If the design goal is to have weapons that can wipe out all life on a planet, and move between planets, then the main problem is just transporting planet-destroying weapons (with existing tech, probably thermonuclear warheads) to other planets, and largely depends on how far away the other planets are, and how much range, desired operating time away from base, and how many planets you want to be able to destroy before returning. And, countermeasures against existing weapons. Every requirement adds weight, which adds to fuel requirements. The most efficient in terms of cost might probably be a stealth vessel that returns to resupply after every attack, depending on the layout of targets, but that would reduce its terror power, since with existing technology, it would take a long time to return to resupply.
The part about building a metallic small moon seems to not help the stated intention much at all. In fact, it makes it infeasible in many many ways, and accomplishes very little against current technology other than making it a great big slow-moving target.
So, missing features of the design listed (compared to Grand Moff Tarkin's Death Star) above include, in ascending order of impracticality:
Omitted features that might be practical and useful in a sci-fi fututre with somewhat higher technology levels and higher-tech-opponents than currently exist:
- No shields.
- No TIE fighter squadrons.
Impractical features that don't materially aid planet-destroying goals, but are quite possible with current technology:
- No pits to knock victims into.
- No trash compactors with monsters living in them.
- No place to land the Millennium Falcon.
- No equatorial trenches.
- No thermal exhaust ports.
Features which are theoretically possible with current technology, but are so impractical that they are almost impossible to do, and are crazy:
- No small-moon-sized massive metal ball.
- No lodging for millions of stormtroopers.
Features which there is no known way to do with current technology:
- No ability to jump the giant metal moon into hyperspace and quickly travel to other star systems.
- No ability to race a giant metal moon around a solar system.
- No conversion of planet into asteroid field.
- No artificial gravity.
- No long-range tractor beams.
- No giant flashy laser effects on planet-destroying weapon.
Given current technology, how many man-years would it take to build? (assume you already have enough steel, see question below)
Practical version: Depends on range specs. To make something to go nuke Mars - ~10 years?
Giant moon version: Insane amounts of man-years - you need to get the workers into space and keep them supplied, etc - use droids - you will still be overthrown (and/or die of old age) first unless you have an actual galactic empire with Star Wars technology.
How much metal is needed to build this ship?
Practical version: Probably not more than for a carrier battle group or two, probably best is light aluminium and other light materials.
Giant moon version: Using heavy metal is probably mostly silly, but if the point is you want a metal moon, then you want crazy amounts of metal. Probably your best bet is to find a way to use an asteroid belt (planet-size quantities, already in space), assuming you have one with high iron content.
Would it really take 833,000 years to get the necessary steel (as quoted in WP article, above)?
Depends on what is working on it in what conditions on what kind of planet etc., but I can imagine trying to model it and getting a result like that, yes. I think you'd be much better starting with an iron-rich asteroid belt or an existing small moon...
What would it cost? (anywhere near the White House's estimate of $850 quadrillion?)
It would cost letting go of the idea that money is meaningful, and imposing dictatorial rule.
Any scientific reason (ignoring the superlaser) why this ship is scientifically impossible?
Practical version - nope.
The big metal moon version:
- It's too heavy to move around.
- No hyperdrive.
- No artificial gravity.
- No long-range tractor beam technology.
- Mad impracticality.