Will McCarthy’s “To Crush The Moon” features some radical planetary engineering to make the Moon more habitable – it’s imploded to ~(.1656)^{1/2} = 0.407 times its present radius to increase its surface gravity to 1 Earth gee. Thanks to the Inverse Square law, to increase a certain mass’s surface gravity, one decreases its size by the inverse square root of its starting radius. For the Moon that’s a drop from 1738 km to just 707 km. That’s a increase of average density by (1/0.407)^{3} = 14.84 times its current density of 3,344 kg/m^{3} to 49,622 kg/m^{3}, which probably means a core collapsed to neutronium density with the normal matter exterior from the outer 40 km of the Moon’s crust. In the process of such a collapse it’d release (1/0.407)-1 = 1.457 times the Moon’s present gravitational binding energy. 1.245E+29 joules total, some 1.7 megajoules per kilogram of Moon mass. If we guesstimate the thermal capacity of Moon-stuff as ~500 J/kg.K, then it’s an average temperature of 3,387 K. That’d radiate away via the 6.3 million kilometres square of the mini-Moon with a characteristic time of 84 years, but it’d be a slower process of radiating heat as molten basalt at maybe ~2,000 K or so. A few centuries of cool down, while puffing out fresh mantle gases. Less radiating time if the collapse process is strongly endothermic and soaks up the excess entropy.

Thanks to the implosion and the conservation of momentum, the Moon’s present sidereal day of 27.321667 earth-days is reduced to 4.5245 earth-days, or a solar day of 4.5812 days. Some 110 hours.