Many gravitational triple systems are in a hierarchical configuration, where two objects orbit each other in a relatively tight inner binary while the third object is on a much wider orbit. If the third object is sufficiently distant, an analytic, perturbative approach can be used to calculate the evolution of the system. In the secular approximation , the two orbits torque each other and exchange angular momentum, but not energy. Therefore the orbits can change shape and orientation (on timescales much longer than their orbital periods), but not semimajor axes. For example, for highly inclined triple systems, the Kozai-Lidov mechanism can produce large-amplitude oscillations of the eccentricities and inclinations.
TA researcher Smadar Naoz has shown that the secular hierarchical triple body problem is qualitatively different from that considered previously. Specifically, she showed that the inner orbit can flip from prograde to retrograde and back, and can also reach extremely high eccentricities. This is potentially of great significance for the explanation of the high eccentricities and inclinations observed in extra-solar planets.