It's obvious that the answer is less than 100%, since a completely solid core would provide no magnetic field. Is there some way to tell whether it's closer to 0.1%, 1% or 10%?

It's not really possible to use enough geothermal for it to have a noticeable effect on the lifespan of the magnetic field. Even completely removing the solid crust of the earth would not really register.

So we could take out some percentage of the heat of the crust, thus lowing the total temperature by some amount, but then that loss would be replenished from further down in the core.

It looks like from the calculations elsewhere in the thread that it probably wouldn't even be physically possible to extract that much energy from the crust. We'd just run out since there would be some lag time in replenishing the heat from the core through to the areas of the crust.

But also let's hope it's not 0.001% because I'm pretty sure the core will cool more than that on its own over a shorter timespan than 19 million years.

19 million years is 1.9% of the billion year rate. So it suggests the core should lose 1.9C in 19 million years. That's about 0.035% of the total temp, using Wikipedia's 5700C as the temp estimate.

That's a great initial guess, given how much uncertainty is (i've recently heard core temp could be 4x the wiki number, and some people estimate the earth's core only has lost a few degrees since it formed, rather than nearly 500 degrees). Neat stuff, thanks for providing the opportunity to look in to this.

No idea how good the source is, however it looks like we have a nice exponential there.

Lets see what the envelope says for an exponent of 2:

Using numbers from parent commentors, log2(6.6 x 10^13) is about 45.9, so we are in our 46th doubling period. A guess on the graph says its 25 years to double.

> The total heat content of the Earth is of the order of 12.6 x 10^24 MJ, and that of the crust the order of 5.4 x 10^21 MJ (Dickson and Fanelli, 2004).

so that's end of crust energy usefulness at the start of the 72nd period and end of Earth energy less than halfway through the 84th period.

So that gives us 500-1000 years of energy from now if we solely use the planets heat. Whether we soley use it or not becomes largely irrelevant due to the exponent, we can stretch it as a major source a few hundred more years or so.

Of course, if in 1000 years we aren't only using this planet we should be good. How many years to the next system again?

We are willing to concede that usage patters from 100 years ago are unrealistic current realities.

However we would simultaneously like to use the current reality to project future realities that are much farther away (in some cases 19 million years away).

Yeah, our dependence on fossil fuels is a huge problem, and not just because of climate change (which might also kill us).

Mobile phones didn't exist when I was young, and there are certainly a lot of them now even if they are low power devices, so it would be interesting to see electrical usage patterns pre-mobile phones vs. today.

The same goes for cars. Cars were using leaded gasoline in the US and getting 8 to 12 mpg, and now 30 to 35 mpg or greater on the highway, but do people drive more frequently, and with single riders?

Another question is would any cooling of the total Earth's heat energy be offset by global warming? The thermal differential would be less thereby slowing the migration of heat to the surface?

Or maybe we want to terraform our own planet to counter climate change. These things could use amounts of energy orders of magnitude higher than we use today.

I'm sure 100 years ago didn't expect we would launch 100,000 airplane flights every day [0] :) Nor did they think we would send spaceships to Mars.

[0] http://www.garfors.com/2014/06/100000-flights-day.html

It seems somewhat unreasonable to assume that our energy usage is going to exponentially increase due to as-yet-unforeseeable future needs and at the same time assume that we'll completely fail to find additional energy sources in the same timeframe.