The forced precession of the Moon's inner core

Abstract The tilt angle of the 18.6 year precession of the Moon's solid inner core is unknown, but it is set by a balance between gravitational and pressure torques acting on its elliptical figure. We show here that to first order, the angle of precession of the inner core of a planetary body is determined by the frequency of the free inner core nutation, ω ficn , relative to the precession frequency, Ω p . If | ω ficn |≪|Ω p |, the inner core is blind to the gravitational influence of the mantle. If | ω ficn |≫|Ω p |, the inner core is gravitationally locked to the mantle and is nearly aligned with it. If ω ficn ≈Ω p , large inner core tilt angles can result from resonant excitation. Viscous inner core relaxation and electromagnetic coupling can attenuate large tilt angles. For the specific case of the Moon, we show that ω ficn is to within a factor of 2 of Ω p = 2 π /18.6 yr −1 . For a rigid inner core, this implies a tilt of 2 to 5° with respect to the mantle, and larger if ω ficn is very close to Ω p . More modest tilt angles between 0 and 0.5° result if viscous relaxation within the inner core occurs on a timescale of one lunar day. Predictions from our model may be used in an attempt to detect the gravity signal resulting from a tilted inner core, to determine the past history of the inner core tilt angle, and to assess models of dynamo generation powered by differential rotation at the core‐mantle and inner core boundaries.