Anything containing the words Star Trek, or any material shown onscreen from Star Trek, including Font, Images, Sound, Terminology/Technology that is copywritten, Etc that is in any part belonging to Star Trek, once published, falls under the Fair Use policy of the Paramount Copywrite of Star Trek....
As such since Star Trek is a theme in the article, it technically would belong to Paramount, however it can be distributed for free across the internet or in hardcopy media...
If your intent is to claim a profit from article, then it is best to not post it, but take it to a publisher that currently holds a Paramount license for Trek material..
It does not matter if it is posted here or on your own private host site.. as soon as the story becomes public access, it falls under Paramount Copywrite and Fair Use policy (anyone can copy and distribute the material at their discression due to it being fan made material of copywritten/tredemarked property).. However the gentleman's agreement concerning Trek Material is that no one will plagerize your stuff (even though they are legal to do so under Fair use clause) or alter your stuff without your explicit permission to do so.. this holds true through out the Trek community.
As far as I am concerned, the original Author has final say on the material.. however being Trek Based, then Paramount Copywrite takes precident, and Fair Use makes your material Open Source for anyone else.. However you can take anyone using your material to Paramount and hit them for plagerism.. Paramount takes over legally from there.