For 10 points, name these trajectories of planets, which for Earth takes 365 days to complete.
Josiah Gibbs names a method for finding these systems that only requires knowing three coplanar position vectors. The velocities of bodies involved in these systems described by this word can be calculated using the vis-viva equation. The most efficient process to move between these utilizes two instantaneous velocity changes and follows a half-elliptical path; that (*) transfer one is named for Hohmann. When that type of system described by this word occurs with respect to a satellite, its most extreme points are known as the periapsis and the apoapsis. The theory of epicycles was developed to explain "retrograde" examples of these paths. For 10 points, name these trajectories of planets, which for Earth takes 365 days to complete.
Josiah Gibbs names a method for finding these systems that only requires knowing three coplanar position vectors.
orbits [accept word forms like orbital or orbital motion)