Which planet is shrinking as its core cools?

Mercury. It is mostly iron - the metallic core takes up something like 85 per cent of the radius, a completely different proportion from anywhere else - and as that core cools it contracts, pulling the surface in with it. The crust, having nowhere to go, has buckled.

The result is visible from orbit as lobate scarps: cliffs hundreds of kilometres long and up to several kilometres high, running across the surface and cutting through older craters, which is how they are dated. Adding up the shortening suggests the planet has lost several kilometres of radius, and images from the MESSENGER mission show small young scarps that indicate it is still happening.

Why it is so metal-heavy is unsettled. The leading account is a colossal early collision that stripped away most of the original rocky mantle and left the core nearly bare. Alternatives have the Sun's heat vaporising the outer layers, or Mercury simply forming from unusually metal-rich material. It also, despite a sunlit surface reaching 430 degrees, has water ice sitting in polar craters whose floors have never seen sunlight.