> The most expensive part of space travel now is getting from the earth's surface to a stable orbit, and a space elevator from the moon does exactly nothing to reduce this cost.
That's not the point, and not actually correct. [1] explains a lot of this. Getting to low earth orbit means you have to climb 100km, and go really fast. The climbing 100km part of this is easy - the going really fast bit is what makes going to space so expensive.
With this proposal, there will be a tether hanging down at the height of geostationary orbit which is travelling slowly around the earth - about 28 times slower than the orbital speed at that altitude. So, the elevator makes getting to the Moon cheaper by two mechanisms. Firstly, it means that a rocket just needs to get to geostationary orbit height, without having to do the speed bit as well. Secondly, you have a space elevator to get you the rest of the way.
Now, admittedly, geostationary height is much higher than low earth orbit, so the saving of not having to build up speed is not as extreme as if the tether hung lower. Geostationary orbit has a speed of 3.07km/s, so if you only have to go 1/28th of that, you are saving nearly 3km/s of delta-v on your rocket. This is not to be sniffed at.
The size of the rocket required to transport a set payload is exponential with the required delta-v, with a logarithmic base of the exhaust velocity of the rocket. So, if we can save 3km/s, and a decent rocket motor has an exhaust velocity near 3km/s, then the size of the rocket can go down by a factor of about e. This is a very nice saving.
One could extend the analogy, if one were to consider a slightly longer tether, and imagine we can get it to hang down to an altitude of 100km without hitting any satellites, then it would be travelling across the sky at around 60km/h. You could use a very small rocket indeed to climb up 100km, grab onto the end, and then go all the way to the moon. At a push, the X15 rocket-plane, plus some decent guidance system could manage it.
That's not the point, and not actually correct. [1] explains a lot of this. Getting to low earth orbit means you have to climb 100km, and go really fast. The climbing 100km part of this is easy - the going really fast bit is what makes going to space so expensive.
With this proposal, there will be a tether hanging down at the height of geostationary orbit which is travelling slowly around the earth - about 28 times slower than the orbital speed at that altitude. So, the elevator makes getting to the Moon cheaper by two mechanisms. Firstly, it means that a rocket just needs to get to geostationary orbit height, without having to do the speed bit as well. Secondly, you have a space elevator to get you the rest of the way.
Now, admittedly, geostationary height is much higher than low earth orbit, so the saving of not having to build up speed is not as extreme as if the tether hung lower. Geostationary orbit has a speed of 3.07km/s, so if you only have to go 1/28th of that, you are saving nearly 3km/s of delta-v on your rocket. This is not to be sniffed at.
The size of the rocket required to transport a set payload is exponential with the required delta-v, with a logarithmic base of the exhaust velocity of the rocket. So, if we can save 3km/s, and a decent rocket motor has an exhaust velocity near 3km/s, then the size of the rocket can go down by a factor of about e. This is a very nice saving.
One could extend the analogy, if one were to consider a slightly longer tether, and imagine we can get it to hang down to an altitude of 100km without hitting any satellites, then it would be travelling across the sky at around 60km/h. You could use a very small rocket indeed to climb up 100km, grab onto the end, and then go all the way to the moon. At a push, the X15 rocket-plane, plus some decent guidance system could manage it.
[1] https://what-if.xkcd.com/58/