|substituting lunar gravitation constant in upper equation|
I don't know if that is valid, but for the numbers above the "g" force would be ??? Actually, the number got larger for some reason. One would think otherwise. In the original equation, it would be over 160 g's. That would be too much for people.
On second thought, a racetrack setup like this may be unrealistic. Perhaps you could set up a "space cannon" type gizmo in order to move stuff around on the moon, or into orbit. Those were tested at hypersonic speeds on Earth already. I wonder if you could build one that would obtain orbital velocity?
Actually, the ground test mentioned here would achieve escape velocity from the Moon.
How could you build something comparable on the Moon? You could load one of these on a space craft that could land on the lunar surface. It would have to be constructed in place and it may need to use materials obtained from the Moon itself. Or, if it couldn't be obtained from the Moon itself, the raw materials could come from the Earth, and processed on the Moon.
By processing, I mean, taking say, basic steel, or aluminum, or some other metal that could be easily transported to the lunar surface. It would then be melted down and cast into a the appropriate shape desired.
Here's an idea that I've considered in connection to landing on the Moon without incurring as large of a mass penalty. You could use solid metals as reaction mass for your descent. The descent should be nearly vertical over the landing area so as to "recycle" the metals later after landing.
You would heat a gas, probably hydrogen hot enough that it could push a larger mass of metal downward with considerable velocity towards the lunar surface. The opposite reaction is according to Newton's laws, and it would slow down the descent as it would with a hot gas. The difference is that the gas dissipates, but the metal remains to be collected later.
Several tons could be expelled in such a manner. Although the final descent should be with a conventional engine setup. This could be considered a dual staged descent.
The discussion of a space gun as an example above mentions a 16 inch 100 caliber Navy gun. Here is a discussion of how big such a gun would be in length. The calculation would be 16 inches x 100 = 1600 inches long. 133 feet! The slug weighed in at 180 Kg. ( nearly 400 lbs).
Now, in order to build a O'Neil colony in space with lunar materials, you would need to somehow break down the pieces to that size and weight, and fire them many, many times. You may want to aim at L4 or L5 Lagrange point in the Earth Moon system. One proposition would be to load up a module of carbon nanotube superstructure at a time. The superstructure would be able to be inflated when it arrives the Lagrange point. Subsequent firings could place stuff inside the superstructure to build it from the inside.
An estimate to its size? Maybe 500 ft to 1000 ft cylinders that would fit end to end so that it could make a torus, or donut shape. Or perhaps, the torus could be made with the carbon nanotubes making up the foundation of subsequent construction. It would be set up in a ring 1 mile in diameter, consisting of 500 to 1000 ft at a time. This would mean 3 to 6 main pieces connected together to form the basic structure.
It might look like a bicycle tire, with the carbon nanotubes making up the rim. You would then build inwards toward the hub with "spokes" to fit towards the middle towards the hub. The spokes could be tethers that fit into a central hub and extended out towards the periphery where the carbon nanotube "tube" is. Like the bicycle tire.
Now, getting the spokes and the hub into position with the space gun may be a challenge. But since they are tethers, they may be coiled inside a container.
By the way, I am making this stuff up as I go along. This is like thinking aloud. The problem I see is that the carbon nanotube that forms the rim may be desirable a habitable space, but since they have to be shot up separately and connected together, they won't be as open as you may like. This may give something of a confining feel to the place.