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Planetary Science Institute
Steve Kortenkamp has been involved in studies of the orbital dynamics of small bodies trapped in 1:1 mean motion resonances with planets. These bodies include Trojan-type companions of Neptune, and so-called quasi-satellites.
Of the several hundred known trans-neptunian objects, only one is known to be a Trojan-type companion of Neptune. This object (2001 QR322) is in 1:1 mean-motion resonance with Neptune, trapped in Neptune's leading L4 Lagrange equilibrium region. Population estimates suggest that Neptune may host more Trojan companions than Jupiter, which presently has over 1600 known Trojans. The existence and suspected abundance of Neptune Trojans may provide important clues to Neptune's origin and the primordial orbital evolution of the giant planets. Kortenkamp has been pursuing these clues by studying the effects of primordial radial migration of all four giant planets on a pre-existing population of Neptune Trojans (Kortenkamp et al. 2003). He finds that rapid orbital migration, with a characteristic exponential migration time scale Þ = 106 years, allows about 35% of pre-existing Neptune Trojans to survive to 5Þ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with Þ = 107 years yields only a ˜5% probability of Neptune Trojans surviving to a time of 5Þ. Interestingly, the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune.
Small bodies trapped in 1:1 mean-motion resonances are typically associated with the Lagrangian equilibrium points L4 or L5, like the Trojan companions of Jupiter and Neptune. A more exotic class of 1:1 resonance is occupied by the so-called quasi-satellites. Quasi-satellites are not associated with any of the Lagrange points but instead are trapped in resonance very near a planet. From a heliocentric perspective these objects are on free heliocentric orbits in 1:1 mean-motion resonance with the planet. However, from a planetocentric perspective they appear to be on very distant circumplanetary orbits, thus the name quasi-satellite. Currently there are no known quasi-satellites amongst the roughly 200,000 known minor planets, but the phenomenon is readily observed in computer simulations. Kortenkamp has been using computer simulations to study the combined effects of solar nebula gas drag and gravitational scattering of planetesimals by a protoplanet (Kortenkamp 2003). He has discovered that a large fraction of scattered planetesimals can become temporarily trapped as quasi-satellites of the protoplanet. These quasi-satellites can subsequently have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture as true satellites on highly eccentric prograde or retrograde circumplanetary orbits. This scenario could help explain the numerous small distant irregular satellites known to be orbiting all four giant planets in our solar system.