Earth may end up like Mars

[K.I.L.E.R]

http://www.chron.com/disp/story.mpl/nation/3808766.html

I hope this happens when the 2 black holes envelope us rather than in 10 years time.

 

[Bouncing Zabaglione Bros.]

IIRC, the difference is Mars has less gravity, and no protective electromagnetic belts. This means that Mars doesn't have enough gravity to hold it's atmosphere, and doesn't have the same kind of protection against the solar wind stripping it's atmosphere away.

 

[nutball]

Right, but the Earth's core is cooling in just the same fashion that Mars' did. Once it freezes solid Earth will likely lose it's magnetic field, and the atmosphere will be spalated just as that of Mars is thought to have been. The real scaremonger line is that this is going to start happening on a rather short timescale (ie. hundreds - thousands of years).

I guess it would be interesting to ask whether, given the relative sizes of the two planets, the continued existence of Earth's magnetic field at this time is a surprise or not -- ie. if you assume a similar formation date and initial temperature, should Earth also have frozen by now, or is there some mechanism keeping it warm (I've seen suggestions that Earth's Moon may have contributed but I'm not sure whether they're crank or not).

 

[Bouncing Zabaglione Bros.]

Right, but the Earth's core is cooling in just the same fashion that Mars' did. Once it freezes solid Earth will likely lose it's magnetic field, and the atmosphere will be spalated just as that of Mars is thought to have been. The real scaremonger line is that this is going to start happening on a rather short timescale (ie. hundreds - thousands of years).

I guess it would be interesting to ask whether, given the relative sizes of the two planets, the continued existence of Earth's magnetic field at this time is a surprise or not -- ie. if you assume a similar formation date and initial temperature, should Earth also have frozen by now, or is there some mechanism keeping it warm (I've seen suggestions that Earth's Moon may have contributed but I'm not sure whether they're crank or not).

Earth is a bit bigger than Mars, maybe has a bigger iron core?

You can see on some of the gas giants' satellites that the proximity of another gravity/electromagnetic field does seem to be able to put energy into a planet by squeezing/pulling at it, so maybe we get a the same effect from the moon, but smaller. After all, we see the world's oceans pulled back and forth, why not the molten core?

 

[nutball]

Earth is a bit bigger than Mars, maybe has a bigger iron core?

Yes but of course the Earth also has a larger surface area from which to radiate away the heat...

You can see on some of the gas giants' satellites that the proximity of another gravity/electromagnetic field does seem to be able to put energy into a planet by squeezing/pulling at it, so maybe we get a the same effect from the moon, but smaller. After all, we see the world's oceans pulled back and forth, why not the molten core?

That was indeed the proposed mechanism. Whether the numbers work out I have no idea.

 

[Thowllly]

Yes but of course the Earth also has a larger surface area from which to radiate away the heat...

The earths radius is roughly double that of Mars. If you double a spheres radius, it will have 8 times the volume, but only 4 times the surface area. I think that would mean it should take longer to cool.

 

[Bouncing Zabaglione Bros.]

The earths radius is roughly double that of Mars. If you double a spheres radius, it will have 8 times the volume, but only 4 times the surface area. I think that would mean it should take longer to cool.

Hmm, that's true. Surface area goes up in squares, where volume goes up in cubes.

 

[nutball]

Right, so one might naively expect cooling time should be proportional to radius.

That article suggests that Mars' magentic field died away ~1.1 billion years after formation. Which one might interpret to mean that Earth's would have been expected to be gone by ~2 billion year after formation. Which it clearly wasn't.

 

[Bouncing Zabaglione Bros.]

Right, so one might naively expect cooling time should be proportional to radius.

I'm pretty sure cooling is down to surface area, so the larger the body, the more it retains heat. The surface area is proportionaly smaller than the volume the bigger you get.

 

[Neeyik]

Another factor to consider is the amount of radioisotopes in the cores of the various inner planets - it's possible that the Earth has an "unusally" high level of such elements for a "typical" rocky planet. This may go part of the way to explaining why the Earth's core has remained so hot for so long (in comparison to the likes of Venus and Mars).

 

[nutball]

I'm pretty sure cooling is down to surface area, so the larger the body, the more it retains heat. The surface area is proportionaly smaller than the volume the bigger you get.

Errrr.... yeah that's what I said. Total energy goes as V~r^3, area as A~r^2, so characteristic cooling time (which is ~V/A) goes as r.

 

[Bouncing Zabaglione Bros.]

Errrr.... yeah that's what I said. Total energy goes as V~r^3, area as A~r^2, so characteristic cooling time (which is ~V/A) goes as r.

Yeah, that works if you have a perfectly smooth and completely round sphere, and we know the earth is neither. So by having the radius of the Earth (which varies depending where you measure it) you can't actually work out the surface area, only the surface area of a similar sized sphere.

A subtle difference, but I think it's important to realise when you're not calculating what you think you are.

 

[arjan de lumens]

Yeah, that works if you have a perfectly smooth and completely round sphere, and we know the earth is neither. So by having the radius of the Earth (which varies depending where you measure it) you can't actually work out the surface area, only the surface area of a similar sized sphere.

A subtle difference, but I think it's important to realise when you're not calculating what you think you are.

I would not actually expect the Earth's cooling rate to depend very much on surface area at all; given its size, I would rather expect the dominant factor to be the thermal resistance from the innards of the planet to its surface; the need to radiate the heat out from the surface into space adds very little additional resistance compared to that of a column of several thousand kilometers of rock.

 

[Bouncing Zabaglione Bros.]

I would not actually expect the Earth's cooling rate to depend very much on surface area at all; given its size, I would rather expect the dominant factor to be the thermal resistance from the innards of the planet to its surface; the need to radiate the heat out from the surface into space adds very little additional resistance compared to that of a column of several thousand kilometers of rock.

That "column of several thousand kilometers of rock" is going to be a lot smaller on a small planet like Mars because as we've said above, volume goes up with size a lot faster than surface area.

I suppose it depends where you are standing though. If you're standing on top of a super-volcano, there isn't thousands of kilometers of rock between you and the molten core of the planet.

 

[arjan de lumens]

That "column of several thousand kilometers of rock" is going to be a lot smaller on a small planet like Mars because as we've said above, volume goes up with size a lot faster than surface area.

The height of the column would be tied to the planet's radius rather than to its actual surface area; in case of both Earth and Mars it would still be thousands of kilometers, and essentially unaffected by whether the planet is covered by heatsinks (->huge surface area) or polished to near-perfect smoothness (->minimal surface area).

If you were to cover the entire Earth with super-duper-hyper-heatsinks and thus increase its heat radiation into space so much that the planet's average surface temperature went down from today's ~290K to Absolute Zero and stayed there, you would then have a temperature gradient from the core to the layers just beneath the heatsinks of about 6000K->0K instead of 6000K->290K - this would increase the temperature differential by about 5% and as such cause the Earth to cool down about 5% faster.

I suppose it depends where you are standing though. If you're standing on top of a super-volcano, there isn't thousands of kilometers of rock between you and the molten core of the planet.

Oh yes there is. The rock may be molten, but it is still much cooler and of a very different composition than the actual core itself.

 

[nutball]

Yeah, that works if you have a perfectly smooth and completely round sphere, and we know the earth is neither.

No the t~V/A works for any body which radiates as a black-body.

You notice there are no physical constants in there? You should worry about that more than the micro-details of the calculations of the surface area!

A subtle difference, but I think it's important to realise when you're not calculating what you think you are.

The difference is trivial compared to all the unknown physics that's been thrown out the window in doing the order of magnitude calculation (hence my liberal use of the '~')!