How important the science is depends on the kind of scifi you're writing. Connie Willis has written some excellent science fiction with almost no science in it. On the other hand, Robinson's Mars trilogy would have been a disaster if he hadn't done his homework. (And I think KSR's degree is in literature, not science.) It sounds like the OP is writing something military, which probably places it somewhere in between the two examples above.
I would say if you're writing military scifi, the two most important things are to understand some relativity, and to understand the difference between how spaceships move and how airplanes move. (As much as I love Star Wars, I'm glad I didn't know any physics in 1977. :-)
"It's only Neutron. We call him that because he's so positive." --from This Island Earth