Capability Development for Modeling the Thermal Evolution of Growing Planetary Satellites, 15-R9701

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Principal Investigators
Robin Canup
Amy C. Barr

Inclusive Dates:  04/01/07 – Current

Background - Studying the similarities and differences amongst the various planetary objects in our solar system provides us with a better understanding of the past evolution and future state of our own planet and of planets in extra-solar systems as well. In particular, planetary satellites are high-priority targets for NASA's near-term exploration and funding plans because planetary satellite systems provide some of the best observable constraints on planet formation processes and timescales. SwRI is developing a new model of the thermal evolution of planetary moons during their formation through collisional accumulation, or "accretion," that links currently observable properties of planetary satellites to SwRI's existing models for satellite formation. 

Approach - The heating and cooling processes occurring during satellite formation were modeled to describe the thermal state of a growing planetary satellite as a function of depth and time. Information about the flux of impactors and their sizes based on results of previous work on satellite accretion are used to calculate the amount of heat delivered to the satellite. Heat transfer in the solid interior of the satellite occurs by conduction, whereas close to its surface, heat is transported due to overturning of near-surface material by successive impacts and radiation into the protoplanetary nebula. The new model can predict sample initial thermal profiles for Earth's moon and Jupiter's satellite Callisto. Results of satellite accretion models are used as initial conditions in the study of the long-term, post-formation evolution of satellites.

Accomplishments - The numerical backbone of the thermal model was developed by constructing a finite difference scheme to model thermal diffusion in a growing planetary body including spatially dependent material properties. A series of equations was also developed that relates the amount of energy deposited in a growing satellite due to an impact of a satellitesimal with a given size and impact velocity. These equations allow the ad hoc "h" parameter used in all prior models of satellite accretion to be eliminated from the thermal evolution models. The fraction of impactor kinetic energy deposited as heat in the satellite's interior calculated using SwRI's analytical treatment obeys a power law as a function of impact velocity, roughly consistent with results from more complex and realistic simulations of impacts into planetary surfaces. Thus the amount of energy deposited in a growing planetary body is significantly smaller than assumed in existing studies. It is expected that when the values of h and the energy deposition functions are incorporated into the SwRI thermal model, it will be revealed that the satellites start out colder than previously thought, and more consistent with their observed properties.

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