Modelling the Eccentricities of the Terrestrial Planets

Statistics – Computation

Scientific paper

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Scientific paper

Numerical models of late-stage planet formation have successfully reproduced a number of the observed characteristics of the terrestrial planets. However, understanding the origin of their orbital eccentricities remains a problem. Earth and Venus currently have very low orbital eccentricities: roughly 0.03 when averaged over long timescales. In general, numerical simulations of planetary accretion produce Earth analogues with significantly larger eccentricities, typically about 0.1. This discrepancy may be due to shortcomings in the models, or because the eccentricities of Earth and Venus lie near one extreme of a wide distribution of possible values for large terrestrial planets. An analysis of previous results suggests that at least part of the problem lies with the initial conditions used in the simulations. In particular, there is a relation between the initial number of planetary embryos N in a simulation and the time-averaged eccentricities e of the planets that form. Other things being equal, small N leads to large e, and vice versa. To date, computational constraints have limited simulations to have N < 200. It is possible that simulations with larger values of N will generate terrestrial planets with orbits more like those observed in the Solar System. Here I will present results of new numerical simulations of planetary accretion with values of N in the range 50 to 1000. I will discuss whether the observed correlation between N and e continues for large values of N, and whether the use of such initial conditions can explain the observed eccentricities of Earth and Venus.
This work was supported by the NASA Origins of Solar Systems program.

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