## 1. Introduction

[2] External torques acting on the rotational bulge of a planetary body may cause motions of the rotation axis, such as the lunisolar precession of the Earth's rotation axis. *Evans* [1866] noted that even in the absence of external torques, reorientation of the rotation axis may occur, as viewed by an observer on the surface of the body, due to mass redistribution. For a rigid spinning body, the lowest kinetic energy state for a given angular momentum corresponds to rotation around the principal axis of inertia with the largest moment, hereafter referred to as the maximum principal axis. Hence it is generally assumed that internal energy dissipation will ultimately drive planetary bodies to this state. Mass redistribution leads to reorientation to a new principal axis rotational state, while the angular momentum vector remains fixed in space. This type of reorientation of the rotation axis is commonly referred to as true polar wander (TPW) to distinguish it from apparent polar wander (APW), which refers to the reorientation of the rotation axis relative to the surface due to plate tectonics. On Earth, observations of star positions taken over the last century indicate TPW at a rate of ∼1°/Myr [*Argus and Gross*, 2004]. The time averaged magnetic pole position can be used to infer the secular TPW history. These studies suggest ∼30° of TPW over the last 200 Myr [*Besse and Courtillot*, 2002], and a ∼90° TPW event during the Cambrian period [*Kirschvink et al.*, 1997].

[3] We will focus on rotational variations due to TPW. Hereafter, we will describe these variations in a reference frame fixed to the rotating body; hence we will refer to the reorientation of the rotation axis, rather than the reorientation of the body. *Evans* [1866] described how a mass deficit would “pull” the rotation axis, while a mass excess would “push” the rotation axis using dynamical arguments. Motivated by this study, *Darwin* [1877] found mathematical TPW solutions by solving the equations for angular momentum conservation, commonly referred to as Euler's equations. *Gold* [1955] argued that while the rotational bulge stabilizes the rotation axis temporarily, its orientation is ultimately determined by those contributions to the inertia tensor which are not associated with rotation since the rotational bulge eventually adjusts to any reorientation of the rotation axis. *Goldreich and Toomre* [1969] demonstrated that if mass redistribution occurs slowly (over time scales that are longer than the slowest of the nutations experienced), the solid angle between the rotation axis and the maximum principal axis is an adiabatic invariant. It then follows that once the planet achieves maximum principal axis rotation, it will continue in this configuration and thus mass redistribution drives TPW as the principal axis of inertia migrates. The final rotation axis orientation (after realignment of the hydrostatic figure) can be found by diagonalizing the non-hydrostatic inertia tensor. This approach has been used to study the long-term rotational stability of planets [e.g., *Melosh*, 1980; *Steinberger and O'Connell*, 1997; *Zuber and Smith*, 1997; *Bills and James*, 1999; *Sprenke et al.*, 2005]. Alternatively, given the time-dependent mass redistribution, it is possible to find TPW solutions by explicitly solving the angular momentum conservation equation [e.g., *Spada et al.*, 1992, 1996; *Ricard et al.*, 1993; *Richards et al.*, 1997, 1999; *Steinberger and O'Connell*, 1997; *Greff-Lefftz*, 2004].

[4] *Evans* [1866] had noted that the presence of an elastic lithosphere may stabilize the rotation axis since it establishes a memory of prior rotation pole locations, that is, a remnant rotational bulge. *Willemann* [1984] revisited this issue and found TPW solutions by diagonalizing the inertia tensor associated with the TPW-driving load and the remnant rotational bulge. We will extend the analysis of *Willemann* [1984] by quantifying the long-term TPW of a satellite with remnant rotational and tidal bulges. The paper is organized as follows. Section 2 focuses on inertia tensor perturbations associated with the effect of mass loads and the deformation driven by changes in the centrifugal and tidal potentials. Section 3 outlines TPW solutions obtained by diagonalizing the inertia tensor. Sections 4 and 5 consider the implications of the new results for estimates of the reorientation of Saturn's moon Enceladus. Finally, section 6 summarizes the main results and discusses some of their consequences.