How much energy would be required to launch a 10km x 10km x 10km cube into LEO?

I know this is a bit of a ridiculous scenario, I am just looking for a very conservative estimate as to how much force would be required to get something orders of magnitude bigger and more awkard than a normal payload into orbit.

Basic Assumptions:

• Per the title, the object is a 10km x 10km x 10km cube
• Density of the cube is 3 g/cm^3.
• Starting position is such that the top of the cube is at sea level. Just assume there is a pit big enough to accommodate this without hitting the sides.
• Orientation is flat side up rather than a corner (terrible aerodynamic profile).
• Located on the 35th parallel north.
• This might be better suited to Worldbuilding since it is completely hypothetical. Apr 11, 2022 at 18:38
• Is that 3 billion tons into orbit? So only thing that dimensiion is gonna do is to add aerodynamic losses. Else point mass can be considered. Or how about, energy required to put 3 ton satellite into orbit multiplied by 1 billion times as an estimate? Apr 11, 2022 at 20:07
• @code-gal You probably mean 'energy' rather than 'force'. The force required would be equal to its weight. Apr 12, 2022 at 5:05
• One way to look at it is that with anything resembling current tech, it would take longer than the Earth has left before it gets swallowed up by the sun. Apr 12, 2022 at 22:39
• The other question is where are you going to get a 10km cube (and hold it up against Earth gravity let alone stresses of flight). Apr 13, 2022 at 5:29

1 Answer

What you are suggesting is currently in the realm of science fiction.

You are proposing to put $$(10~\mathrm{km})^3 \times 3~\mathrm{g/cm^3} = 3 \times 10^{15}~\mathrm{kg}$$ or 3 trillion metric tons in orbit.

To get some idea of what this means, a recent payload record for the SpaceX Falcon 9 was putting 16.25 metric tons in orbit. So you would need something like the equivalent of 200 billion Falcon 9 launches to put your cube in orbit. Moreover, the total mass of put into orbit by humans is something like 15,000 metric tons.

Doing what you propose with current technology would destroy the biosphere long before you got anything near 3 trillion tons in orbit. The energy requirements, mining, materials production, and pollution would make all previous human endeavors look tiny in comparison. For instance, it's been estimated that a single rocket launch puts 300 tons of CO2 into the upper atmosphere. Multiply this by 200 billion launches, you get 60 trillion tons, which is more than 1000 times the current worldwide output per year (already causing global warming) and is also like 30 times the amount of CO2 currently in the atmosphere (2 trillion tons). So you couldn't do this without causing massive global warming.

There would have to be a major change in technology and infrastructure to enable such a launch. The materials, resources, and energy required to undertake such an endeavor likely exceeds that produced in the entirety of human history. The dry mass of a Falcon 9 is 22.2 metric tons. Let's say this consists of about 20 metric tons of aluminum. For 200 billion Falcon 9 launches we'd need 4 trillion tons of aluminum. Only 64 million tons of aluminum were produced were produced worldwide in 2019, so you'd need to maintain our yearly production of aluminum for 62,500 years just to have enough aluminum to build the rockets. Most likely, all known ore deposits would be exhausted long before you obtained this much aluminum.

• The annual global energy consumptoin is estimated as a bit less than E = 6 * 10^20 J. That's (very) theoretically enough to accelerate m = 3 * 10^15 kg to a velocity v = sqrt(2E/m) ~ 632 m/s². That's less than 10% of what we need, so we need more than a century's global energy consumption (and a perfect drive instead of rocket propulsion) Apr 12, 2022 at 21:56
• Thanks, and it is definitely in the realm of science fiction. This question came out of a discussion about how big of a chunk of Earth we could get off of a dying Earth so destroying everything and anything in the process is on the table. Apr 13, 2022 at 18:17