Uploaded by the authors to the arXiv here.
Essentially, as the Sun increasing in luminosity, the biogeochemical draw-down of CO2 will ultimately cause the collapse of the oxygenated biosphere. Life makes free oxygen more efficiently than non-biotic sources and the production rate is higher than the draw-down rate (oxidation of erosion exposed reductants like carbon, methane, etc) so O2 builds up. But once the free CO2 reduces too low, the oxygen producers will collapse in population, quickly ending the net positive O2 production. The estimated time space is about 1 Gyr +/- 0.5 Gyr so there’s a time-limit to the biosphere as we know it.
However, the key assumption is that the length of day remains the same. Climate studies of primordial Venus, and slowly rotating exoplanets, typically show that slow rotating planets develop sub-solar cloud masses that increase the insolation a planet can still maintain a stable climate under, reducing the rate of the CO2 draw-down. The key transition speed is when the solar day is 16 times Earth’s current day – 384 hours. So how do we slow down Earth’s spin? And what else is it good for?
Earth’s angular kinetic energy is immense – 2.15 x 1029 joules or 6.8 billion TW-years. Several terawatts are dissipated in the Earth’s oceans thanks to the tides, and have been for aeons. J.B.S Haldane fictionally described humans using tidal power generators to extract the energy and cause the Moon to ultimately crash into the Earth all within 30 million years. That’s highly improbable since the Moon will move away from the Earth to conserve their mutual angular momentum as it gains energy, ultimately becoming synchronous with the Earth’s axial rotation rotate when their period hits 48.5 days. At that point, there’s no longer energy exchange between the two.
Alternatively we can alter the Earth to make it spin slower. The Moment of Inertia is proportional to the square of the radius for the mass of a sphere. Turn Earth into a shell about 4 times larger in radius and it will turn 16 times slower as well as provide 16 times more surface area. Actually, due to geometry of the Moment of Inertia, the shell would only need to be about ~3.1 times the Earth in radius. The energy required to transform Earth into a shell would far surpass the rotational energy and thus wouldn’t be a very efficient approach to the problem.
Turning all the coastlines and shallow waters of the Earth into arrays of tidal power generators would increase the energy dissipation efficiency, but with undesirable effects on the oceanic biosphere. A different approach would be to couple the Earth and Moon electromagnetically and drain power that way, while transferring the excess angular momentum to the Moon. If the process takes millions of years, then all life would ultimately adapt to the lengthening days. Exactly what changes would arise, imagine each “Big Day” as periods of “Light” and “Dark” each at least 192 hours long.