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Simply inject heat into the core of Mars should do.

Recently NASA said that there was possibly ocean on Mars, if that's true, then the loss of water couldn't be related to it being lost in space. The only other explanation is that the water sank into the mantle.

So why didn't water on Earth sank into the mantle? Because of the internal heat from Earth's core.

So how much energy is required to reheat the core of Mars? Now earth's internal heat budget is only 47 terawatts, while the solar radiation falling on earth's surface is 173,000 terawatts. Then it looks like it's fairly easy to meet the energy requirements.

After the core is heated up, we'll possibly get the geomagnet working too.

So the question is whether Earth's water is held at the surface because of the internal heat, because I've heard people saying the reason is that rock and iron is heavier, of which I'm skeptical.

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  • $\begingroup$ Where does this idea come from: "... the loss of water couldn't be related to it being lost in space." Are you citing some research or posting your own theories? $\endgroup$
    – uhoh
    Commented Jun 14, 2016 at 4:28
  • $\begingroup$ That's my own theory. Because there was ocean, that means the loss of water in space was very slow, otherwise there wouldn't be vast amounts of water to form an ocean. $\endgroup$
    – seilgu
    Commented Jun 14, 2016 at 4:43
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    $\begingroup$ @seilgu Your new addition to the question is an Earth Science question which doesn't belong here, but we do have a site for that: earthscience.stackexchange.com $\endgroup$
    – called2voyage
    Commented Jun 14, 2016 at 16:18

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There's a problem with your idea:

This 47TW is not a measure of the heat stored in the earth, it's just the loss. Since the earth did dissipate heat for billions of years and will continue to do so for billions of years, the total amount of heat energy in the earth is tremendous.

Let's estimate how much time it takes to re-heat the earth:

The core of the earth has a radius of 3500km. Given an average density of 11g/cm³, it weights about $2\cdot10^{24}kg$ (Entire earth: $6\cdot10^{24}kg$). Assuming a heat capacity of 400J/(kg K) and a temperature of 4000K, the heat energy inside the earth is $3.2\cdot10^{30}J$. Divide this by your power from the sun, and you get 590,000 years. This is roughly the time it takes to heat up earth's core by sunlight.

But this is a very low estimation. The inner core has a temperature of 6000K and consists mainly of iron with higher heat capacity. And the mantle of the earth also contains lots of heat. I would not wonder if the real value is several times larger, but I don't want to do the math for a more precise estimation now.

Now let's assume Mars is a little (shrinked) earth. It's about 50% farther away from sun (reduces sunlight power per surface to 1/(1.5²)=44%) and has a radius of 3400km (reduces cross section to 3400²/6370²=28%. So the entire sunlight power is 12.7%. The volume of mars is 3400³/6370³=15.2% of that of the earth, and so the heat energy is.

It would take about 15.2/12.7=20% more time, i.e. 708,000 years to heat up mars.

This isn't feasible. Even if, how could the entire sunlight be used to heat the core? Painting the entire planet black would heat up the surface, and the heat would rather dissipate to space than into the planet.

Note again: My calculations are in no way precise. They use lots of assumptions, which are chosen so that the numbers are better for your idea, and neglect effects that would make the numbers worse.

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  • $\begingroup$ OK, i see your point. But the problem about terraforming is always the water. The energy requirements however can be achieved with something like the Dyson sphere. $\endgroup$
    – seilgu
    Commented Jun 14, 2016 at 8:50
  • $\begingroup$ @seilgu: Well, you claimed the water is inside the planet, and heating it would bring it back to the surface. So I focussed on heating the planet. I guess a civilization that can build a dyson sphere to heat mars can also just bring new water to the planet. But this is so far beyond the current scope of mankind, that it's more science fiction than a possibility. $\endgroup$
    – sweber
    Commented Jun 14, 2016 at 9:26
  • $\begingroup$ But getting water isn't that easy, you can't make them using E=mc^2, that would be too slow. The other option I can think of is to collect water from asteroids, also sounds infeasible. However building a dyson sphere, or only a portion of dyson sphere, should be a little easier. You don't need to transport tons of water in space. If you get a solar sail to orbit the sun closely, you can collect the same amount of energy with less surface. $\endgroup$
    – seilgu
    Commented Jun 14, 2016 at 9:43
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    $\begingroup$ @seilgu We are a lot closer to bringing comets to Mars than we are to building any kind of Dyson-sphere-like structure. $\endgroup$
    – called2voyage
    Commented Jun 14, 2016 at 14:40
  • $\begingroup$ You need hundreds of asteroids perhaps. And the water you get will still sink below Martian crust. $\endgroup$
    – seilgu
    Commented Jun 14, 2016 at 15:55

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