Mining the Moon and the Tides
A few years ago I was chatting with my older brother about my excitement for the potential of mining the moon to expand our ability to explore space, he expressed curiosity about the risks associated with how mining the moon would impact things like tides here on Earth. Today I decided to sit down and do some quick estimations in excel to estimate how much mass we would need to remove from the Moon for us to notice here on Earth.*
The Moon has been slowly drifting away from Earth for millions of years, expanding its orbit by about 3 cm/year (values I found ranged from 2.82-3.82 cm/year, and because I like whole numbers I chose 3 cm. This gives us a boundary estimation of how much the moon’s tidal forces change during a given year. Today the Moon’s semi-major axis is 384,400 km, that means a year from now** this value will be about 3 cm larger, now there are some notes about significant figures and other more detailed notes, but we’re only concerned about general trends. This 3 cm is vanishingly small on the scale of space and even smaller when we look at the gravitational acceleration the Moon applies to objects here on Earth.
Using the equation for gravitational acceleration a=Gm/r^2 for our year zero distance and year one distance, we find that the moon applies an acceleration of about 3.32E-5 m/s^2 fractions of a mm/s of acceleration, with the difference between the year zero value and year 1 value being 5.18*10^-15 m/s^2. so small I needed to look up the term, femto. 5.2 femto meters is the size of roughly 7 protons lined up, not atoms, protons, way smaller. So year after year the relative difference in attraction between objects on Earth and the Moon is practically zilch. So now we get to ask, how much material can we remove without things noticing on the time scale of millenia?
Basically we change which part of our equation is a variable, instead of treating the radius as dynamic, we are going to see how much mass the moon could lose in a year to have about the same effect as a year of the moon drifting away.
For my purposes I am limiting the extraction rate per year to be the equivalent of the rate of tidal loss of lunar drift, aka it would be as if the moon was now drifting away at twice the rate. Using these boundaries it looks like we could extract the equivalent of 14.5 billion tonnes of material from the lunar surface each year and be within my arbitrary boundary. To put that number into perspective humans extract about 90 billion tonnes of resources from planet Earth each year. Which is just a lot of stuff.
To further qualify this 14.5 billion tonnes estimate, we are assuming the materials being mined from the moon are permanently being shipped off the Lunar surface to go somewhere else. In 2022, about 2,000 tonnes of material was launched into space. That means lunar mines would need to be launching over 7 million times as much mass into space each year as humanity did in 2022 to reach our model. Additionally this assumes that the moon isn’t bringing in asteroids/comets and other materials to ensure a diverse enough portfolio of chemistries for an advanced economy.
TL:DR mining the moon is more likely to be a net benefit for human goals with space exploration and the impact on Earth from the perspective of changing tides is pretty negligible .
Hopefully this was at least moderately interesting, if you have any questions, suggestions for other posts, please let me know.
*please note I am only looking at a mass function question, there are some legitimate questions as to how if we changed the surface of the lunar surface in such a way to raise or lower the albedo of the lunar surface (aka how reflective the moon is) how would that impact things here on Earth. That’s a harder thing to estimate because you would need to do a deep dive on countless species’ use of lunar light as part of their evolutionary adaptations.
**roughly speaking