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Someone put a lot of thought into this:
http://www.buildtheenterprise.org/
Of course, the one trillion dollar price tag will take some persuading....
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I doubt the wisdom of building something arbitrarily to the shape of a science fiction design. But, I like the idea of building an orbit-to-orbit transport of some kind. That idea makes a great deal of sense. You add a "landing boat" for visiting the surface, if needed.
Based on what we currently and demonstrably know how to do, I think that such a craft craft would be assembled from cylindrical docked modules, like the ISS. I also think that the habitable volume will be very small compared to the propellant volume, based on propulsion we know how to do and have done, at one time or another.
I rather think the ship we might build will be a slender linear stack of modules with habitat at one end and engines at the other, more like the "Discovery" in the movie "2001 A Space Odyssey". Except, rather than building a centrifuge inside the habitat, it would be easier just to spin the ship end-over-end, while in coast, to provide one full gee at the habitat module, at very low rpm, and with no bearings or anything else to worry about. Short term exposures to zero gee while de-spun for maneuvers should be no problem at all.
As for propulsion, with chemical rockets, the propellant volume is huge, and empty tanks will have to be staged off. The rocket equation evaluated at realistic mass ratios confirms this. It is even true for LH2-LOX, the very best we have. The trip is a "slowboat" minimum-energy orbit of 7-9 months one-way. That cannot be avoided. Given the wait for orbits to be right for return, this is about a 3 year mission.
4 decades ago we came within about a year of flying a solid-core nuclear thermal rocket engine called NERVA that used LH2 for propellant. It has been forgotten to death, and slandered with irrational fears, ever since. Using that technology, a modular Mars vessel is 3-4 times smaller. But it still must stage off empty tanks, and it must still fly by the "slowboat" min energy orbits. It's still about a 3 year mission.
The kind of propulsion we need for the fast trajectories does not yet quite exist in a usable form. Claims have been made about trips anywhere from 30 to 90 days one way using ion or VASIMR electric schemes. These have the specific impulse, but not the thrust per unit engine weight to pull that kind of a trip off. Basically you get a thrust measured in single-digit pounds for an engine system weighing tons, mounted in a vehicle weighing dozens to hundreds of tons. Just the getaway from LEO is months long. Whether you use nuclear or solar power, a MW-class electric generator is simply going to weigh many, many tons.
It might be wiser to put high-thrust chemical or nuke rockets for the getaway and arrival burns, and apply the electric stuff to speed up the coast in between. That might actually help. In that case, a slowboat mission might be done without staging empties off. Maybe even a bit faster.
There are some other concepts that might provide higher thrusts for the weight at high specific impulse. I am not familiar with them all. One I am familiar with is gas core nuclear thermal rocket. Some of the benchtop feasibility experiments were done 40 years ago. But no test devices were ever built. These are entirely "mythical" at this time, but the projected performance looked good enough back then to make one-way trip times to Mars in the 30-90 day range possible, all single-stage and completely re-usable. But until and unless someone actually builds one, these things remain speculations.
GW
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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