Global Nudging

This post was inspired by a discussion I had with a couple friends awhile back. Since then, we've had a heat wave, some sort of rainless hurricane, and a snowstorm.

I don't really know anything about weather or climate science, but I do know a bit about thermodynamics. In thermo, you learn ever more esoteric definitions for temperature until you're no longer sure what's fundamental and what's just human convention. Maybe it's all information!?

The first proper definition you get is that temperature is a measure of the average speed of particles in some system, which relates to the average kinetic energy. A little later you learn a more precise definition: the higher the temperature, the wider the distribution of particle speeds. As you pump in energy, more and more particles collide and transfer momentum in unlikely, chaotic ways.

Can this statistical, microscopic argument be scaled up to the entire globe? If the surface temperature of the Earth rises, are we going to get even weirder weather? There is evidence from modeling and observation to support that hypothesis.

Anyway, my friends asked whether it was feasible to counteract global warming by pushing the Earth a little farther away from the sun. Of course, there are reasonable solutions to this looming crisis, but we seem increasingly less likely to opt for reasonable, so let's go with bananas instead. Most people seem to agree that letting the Earth warm by another 2° C would be unfathomably catastrophic; let’s assume we botch that and try for the Spaceship Earth solution.

The sun pumps out an inconceivable 380 yottawatts of power (about 50 million billion times more than our best nuclear plant), but we're so small and far away that we only catch about one half of one billionth of that energy. We also don't absorb all of it. You can tell because, uh, we can see the Earth from space; about 30% bounces back immediately.

The rest is absorbed and eventually radiates back out after heating the planet. Because the Earth is cooler than the sun, this radiation is mostly long wavelength, low energy infrared instead of visible light. When we take the temperature of stars, planets, and other celestial bodies, we're doing so by sampling that spectrum. But just based on the fraction of energy the Earth receives and its albedo, we can predict what temperature a distant alien astronomer would measure for the Earth with the Stefan-Boltzmann law.

The law relates the power output of a black body to its temperature. For a perfect black body, power out conveniently equals power in—our share of the sun's energy—which is a good enough approximation here. If we also know the sun's temperature (~6000 K), out pops the Earth's: 255 K (about -1° F).

A bit chilly? Yes, but this is roughly the effective temperature (another definition: the temperature of a black body with the same power output) aliens would measure via spectral analysis. If the aliens were smart, they would also notice trace amounts of water vapor and carbon dioxide in our atmosphere and be confident that conditions on the ground were a bit more comfortable. Why? Because those are both smurghouse—oh, sorry, greenhouse—gases.

The atmosphere is mostly transparent to the sun's visible light, but to the great frustration of infrared astronomers, it is not transparent to Earth's thermal radiation. So instead of streaming back out to space unimpeded, infrared photons keep getting knocked about and turned around by water vapor and CO2 molecules. This molecular mugging robs the photons of energy—raising temperatures on the ground—and slows their escape.

Atmospheric absorption by wavelength. Credit: NASA

All this action makes the average across the surface a reasonably pleasant 288 K (59° F). But of course a little more smurghouse gas and we start contemplating pushing the Earth away from the sun. So let's get back to that.

Reducing the effective temperature of the planet from 255 to 253 K is a 0.8% decrease. From the Stefan-Boltzmann law, that requires a 3.1% decrease in energy received from the sun, which we can get by just pushing the Earth a mere 1.6% farther away (2.3 million km). Can we do that?

(This is less than the 5 million km swing due to Earth's elliptical orbit, but as an average, sustained change, it will have a greater effect on temperature. Think about quickly running your hand through a candle flame versus holding your hand over the flame.)

First, let's look at the question from an energy budget standpoint. Any orbit represents a specific balance between kinetic energy from motion and potential energy from gravity, which adds up to a total orbital energy. To move from one orbit to another, you must pay—by some means—the difference in energy between the orbits. In our case, that requires about 7 MJ/kg. That's a 60-watt light bulb operating for 32 hours. But the Earth has a lot of kilograms, so... light bulb comparisons are a little inadequate; it comes out to the energy of a hundred million dinosaur-killing asteroid impacts.

But as we know from the Chicxulub crater and the fact that dinosaurs are now turkeys, celestial bodies don't smack into each other like perfect billiard balls. Collisions between them are very inelastic, with much energy being lost to superheating the atmosphere, excavating dirt, and forging cool new minerals instead of moving the planet. All in all, I would not recommend countering global warming by annihilating three quarters of all life a hundred million times.

Part 1 of 100,000,000. Credit: NASA

Maybe rockets instead? Here the relevant quantity is the delta-v required for an orbital maneuver—that is, the fuel necessary to change a body's velocity. If we want to move the Earth farther out, it will have to orbit at a slower speed. But this is a two-step process. First we accelerate outward, changing the orbit to an ellipse between our current distance and our desired distance. Then we hit the brakes and lose energy, which circularizes the orbit at the new distance.

All told, the Δv is just 0.3 km/s. The most advanced rocket that actually kind of exists right now is the VASIMIR ion rocket, which uses magnets to propel plasma out the back. Conservation of momentum makes this work: expel a lot of tiny particles very quickly in one direction (300 km/s for our ions), push a heavy object a moderate speed in the opposite direction. Plugging all this into the Tsiolkovsky rocket equation tells us how much of our rocket (engine+Earth) needs to be fuel. The answer: just 0.1%!

VASIMIR uses argon, which is one of the most abundant elements in our atmosphere and the universe at large. If we distill all the argon out of our atmosphere, which is 1.3% argon by mass, we're... 0.001% of the way there.

How about a solar sail? Despite being massless, photons still impart momentum. The total amount we need is Δv times the Earth's mass. To get the required impulse before 2100, which people seem to think is important, we'd need a sail with an area of... well let's just say it's way, way bigger than the sun and move on.

Okay, all in all this looks like a pretty bad idea. But while we're on the topic of solar sails, catching the sun's photons would have the added benefit of preventing said photons from reaching Earth. In that case, why bother moving the planet at all?

Indeed, one of the least implausible recklessly dangerous solutions to global warming is to change the Earth's albedo. We could do this with a sun shield, or particulate matter in the atmosphere, or any number of other options that would no doubt have catastrophic unintended consequences. But as we saw, we only need to get rid of 3.1% of the sun's energy, which we can do by just increasing the current albedo from 0.3 to 0.32. Easy peasy!