Episodic glaciation subjects Earth’s crust to loading and unloading by ice. The last major ice age was 10,000 years ago, and the subsequent unloading produces a nontidal contribution to the acceleration of Earth’s rotation rate of order |Ω|/|Ω̇| ≈ 6 × 10¹¹ yr, detectable from observing the positions of distant stars. Corresponding changes in Earth’s oblateness produce a decrease in the rate of nodal line regression of the geodetic satellites LAGEOS.

(a) Estimate the speed with which the polar regions (treated as spherical caps of radius∼1,000 km) are rebounding now. Do you think the speed was much greater in the past?

(b) Geological evidence suggests that a particular glaciated region of radius about 1,000 km sank in ∼3,000 yr during the last ice age. By treating this as a low-Reynolds-number viscous flow, make an estimate of the coefficient of viscosity for the mantle.