2010 Annual Research Report

 

  Kortenkamp worked on a number of research projects in 2010 including:

 

Evolution of Quasi-Satellites During Planetary Migration:

 

We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune.  Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance.  Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values.  From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale tau (the e-folding time).  We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites.  We find that the libration frequencies of Trojans are similar to those of quasi-satellites.  This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration.  This exchange is facilitated by secondary resonances that arise whenever there are multiple migrating planets. Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance.  High-resolution simulations of this escape process reveal that ~80% of Jovian quasi-satellites experience one or more close-encounters within Jupiter's Hill radius (R_H) as they are forced out of the quasi-satellite resonance.  As many as ~20% come within R_H/4 and ~2.5% come within R_H/10.  Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet.  Finally, the exchange and escape of Trojans and quasi-satellites continues to as late as 6-9 tau in some simulations.  By this time the dynamical evolution of the planets is strongly dominated by distant gravitational perturbations between the planets rather than the migration force.   This suggests that exchange and escape of Trojans and quasi-satellites may be a contemporary process associated with the present-day near-resonant configuration of some of the giant planets in our solar system. [This work was supported by a previous NSF research grant and a manuscript was recently submitted to Icarus (astro-ph preprint 1101.2211).] 

 

Trapping of Interplanetary Dust Particles in Earth’s Quasi-Satellite Resonance:

 

We used numerical integration to study the orbital evolution of IDPs decaying towards 1 AU under the influence of radiation pressure, Poynting-Roberston light drag, solar wind drag, and perturbations from the planets. The ratio of radiation pressure to solar gravity was b = 0.005, corresponding to IDP diameters of about 100 microns.  In our initial simulation 100% of the IDPs became temporarily trapped in mean-motion resonances just outside Earth's orbit.  Eventually the particles slipped out of these resonances and their orbits continued decaying. Subsequently, 20-30% of the population became trapped in 1:1 co-orbital resonance with Earth. In addition to traditional horseshoe type co-orbitals, IDPs became trapped as so-called quasi-satellites.  Quasi-satellite IDPs always remain relatively near Earth (0.2-0.3 AU, or 20-30 Hill radii, R_H) and undergo two close-encounters with Earth each year.  While resonant perturbations from Earth halt the decay in semi-major axis of quasi-satellite IDPs their eccentricities continue to decrease, forcing the IDPs onto more Earth-like orbits.  This has dramatic consequences for the relative velocity and distance of closest approach between Earth and the IDPs.  After ~10^4 years in the quasi-satellite resonance IDPs are typically less than 10 R_H from Earth and consistently coming within about 3 R_H.  In the late stages of quasi-satellite evolution IDPs can have deep close-encounters with Earth significantly below R_H.  Relative velocities between quasi-satellite IDPs and Earth during these encounters is a few hundred m/s, well below the average values of 2-4 km/s for non-resonant IDPs with similar initial orbits.  This factor alone leads to about a 10-100 fold increase in Earth's gravitational cross-section for quasi-satellite IDPs compared to non-resonant IDPs. Because quasi-satellite resonant trapping is dependent on the planet’s eccentricity, accretion of quasi-satellite IDPs will likely vary with Earth’s eccentricity on ~10^5 year time scales. [This work is supported by current NASA PG&G grant NNX10AJ61G.] 

 

Dynamical Evolution of NEOs Trapped in Earth’s Quasi-Satellite Resonance:

 

We are investigating the quasi-satellite resonance as a mechanism for shepherding near-Earth objects (NEOs) very close to Earth and the other terrestrial planets.  Our objective is to determine whether this mechanism is a significant factor in the dynamical evolution and interaction of terrestrial planets and NEOs.  This work involves several specific tasks.  First, we are performing numerical simulations of the orbital evolution of Earth quasi-satellites using all eight planets.  This modeling will allow us to determine; i) the range of orbital elements to be expected in Earth's current population of stable quasi-satellites and develop observational constraints for where and when to best look for Earth's quasi-satellites, ii) the dependence of a quasi-satellite's time in the resonance on Earth's orbital evolution over 10^8 to 10^9 year time scales, and iii) the role that escaping quasi-satellites play in close-encounters and impacts with Earth.   Second, we are studying the dynamics of quasi-satellites of the other terrestrial planets in order to determine; i) the relative sizes of the quasi-satellite populations of Mercury, Venus, Earth, and Mars and develop observational constraints for where to best observe quasi-satellites of the other terrestrial planets, ii) the possible dynamical transition of Martian Trojans into quasi-satellites, and iii) the likelihood that escaping Martian quasi-satellites could be captured by Mars as satellites similar to Phobos and/or Deimos. [This work is the subject of a proposal submitted to the NSF in November 2010.] 

 

Enhanced Visualization Techniques for Planetary Science and Education:

 

Development of ray-tracing code for production of high-resolution animations for professional and educational purposes.  To date this includes over 100 unique animations demonstrating concepts such as planet formation, planetary dynamics and historical experiments (e.g., Romer's speed-of-light observations).

 

 

 Publications

 

Abstracts

 

Kortenkamp S.J., Resonant trapping and subsequent accretion of interplanetary dust particles through Earth’s quasi-satellite resonance, abstract 17.02, 42^nd DPS (2010).

 

 Lebofsky, L.A.; Anderson, S.W.; Bleamaster, L.F.; Canizo, T.L. Croft, S.K., Crown, D.A., Kortenkamp, S., Pierazzo, E. Professional development workshops for K-8 teachers at the Planetary Science Institute, abstract 1192, 41^st LPSC (2010).