Year: 2026
Type: preprint
Abstract: Motivated by Kepler's long battle with the orbit of Mars, we present a family of orbits that satisfy his second law, conserving angular momentum around a central mass, and also fulfill Ptolemy's belief in an equant --- a point around which the angular speed is constant. For specific values of the angular momentum, these orbits can be written in terms of Legendre polynomials and functions of the second kind. They are analytic except at perihelion where they are twice differentiable. They resemble the "ovoid" (egg-shaped) or "metopoid" (face-shaped) orbits that Kepler considered on his way to the ellipse.
Source: arXiv (Cornell University)
Institutions: Santa Fe Institute, Otto-von-Guericke-Universität Magdeburg
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220730973