vectors? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 large ensembles of state vectors? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 5 added 1 character in body edited Dec 29 '18 at 6:17 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles?Algorithmic methods or techniques to find conjunctions in high N state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. Notice removed Draw attention by uhoh occurred Aug 16 '18 at 7:37 Bounty Ended with LeWavite's answer chosen by uhoh occurred Aug 16 '18 at 7:37 Tweeted twitter.com/StackSpaceExp/status/1028114281710198784 occurred Aug 11 '18 at 3:02 Notice added Draw attention by uhoh occurred Aug 10 '18 at 6:16 Bounty Started worth 100 reputation by uhoh occurred Aug 10 '18 at 6:16 4 added 12 characters in body edited Aug 7 '18 at 2:18 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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. SOCRATES), and I had simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 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 simple Keplerian orbital elements, not necessarily osculating element tables nor first time derivatives of the elements (though an answer about that would be great!) I could propagate those simple one-body Keplerian orbits 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? 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 state vector ensembles? because it specifically asks about methods that operate on Keplerian elements. For example, in the case of simple Keplerian elements, you can immediately rule out some combinations at the beginning if one's periapsis is more than $$d_{conj}$$ larger than the other's apoapsis. 3 added 42 characters in body edited Aug 7 '18 at 2:11 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges 2 added 16 characters in body edited Aug 7 '18 at 2:04 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges 1 asked Aug 7 '18 at 1:59 uhoh 53.3k2424 gold badges208208 silver badges678678 bronze badges