The whole point of establishing a base on the moon is to set up a factory for making parts for a space habitat at the Lagrange Point L4. A habitat is going to be a very large construction project, just the launching of all the material into a lunar orbit is going to be an enormous undertaking. We could use rockets, but there may be a better way. Build a magnetically levitated rail line. Have a single car large enough to accommodate the largest item you are going to want to launch into orbit. Accelerate the car to something greater than orbital velocity, and release the item. It will float upward into orbit around the moon. It should be no great shakes for a small rocket to boost it from there up to the Lagrange point.
Build a magnetically levitated rail line. That sounds simple enough, we have done that here on Earth. If we can do it here we should be able to do it on the moon. Stands to reason, eh? Build a magnetically levitated rail line that can propel a car to 3,000 MPH, which is roughly how fast you would have to go in order to put something in orbit around the moon. That might be a bit of a challenge. We certainly are not going to do that here on Earth, wind resistance might be a bit of a problem. Keeping the car from incinerating might be a bit of a problem. On the moon, there would be no air resistance, so that would not be a problem. Still, getting a device like this to go this fast could be a bit of a trick. How long would this rail line need to be? If you could accelerate at one gravity (32 feet per second, per second), it would take almost 60 miles to reach orbital velocity. At this point you are travelling about one mile per second, so you don't want to delay releasing the payload. Every second you delay you consume another mile of track. And then you would need as much or more track to slow down.
And let us not forget that the weight of the payload goes down as we accelerate, although at one gravity of horizontal acceleration, the downward force of the moon's gravity is only small part of the force acting on our maglev rail car. When we finally reach our release velocity, the weight of the payload, and the whole car for that matter, will be negative, so the magnetic levitation at this point will need to be working in the opposite direction, holding the car down instead of supporting it.
The supports for this rail line are going to need to be more sophisticated than the rail line itself. Maglev operates with a clearance in the neighborhood of an inch. I have no doubt we can construct a line that will be straight enough for a maglev rail car to work, but how long will it stay that way? Thermal expansion and contraction, shifting of the moons surface, moon quakes, the stresses imposed by accelerating many ton payloads will all try to deform a rail that needs to remain perfectly straight. Okay, perfectly curved, as it will be following the curvature of the moon.
The supports will need to be self aligning, allowing shifts to the left and right as well as up and down. Further, they will need to let the rail float in the direction of travel to allow for thermal expansion and contraction, but when it is launch time, they will need to clamp down to provide something for the rail car to push against when it accelerates and when it brakes. And what kind of effects is the launching itself to going to have? Will the rail itself stretch? Heat up? Deform? A great deal of experimentation will need to be done before we start building this maglev launcher on the moon.
3 hours ago