Mathematics – Probability
Scientific paper
Jul 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010jgre..11507002c&link_type=abstract
Journal of Geophysical Research, Volume 115, Issue E7, CiteID E07002
Mathematics
Probability
1
Planetary Sciences: Solid Surface Planets: Orbital And Rotational Dynamics (1221), Geodesy And Gravity: Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250)
Scientific paper
The observation that the spin period of Venus is extremely close, although not equal, to the p = -5 spin-orbit resonance with the Earth makes it very improbable that such a situation is fortuitous. This leads one to explore hypotheses in which the Earth spin-orbit resonance plays some role in Venus's observed spin rate. This paper proposes one such hypothesis. Venus's core is assumed to be composed of a liquid outer core surrounding a solid inner core, the latter undergoing a 0.31 degree/year differential rotation with the mantle. Due to gravitational coupling, however, core-mantle differential rotation would be impossible, unless isostatic compensation exists with an effectiveness of 99.9998%. Within that assumption, it is proposed that Venus is trapped in the p = -5 spin-orbit resonance with the Earth, but that this resonance concerns the inner core rather than the mantle. Stable resonance requires that the inner core should depart significantly from spherical symmetry, while its material should still be able to sustain the stress differences produced by such asymmetric mass distributions. Compatibility between those two conditions is studied, leading to constraints on the size of the inner core. An appreciable probability of stable resonance is found to be achievable, provided that the average inner core radius is larger than a minimum, which is estimated as 1300 km within the heating at the ground hypothesis for atmospheric thermal tide. That condition would become considerably less stringent if solar heat absorption in the upper atmosphere rather than at the ground were assumed.
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