Mathematics – Number Theory
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufm.p51b0930m&link_type=abstract
American Geophysical Union, Fall Meeting 2005, abstract #P51B-0930
Mathematics
Number Theory
5450 Orbital And Rotational Dynamics (1221), 5455 Origin And Evolution, 6225 Mars, 6299 General Or Miscellaneous
Scientific paper
The long-term (secular) rotational stability of planets subject to loading is a classic problem. Gold [Nature, 1955] and Goldreich and Toomre [JGR, 1969] considered the true polar wander (TPW) of a hydrostatic planet driven by an uncompensated surface mass load; they concluded that a mass of any size (e.g., a `beetle') would ultimately reorient the load to the equator. Their work was extended by Willemann [Icarus, 1984] to treat the case where the presence of a lithosphere leads to both imperfect load compensation and a remnant rotational bulge. Willemann [1984] adopted axisymmetric loads and concluded that the equilibrium pole location was governed by a balance, independent of elastic (long-term) lithospheric thickness, between the load-induced TPW and stabilization by the remnant bulge. We revisit Willemann's analysis using a theoretical development based on the fluid limit of viscoelastic Love number theory. We demonstrate that the equilibrium pole position is, in fact, a function of the lithospheric strength; a convergence to Willemann's results is evident only at very high values of elastic thickness (>400 km for an application to Mars), while we predict significantly larger TPW for planets with thin lithospheres. We also explore the rotational stability in the case of non-axisymmetric surface mass loads and internal (convective) contributions to the non-hydrostatic inertia tensor. We find that such contributions, even when they are small in comparison to axisymmetric contributions, can profoundly influence the rotational stability. Indeed, we quantify the relatively permissive conditions under which a non-axisymmetric forcing initiates a so-called inertial interchange TPW (IITPW) event (i.e, a 90° pole shift). These results suggest that Willemann's [1984] axisymmetric load analysis underestimates the potential excursions of the planetary rotation vector. Finally, Willemann's study 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 above-noted destabilizing effects of load asymmetry, the equations governing the rotational stability permit higher excursions of the Martian rotation vector than have previously been appreciated.
Manga Michael
Matsuyama Isamu
Mitrovica Jerry X.
Perron J.
Richards Anita M.
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