Mathematics – Number Theory
Scientific paper
Feb 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006jgre..11102003m&link_type=abstract
Journal of Geophysical Research, Volume 111, Issue E2, CiteID E02003
Mathematics
Number Theory
19
Planetary Sciences: Solid Surface Planets: Orbital And Rotational Dynamics (1221), Planetary Sciences: Solid Surface Planets: Origin And Evolution, Planetary Sciences: Solar System Objects: Mars, Planetary Sciences: Solar System Objects: Extra-Solar Planets
Scientific paper
We revisit the classic problem of the secular rotational stability of planets in response to loading using the fluid limit of viscoelastic Love number theory. Gold (1955) and Goldreich and Toomre (1969) considered the stability of a hydrostatic planet subject to an uncompensated surface mass load and concluded that a mass of any size would drive true polar wander (TPW) that ultimately reorients the load to the equator. Willemann (1984) treated the more self-consistent problem where the presence of a lithosphere leads to both imperfect load compensation and a remnant rotational bulge. Willemann considered axisymmetric loads and concluded that the equilibrium pole location was governed by a balance, independent of elastic lithospheric thickness, between the load-induced TPW and stabilization by the remnant bulge. Our new analysis demonstrates that the equilibrium pole position is a function of the lithospheric strength, with a convergence to Willemann's results evident at high values of elastic thickness (>400 km for an application to Mars), and significantly larger predicted TPW for planets with thin lithospheres. Furthermore, we demonstrate that nonaxisymmetric surface mass loads and internal (convective) heterogeneity, even when these are small relative to axisymmetric contributions, can profoundly influence the rotational stability. Indeed, we derive the relatively permissive conditions under which nonaxisymmetric forcing initiates an inertial interchange TPW event (i.e., a 90° pole shift). Finally, Willemann's analysis is often cited to argue for a small (<18°) TPW of Mars driven by the development of a Tharsis-sized load. We show that even in the absence of the destabilizing effects of load asymmetry, the equations governing rotational stability permit higher excursions of the Martian rotation vector than has previously been appreciated.
Manga Michael
Matsuyama Isamu
Mitrovica Jerry X.
Perron Taylor J.
Richards Anita M.
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