text: A set of coupled differential equations modeling more than one of these systems is the Clohessy-Wiltshire equations.
full_question: A set of coupled differential equations modeling more than one of these systems is the Clohessy-Wiltshire equations. Jacob Thorne gave a list of power series solutions to a two point boundary value problem modeling these systems. Solving that problem is equivalent to to solving Lambert's problem and finding one of these systems. The method pioneered by Josiah Gibbs to determine one of these systems merely requires three coplanar position vectors. By using station keeping, one can make one of these systems that resembles a Lissajous curve. The energy conservation equation of these systems is the vis-viva equation. Switching from one of these systems to another can be achieved with a Hohmann transfer, and the point of greatest distance of one of these systems is the apoapsis. For 10 points, name these paths of astronomical objects, which may be periodic.
first_sentence: A set of coupled differential equations modeling more than one of these systems is the Clohessy-Wiltshire equations.
raw_answer: astronomical orbits [or trajectories; or flight paths; or intercepts until "station keeping" is read]