"Weapon platform" or "weapons platform"?
Solution 1:
I think they're both possible; the difference to my ear is that I would expect an "orbital weapons platform" to be some sort of, well, platform, which supports or can support multiple weapons, while an "orbital weapon platform" could just be shortened to "orbital weapon."
Solution 2:
"Orbital weapon platform" sounds like there might be only one (very large) weapon on the platform, whereas "Orbital weapons platform" sounds like it might be bristling with many weapons.
That's how it sounds to my native English ears.
Solution 3:
It's the singular of a noun that is normally used as modifier for another noun.
Apple will publish the new version of its 64-bit operating system very soon.
The new orbital weapon platform will be operative before the end of June.
If I look at weapons platform on the Corpus of Contemporary American, I find eleven instances of the phrase (with six instances used in fiction contexts), and two instances of weapon platform). Five instances of weapons platform have been used in the period 2005-2010.