Very precise measurements of the lunar gravity field could detect a solid inner core. For synchronous rotation, the equator planes of the inner core and mantle should be tilted with respect to the ecliptic plane and precess along that plane with the same 18.6 yr period. Generally, two different tilts would cause a static inner core gravity field to appear as small periodic (27.212 d) variations in the mantle-referenced C 21 and S 21 coefficients. Tidal variations also contribute to the C 21 variation so a much improved k 2 Love number would be required. Model computations suggest that the inner core signature is likely to be very small requiring sensitive gravity measurements. In principle, a signature analogous to the Moon's should be present for other synchronous satellites with interior liquid layers and also Mercury.