[NeilBrainstrong]

I think it might be easier to construct some generation spacecraft in order to migrate to some habitable exoplanet instead of moving the entire earth.

In fact, I’m sure people will do this long before the sun burns out. Fusion propulsion for large interstellar rockets might be available as early as mid-22nd century. In a few millenia, a lot of exoplanets may have been colonized.

[NeilBrainstrong]

Okay, here are my complete calculations – initially I got some figures wrong, so these are the correct results.

The World Ocean has a mass of about 1.332*10^18 t.

In each ton of ocean water, there are 4.4 g of Boron.

This means that the total mass of Boron in the Ocean is about

MB = 1.332*10^18 t * 0.0044 kg / t = 5.86 * 10^15 kg.

81% of these are 11B:

M11B = 0.81 * 5.86 * 10^15 kg = 4.75 * 10^15 kg.

Which accounts to a number of 11B atoms of:

n11B = 4.75 * 10^15 kg / (11.01 * 1.66*10^-27 kg) = 2.6 * 10^41
(where 1.66*10-27 is the Atomic Mass unit, and 11.01 the Atomic mass of 11B).

Let’s suppose we can extract 10% of these – this gives an amount of

n11B_ex = 2.6 * 10^40.

Now, each fusion reaction produces

Ef = 8.7 MeV = 8.7 * 10^6 * 1.6 * 10^-19 J = 1.4 * 10^-12 J.

Fusing all the n11B_ex atoms will give a total energy of:

Etotal = Ef * n11B_ex = 3.64 * 10^28 J.

Let’s divide this between 10 billion people and use it over 1000 years = 3.16 * 10^10 s. This gives an individually usable primary power of:

Pind = Etotal / (10^10 * 1000 yrs) = 3.64 * 10^28 J / (10^10 * 3.16 * 10^10 s) = 115.2 MW.

-> Individual power consumption by country on Wikipedia

Using the Kardachev scale with Carl Sagan’s decimal refinement, the above power consumption puts us at:

K = 1 + 0.1 * log10 [115.2 * 10^6 W * 10^10 / 10^16 W ] = 1.206.

Today, we are at about K = 0.71.

PS: If we use the energy on the level of the present-day USA (10381.2 W / person), the energy resource would last for:

t_EnergyUSA = Etotal / (10^10 * 10381.2 J/s) = ~ 11 million years

This more moderate consumption rate would of course be wiser, as burning it all up over 1000 yrs would cause the planet to overheat quickly. Naturally, this problem would not arise if a lot of power is not used on earth itself but for spacecraft propulsion.

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