P42B-01 INVITED
The Origin of Three Double Planets in the Inner Solar System
The fission hypothesis is a valid generic formation mechanism for all major planets and moons in the solar system, neatly solving the angular momentum and accretion paradoxes of the standard model. This makes fission the most probable mechanism for the Moon's origin, as independent evidence had earlier concluded. (See chapter 14 of "Dark Matter, Missing Planets and New Comets", T. Van Flandern, North Atlantic Books, Berkeley, 2nd ed. 1999.) Its main strength is that no helper hypotheses are needed to meet all important constraints. R.S. Harrington's backwards integration of the Moon showed that the original obliquity of Earth at the time when the Moon fissioned in Earth's equatorial plane was 8 degrees, similar to the Sun's present axial tilt. J.A. O'Keefe showed that the original lunar mass was about 10 percent of Earth's, making the term "binary planet" apropos. Most of what we know about Venus and Mercury supports the hypothesis of an origin very similar to Earth-Moon. But Mercury's relatively higher mass resulted in escape from Venus about 500 million years after formation. (See "A dynamical investigation of the conjecture that Mercury is an escaped satellite of Venus", T.C. Van Flandern and R.S. Harrington, Icarus 28:435-440, 1976.) Most of what we now know about Mars supports a similar origin for Mars and a now-exploded parent planet. (See "The challenge of the exploded planet hypothesis", Int'l J.AstroBio. 6:185-197, 2007). That scenario is now encapsulated in an attractive 4-minute video showing the connection of that explosion to the K/T boundary event on Earth. http://metaresearch.org/solarsystem/originalss.asp
P42B-02 INVITED
Finite Element Modeling of Tidal Deformation of the Entire Earth
Tidal deformation of the Earth is normally calcaluted using the analytical solution with some simplified assumptions, such as the Earth is a perfect sphere of continuum media. This paper proposes an alternative way, in which the Earth crust is discontinuous along its boundaries, to calcualte the tidal deformation using a finite element method. An in-house finite element code is firstly introduced in brief and then extended here to calcualte the tidal deformation. The tidal deformation of the Earth due to the Moon was calculated for an geophysical Earth-model with the non-continuum outlayer layer and comapared with the continuum case. The preliminary results indicate that the discontinuity could have different effects on the tidal deformation in the local zone around the fault, but almost no effects on both the locations far from the fault and the global deformation amplitude of the Earth. The localised deformation amplitude seems to depend much on the relative orentiation between the fault strike direction and the loading direction (i.e. the location of the Moon) and the physical property of the fault. The rotation due the unsymmetric geometric shape of the earth has also been investigated.
P42B-03
Solid Planetary Tides and Differential Motion of Deep Layers in the Earth-Moon Binary Planet System
Orientations of faults and lineaments of the Earth's crust, as well as fractal statistics in spatial distribution of faults and lineaments were studied. It is shown that regularities in the orientation of faults as well as the fractal distribution of their lengths and sizes is the result of hundreds of million years of gravitational interaction between Earth and Moon. On the basis of this study, it was assumed that the Earth's crust, lithosphere, and, probably, deeper layers, when acted on by the Sun and Moon tidal deformations can be treated as comminuted scale- invariant hierarchical substances. An important implication of this rheology is that the Earth's material can be treated as a loose granular substance. Mathematical modeling of loose substance tidal deformations demonstrated that the radial planetary tides are being transformed into lateral motion of planetary layers. The rate of lateral motion of planetary layers depends on the magnitude of the rate of radial tidal deformations, k(r). Mathematical modeling of tidal deformations for different distributions k(r) showed that the radial variation of this coefficient produces differential motion of deep planetary layers resulting in: a) westward drift of the surface layers with a rate of up to 4cm/year, and b) internal frictional heating of deep layers which can raise temperatures at given depths to the melting point of the material. This melting can be one of the factors influencing and amplifying the magnetic field in a planet. Experimental modeling (Revuzhenko, 2006) of tidal deformations in loose granular substance is in good agreement with the results of mathematical modeling. Thus, Earth, as an element of a binary planet system possesses such peculiarities in its structure and evolution which a single planet could not have.
P42B-04
The Early Lunar Orbit and Principal Moments of Inertia
If taken at face value, the principal lunar moments of inertia suggest that the Moon froze in a past tidal and rotational state during a high eccentricity orbit [1]. At this time the Moon may have been in either synchronous rotation or in a 3:2 resonance of spin and mean motion. We have performed further investigations of the plausibility of past high eccentricity lunar orbits on the basis of orbital evolution, the dynamics of entry into any past 3:2 resonance, and tidal dissipation. We have found that the requisite permanent (B-A)/C (where A, B, and C are the principal moments of inertia) for a 3:2 resonance can be achieved in a magma ocean if a density anomaly is present shortly after lunar accretion. In a high eccentricity orbit, tidal dissipation will affect the Moon's ability to develop lithospheric strength. The Moon is presently able to support degree-two loads, while Io, which is approximately the same size as the Moon and strongly heated by tidal dissipation, probably cannot [2]. Therefore, somewhere between the present lunar radioactive heating rate (~1012 W), and Io's observed dissipation (~1014 W), the Moon may develop lithospheric strength. We use 1014 W as a loose upper bound on where freeze-in may begin and find that in a 3:2 resonance tidal dissipation [3] can drop below 1014 W at a = 25 RE and e = 0.17, and the present moments of inertia can be approximately reproduced for lunar values of QM = 475 (where a is the lunar semimajor axis, RE is the Earth radius, and Q is the specific dissipation function). This value of QM is somewhat large, but the biggest problem with a 3:2 resonance that lasts until 25 RE is how to achieve the current low eccentricity synchronous orbit. The required damping cannot be easily achieved unless the Moon is knocked out of a 3:2 resonance by an impactor that would produce a crater approximately 800 km in diameter. In sum, there is no single strong constraint that completely rules out a 3:2 resonance, but it would require a rather specific set of circumstances. For the high-eccentricity (e = 0.49) synchronous solution to the moments of inertia, we have found that dissipation at e = 0.49 is several orders higher than 1014 W for QM less than 500 and k2 = 1.5 (where k2 is the second degree tidal Love number), and therefore freeze-in during such a scenario is almost completely ruled out (in agreement with Wisdom, unpublished notes). During the magma ocean phase of lunar history it is also possible that the lunar gravity field was too homogeneous to provide a sufficient permanent (B-A)/C for even synchronous rotation. In this case the Moon would achieve an asymptotic spin rate slightly faster than synchronous [4]. If during this very early time in lunar evolution, the Moon froze in even a small amount of its shape, it would be entirely rotational, and provide an alternative explanation for the high relative amount of rotational potential in the present degree-two gravity field. References: [1] Garrick-Bethell, I., Wisdom, J., Zuber, M. T. (2006) Science 313, 652-655. [2] Anderson, J. D. et al. (2001) J. of Geophys. Res. 106, 32963-32970. [3] Wisdom, J. (2007), in press. [4] Peale, S. J.; Gold, T. (1965) Nature 206, 1240.