How far does Earth's orbit need to move to "fix" global warming

If a Godlike power wanted to shift the Earth’s orbit outwards so the Global Mean Surface Temperature stopped increasing, or even went down to pre-industrial, how far would it have to move? And how long would a year then suddenly be?

I realize the answer will have to use some assumptions, and I plan on having a go myself using a desired reduction of 0.6 W/m^2, which is the only estimate I have found, but I was hoping someone with the various astrophysics and orbital mechanics formulae closer at hand would be curious enough to do it first.

No movement is necessary. The Earth’s temperatures are within normal variations. Of course, I’m talking of timescales in the tens of millions of years. The tenths of degrees that have us so vexed right now are nothing. Remember that we’re actually still in an ice age. Once Antarctica clears the South Pole, in some tens of million years, temperatures will rocket.

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This is not responsive to the OP. The OP is asking what decrease in solar radiation would result in global mean surface temperatures reverting back to pre-industrial levels, and what change in earth’s orbit would result in that decrease. Obviously we need to hold all other variables fixed to engage in this thought experiment, so where we are in terms of temperature oscillations on a geological time scale isn’t relevant.

[Moderating]

Quartz, the OP was not asking whether it is necessary to counteract global warming. That’s a GD topic. The OP was asking how much orbital change would counteract the factual amount of global warming. That’s a GQ topic. Please save the political debates for the correct forum.

Assume the earth is a blackbody at an average temperature of 300K. The power radiated by a blackbody goes as 4th power of temperature, so bringing it down to 299K means the heat output needs to reduce to (299/300)^4=0.987. Which means the heat input needs to reduce to that level too. Heat input goes as square of distance, so it needs to increase to 1.0067, or 0.67% further away from the Sun. Which is right around 1 million km.

Interesting approach. I took the current best knowledge numbers for average incoming radiation 340W/m^2 at the top of the atmosphere, 240W/m^2, ditto measured energy imbalance 0.6W/m^2 and looked at how much the (simplified to circular) orbit would have to change to bring either of those down the required .18-.25%.

Which gave me 135 000 km to 190 000 km, an increase of abt. .1 percent. But of course that would only give us a equilibrium.

The one million km shift though would, all other things being equal (and massive assumptions taken), change us from a 0.6W/m^2 positive imbalance, to a 2.5-3W/m^2 energy deficit.

I guess the next step is to ask the world’s climate scientists to redo their models for my scenarios … (Actually the models might already exist as simulations considering how much the natural variations of the sun’s output influence climate.)

How would you do it? Assuming you could accelerate the Earth, of course? Would you speed it up to a larger elliptical orbit, wait until it reaches apogee and then accelerate it again to get to stay in a new circular orbit?

This is called the Stefan-Boltzmann Law, with the Wiki article having a section on applying the calculation to Earth. The Wiki explanation is complicated by three different Earth temperatures: the actual temperature, the “effective” temperature, and what the temperature would be if the Earth were pure black body.

I’m eager to hear from the experts, but am betting that scr4 is basically correct!

Science magic, I don’t think there are “real ways” to do it.

I looked into the energies required though, and it looks to me like if you, through said science magic, could access a little of Earth’s rotational energy, the required energy would be a drop in the ocean and the we’d be hard pressed to notice the longer days.

Which is kind of annoying, as my original motivation for this thought experiment was to change the number of days in a year.

Move all the robots to an equatorial island and have them vent their exhaust in one direction at the right time.

Duh.

You could fly an asteroid alternately by the Earth and Jupiter. If it passes by the two planets in the right locations, it would transfer orbital energy from Jupiter to the Earth, thereby gradually moving the Earth to a higher orbit.

If I recall the little I’ve learned about orbital mechanics correctly, you would slow the Earth to move it to an orbit with a larger radius, not speed it up.

Someone smart will be along soon to confirm or refute me.

It will end up moving slower when it’s in a larger orbit, but you don’t actually get there by slowing it down. First you increase the speed; this puts the Earth into a more elliptical orbit, with perihelion at a point on the original point and the aphelion further away from the Sun. As it climbs towards the aphelion, it will lose speed. At aphelion you add a bit more speed to circularize the orbit (raise the perihelion). So in the end you are moving slower than in the original orbit, but you get there by increasing speed twice (or more).

I guess Kepler was pretty smart… Yes, the orbital speed is slower in a higher orbit. (Consider for example a circular orbit. If your distance from the sun is changing, so is your speed, as a result of gravitational acceleration.)

ETA to change your orbit, you need to do a little accelerating of your own, as the post above describes. The higher orbit has more energy!

ETA 2: the virial result here is that the average potential energy is -2 times the average kinetic energy. (Again, consider a circular orbit.) That is why the higher orbit has more energy even though you are slower.