Earth's orbital history revised

Ferenc Varadi ¹ and Bruce Runnegar ^1,2; astrobiology.ucla.edu

¹Institute of Geophysics and Planetary Physics

²Department of Earth and Space Sciences

University of California, Los Angeles, CA 90095-1567

WE carried out several long-term simulations of planetary orbits in which the equations of motions were directly integrated using an accurate multi-step scheme. The physical models, with increasing complexity, include corrections to the Newtonian attraction of point masses: General Relativity, analytically averaged models of the lunar orbit and the J₂ term of the solar gravity field. The model used by Quinn et al. (1991) turned out to be inadequate upon comparison with the case in which the Moon was resolved as a separate body (R5). We found by empirical means a much better model which is used in R7, R8 and R9.

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Comparisons

Chaotic transitions

Summary of simulations
Simulation designation	General Relativity	Modeling of Moon	Solar J2	Step size (days)	Length (Ma)	Still running?
R1	no	barycenter	no	0.25	100	no
R2	yes	barycenter	no	0.3125	212	no
R3	yes	barycenter	no	0.25	89	no
R4	yes	AM	no	0.3125	123	no
R5	yes	resolved	no	0.03125	23	yes
R6	yes	AM+ICA	no	0.3125	6	no
R7	yes	MAM	no	0.3125	180	yes
R8	yes	MAM+MICA	no	0.3125	10	no
R9	yes	MAM	yes	0.3125	150	yes
AM: The avereged Earth-Moon model of Quinn et al. (1991) MAM: Modifief average Earth-Moon model. ICA: Initial conditions adjusted for consistency (Quinn et al., 1991) MICA: Modified adjustment of initial conditions.