发表机构
Santa Fe Institute; The MASTERS program, Santa Fe, New Mexico; Otto-von-Guericke University, Magdeburg, Germany（圣塔菲研究所; MASTERS项目，新墨西哥州圣塔菲; 奥托·冯·格里克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
受开普勒火星轨道研究启发，提出一族同时满足开普勒第二定律和托勒密偏心点假设的轨道，用勒让德多项式表示，类似卵形轨道。
AI 中文摘要
受开普勒长期与火星轨道斗争的启发，我们提出一族轨道，这些轨道满足他的第二定律，即绕中心质量角动量守恒，同时也符合托勒密关于偏心点的信念——即一个角速度恒定的点。对于特定的角动量值，这些轨道可以用勒让德多项式和第二类函数来表示。它们在近日点处是解析的，但在那里仅二次可微。这些轨道类似于开普勒在通往椭圆过程中考虑过的“卵形”（蛋形）或“面形”（脸形）轨道。
英文摘要
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.
