Another interresting topic, Slipweed.
Normally, to be complete a sentence must have a subject and a verb;
depending on the verb, it may also require an object. I say,
normally, because sometime for effect a very short sentence is used
with just a verb, or just a noun, or even just an adjective or
adverb. e.g.
"I was becoming desperate. What could I do? Think."
or, "In the nick of time the police arrived. A miracle."
or, "The police did arrive, but they were late. Very."
A sentence does not have to contain within itself all the
information needed to make sense, particularly if it uses pronouns
that refer to something else; they are expected to be read in
context.
What I didn't like about the Saturn quote above, however, was the
use of the word 'however'. To my mind that should have been the
start of a new sentence. Without the 'however' the semicolon is
fine; 'this' refers to the fact revealed in the previous statement
and so makes a complete sentence.
I hope this helps and that I haven't, inadvertently, used any
semicolons incorrectly!