Interesting. Most people claim both that we will run out of natural resources and that population will grow indefinitely, which is impossible. Cool paper
It is extremely sad that we have not traveled beyond Earth orbit since the end of the Apollo program in 1972. Space exploration inspired many of us to study math and CS and fostered innovation. The majority of the most relevant people in tech in the last 30 years (Bill Gates, Jeff Bezos, etc.) have repeatedly commented how the Apollo missions were inspiration for the their studies and careers.
Correction: humans haven't travelled beyond low Earth orbit since 1972.
No human has ever travelled beyond Earth orbit. I believe the Apollo missions may have achieved Earth escape velocity, though their destination was Lunar orbit, which remains within Earth's.
It's a marvellous fact that the Apollo missions achieved escape velocity, or close enough that they could have done so with small design modifications.
The calculation is fun:
The kinetic energy required to escape Earth's orbit entirely is: G M / R, where G is Newton's constant, M is the mass of the Earth, and R is the radius of the Earth.
The kinetic energy required to get to the Moon is: G M / R - G M / r, where r is the distance to the moon.
To compute the ratio of the second quantity to the first, note that the GM factors cancel. So the ratio is:
(1/R-1/r) / (1/R) = 1 - R / r
The distance to the moon is about 60 times the radius of the Earth. So:
Kinetic energy required to get to moon / Kinetic energy required to escape Earth's orbit entirely = 1 - 1/60 ~ 98 %.
In other words, the Apollo missions had at least 98% the kinetic energy required to escape Earth orbit's entirely.
The program did serve as inspiration, no doubt, but the fair question to ask is whether it was a better way to spend money than .. you know, actual science. Was society better from this than for example developing nuclear fusion or cancer treatments, which probably weren't more outlandish ideas at the time than going to the moon?
What truly boggles the mind is that the US at the time was a country of housewives, racial segregation and prosecutions of gays and bisexuals. Yet, or perhaps because of that, they decided that the way forward was to build a moon ship. It says a lot about society at the time.
