So long, and thanks for all the Fish Planets
The captions in the NASA Ames Research Center video What Will Happen to NASA’s Kepler Spacecraft? read as follows:
NASA’s Kepler space telescope found thousands of planets outside our solar system. With its mission completed, the telescope will remain 94 million miles away in an orbit trailing Earth.
Kepler is traveling in a somewhat larger, slower orbit than Earth. Over time it will trail farther and farther behind.
By 2060, Kepler will fall so far behind that Earth will almost catch up to it.
As Earth approaches, its gravity will tug at the telescope and send Kepler into a closer, faster orbit around the Sun.
In its closer, faster orbit, Kepler will slowly speed ahead of our planet.
In 2117, the telescope will almost catch up to Earth from behind. Earth’s gravity will tug on the telescope as before, but this time pull it back into the wider, slower orbit.
For the foreseeable future the pattern repeats as Kepler is tugged inside and outside Earth’s orbit. The telescope never comes closer than a million miles to Earth — more than four times the distance from Earth to the Moon.
This suggest that roughly every 108 years Kepler's orbit will complete one full cycle, spending the first half, or one synodic period (also here) in a heliocentric orbit higher and slower than Earth's, then another synodic period in a faster, lower one.
Question: RIP Kepler, how shall we call your orbit? Does this cyclic flip-flop process have a name?
animated GIF: