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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.

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source | link

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.

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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.

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