A recent paper in Nature "Planetary science: Reckless orbiting in the Solar System" (Morais & Namouni, 2017) presents the following series of four co-orbital states:
While I understand the development of the quasi-satellite and trisectrix states, I am unable to inuit the development of the tadpole and horseshoe co-orbital states.
From explanation provided in the article:
The tadpole and horseshoe shapes arise because the planet's gravitational attraction alters the body's orbital path — the body goes through a cycle of catching up with the planet and falling behind, seeming to change direction from the perspective of the planet.
How, when approaching the planet, does the body "fall behind" instead of continuing to accelerate toward the planet?
The only means that comes to mind is if the planet orbits faster than the body, but then I imagine it would
- No longer be considered co-orbital (because it would have a different orbital period), and
- Would eventually be overtaken by the planet.
How, then, do these first two co-orbital states work?