The Space of Keplerian Orbits and a Family of Its Quotient Spaces

The distance functions on the set of Keplerian orbits play an important role in solving problems searching for parent bodies meteoroid streams. A special kind function is distances quotient spaces orbits. Three metrics this type were developed earlier. These allow disregarding longitude ascending node or argument pericenter, both. Here, we introduce one more space, where two are considered to be identical if they differ only their longitudes nodes and arguments pericenters, but have same sum these elements (the pericenter). Function $${{\varrho }_{6}}$$ defined calculate between equivalence classes algorithm calculation from given provided along with a reference corresponding program written C++ programming language. Unfortunately, not full-fledged metric. We proven that it satisfies first axioms metric space; however, does satisfy third axiom: triangle inequality hold, at least case large eccentricities. However, there cases when axiom satisfied: three circular pericenters all coincide. Perhaps, holds elliptic orbits, matter further research.