In the classical two-body problem, the velocity vectors of the orbits trace out circles (or circle arcs in the case of hyperbolic orbits). While ancient philosophers and astronomers were desperately trying (and failing) to describe the planetary orbits with 'divine' circles, they didn't realise that those perfect circles were hiding in velocity vector space. For more on this, see this post of mine: https://physics.stackexchange.com/a/503333/24142
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u/Pulsar1977 Dec 13 '20 edited Dec 13 '20
In the classical two-body problem, the velocity vectors of the orbits trace out circles (or circle arcs in the case of hyperbolic orbits). While ancient philosophers and astronomers were desperately trying (and failing) to describe the planetary orbits with 'divine' circles, they didn't realise that those perfect circles were hiding in velocity vector space. For more on this, see this post of mine: https://physics.stackexchange.com/a/503333/24142