Increasing venus’ rotation using radiation pressure

Question

I know, I know; I said I was giving up on Venusian terraformation, but this is gonna haunt me for the rest of my days if I don’t come up with some way to render this planet habitable. So, back to the drawing board…

To speed up Venus’ rotation to 24 hours, half the planet is enclosed in a giant “ultrawhite” shell that is 99.6% reflective of visible light. This shell is supported above the thick atmosphere by oxygen-filled balloons, and is tethered to the surface by nanotube-based cables. (Most of the atmosphere’s acid content been removed by this point, preventing corrosion).

A swarm of huge parabolic mirrors are then built in geostationary orbit around Venus. Like the shell, these are ultrawhite, and constantly direct intensified beams of sunlight onto the shell-covered half of the planet. The radiation pressure serves to gradually increase the planet’s rotation until it reaches 24 hours.

Assuming that every inch of the half-shell is constantly under irradiance, how long will it take for this system to accelerate Venus’ rotation to 24 hours?

Answer 1

Anything energetic enough to speed up a planets rotation is likely to blow a large chunk off the planet, or, at the very least, turn the crust molten

I think the physics here speaks for itself. Planets are really, really heavy. You need a lot of energy to change their momentum. That energy, fundamentally, is always going to be unfocused. That means dumping, essentially, a ludicrous amount of heat onto the surface. Heat radiates out poorly to space - it's likely the surface would be uninhabitably hot, even for Venus, for many hundreds of thousands of years. This method is either not going to do that, in which case it won't do anything, or it'll be energetic enough, in which case the surface, and a good chunk of the mantle, will liquify in the process

Your best bet, though, is probably Mercury. That place is uninhabitable, so we can dump the output from your civilization's massive solar particle cannons or whatever you have into the surface of it, blow a very precise, huge chunk off of it, and send it hurtling into orbit around Venus in such a way that the rotation slows.

Mercury becomes a moon, which may or may not be orbitally stable, but, hey we've solved this problem, let's get paid before the Venusians wonder why this radioactive moon that appeared in their sky is getting closer.

Disclaimer: I am a biologist, not a physicist, and have absolutely no experience in orbital mechanics, solar particle cannons, or really any physics beyond high school. Do not attempt except under supervision from a qualified solar engineer.

Answer 2

My quick calculation says it would take a timescale comparable to the current age of the universe.

You're basically describing a modified version of the YORP effect, which does measurably affect the rotation rates of asteroids and other small bodies. Unfortunately, it depends strongly on the size of the body; you can show that the change in angular frequency scales like $$\frac{\mathrm{d}\omega}{\mathrm{d}t}\propto\frac{F}{R^2}$$ with $F$ the flux received and $R$ the body's radius. Small asteroids in the inner Solar System experience angular accelerations on the order of $\sim10^{-11}$ rad/s/yr -- and they have radii on the order of kilometers to tens of kilometers. Venus has a radius of roughly 6000 km. The scaling on that gives us an angular acceleration of $\sim3\times10^{-17}$ rad/s/yr for the typical solar flux.

Your mirrors will certainly increase the available flux, by . . . let's say a factor of 100, being extremely generous to the engineers behind them. To reach Earth's current rotational rate of $\sim10^{-4}$ rad/s would then require a timescale of ~10 billion years or so -- at which point the Sun will have expanded to engulf Venus, and the whole problem will be moot.

Now, you could quibble with this timescale a bit by arguing that the YORP effect on small bodies only arises because of irradiation differences in small parts of the surface, rather than half of the body, and that my answer therefore overestimates by a couple orders of magnitude (fair, and arguably not a quibble). You could also note that the difference in albedo in your scenario is even more extreme than what we see in nature (also fair, though certainly not as important). I would counter, though, by saying that increasing the solar flux by a factor of 100 is an extremely challenging task and that I was a little over-generous with that.

So perhaps 1 billion years is a better estimate. Either way, though, this would take a long time. At some point, future generations of humans will start questioning whether it's worth the effort.

Answer 3

Venus has a molten core. The sun will make tides in this. One of the first pieces of evidence of the Earth's molten core was Michelson's interferometer experiments, which could see the flexing of the earth while trying to measure the speed of light.

If you try to speed up the rotation of Venus, you haven't got forever: you have to work harder than this tidal effect that will eventually lock Venus so the same side always faces the sun.

There are other sticking points. Mercury is tidally locked but in a 3:2 resonance with its orbit, so it still sees the sun move, but at a rate that has been locked to its orbit, and it is retrograde. You will have to get the planet out of that potential minimum, faster than any tidal locking will draw it back. We do not know exactly how large the molten core of Venus is, though it does have huge volcanoes.