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Lets say that we have an interplanetary society using the ice from asteroids to convert it into rocket fuel, how long would it take before we have used up all the ice on the asteroids.

Conditions:

  • We would have a much higher population. Currently it is around 8 Billion people. For this questions we assume we have a popular of around 100 Billion
  • There would be around 50000 rockets every day needing to get refilled
  • Let’s assume that reuse able rockets are filled on Earth and land there, so only the small capsules are refilled. Even though the size I am thinking of isn’t so small. Something of the size of a Starship capsule.
  • Also the rockets will only be 80% filled because I assume there would already be some fuel left on the rocket from beforehand.
  • To make calculations easier, lets say each capsule weighs about 250 tons.
  • In the calculations only consider the ice from the asteroids in the inner asteroid belt. Nothing from the Kuiper Belt
  • The rockets will have on average 5km/s of delta V after being refilled.

With these conditions, how long would it take before all the ice on the asteroids will be used up?

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  • $\begingroup$ Is there much water in the inner asteroid belt? It's on the hot side of the frost line (I think). $\endgroup$ Mar 22, 2023 at 16:10
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    $\begingroup$ Isn't this completely hypothetical question a better fit for Worldbuilidng? $\endgroup$ Mar 22, 2023 at 16:41
  • $\begingroup$ @OrganicMarble, I also agree that this would be better for Worldbuilding. Since I do not have an account on Worldbuilding I wanted to try it here. If it doesn't work I will move it to Worldbuilding. $\endgroup$ Mar 22, 2023 at 17:07
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    $\begingroup$ I’m voting to close this question because it belongs on worldbuilding $\endgroup$ Mar 22, 2023 at 23:28
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    $\begingroup$ @Starshipisgoforlaunch "because belongs on" is not a close reason. We close a question when it's off-topic where it's asked. Suggesting another site is also helpful but should be done separately. $\endgroup$
    – uhoh
    Mar 23, 2023 at 22:54

1 Answer 1

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Before we see how long it would take before all the ice would be used up, lets see how much fuel is being used.

In the question it says that 50k spacecrafts will be filled up to 80% every day. Each spacecraft will weigh around 250 tons.

If we use the Tsiolkovsky formula: $$\Delta v = v_e \cdot \ln\left(\frac{m_o}{m_f}\right)$$ It would be used possible to find out how much of the mass is fuel.

  • Delta V of 5 km/s
  • ISP of 300
  • Starting mass 250 tons
  • G of 9,81

When I put the numbers in my calculator I got around 45,7 tons dry mass. Meaning that a full tank would have 204,3 tons of fuel. 80% of that would be around 163,4 tons. So every rocket would need on average 163,4 tons of fuel when being filled.

If 50k spacecrafts are being filled every day and each needs on average 163,4 tons of fuel, then that means that each day around 8.172 million tons a day of fuel will be needed.

Currently there is not a lot of data about how much ice there is in the inner asteroid belt so I decided to just make a chart.

Amount of ice in the solar system in tons Time it would take before it will be used up
1M 3 hours
10M 1 day 5 hours
100M 293 days
1B 8 years
10B 80,4 years
100B 804,6 years
1T 8 046 years
10T 80 461,8 years
100T 804 618,51 years

Looking at this chart, I think that if there is somewhere between 100B to 1T tons of ice if not more then we could use it as a rocket fuel without worrying.

--edit--

In this answer https://space.stackexchange.com/a/63202/44505 it says that there is around 250 trillion tons of ice. According to my calculations it would be enough ice to support an interplanetary society like in the question for around 2 million years.

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  • $\begingroup$ Large range @The Rocket fan $\endgroup$ Mar 23, 2023 at 12:03
  • $\begingroup$ @Starshipisgoforlaunch that was purposeful because I couldn’t find any information about how much ice there is in the asteroid belt. $\endgroup$ Mar 23, 2023 at 13:49
  • $\begingroup$ Then this isn't that useful of an answer, is it. If i say this rocket has delta-V from 2000 m/s to 20000 m/s would that be useful. NO @The Rocket fan $\endgroup$ Mar 23, 2023 at 13:54
  • $\begingroup$ The question was how long would it take before all the ice was used up. Not about delta V. It did say in the questions that the rockets would have 5000m/s of delta V @Starshipisgoforlaunch. I don’t get your point. $\endgroup$ Mar 23, 2023 at 13:57
  • $\begingroup$ Just using a different example to demonstrate a point @The Rocket fan $\endgroup$ Mar 23, 2023 at 13:59

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