Yeah, the explore feature is a known bug, cdunn100, and has been for a while. I'm not sure if Mike (The developer) knows what the cause is - yet - though.
Would it be possible for you to time how long it takes to process a game for us? If you could time how long it takes for a new game to load (From the moment you click on ok to the moment that the galactic map appears on screen) and how long turn 1 and turn 10 take to process, we would have figures and be able to tell you if you are experiencing a significantly slower processing time than most other people.
For me, a small map with dense stars, dense planets, and many minor races takes about 30-40 seconds to load, turn 1 takes about 5-7 seconds to process, and turn 10 takes about 5-8 seconds to process. I have Windows XP Home, Pentium 4 Processor @3.21Ghz, 1Gb RAM, and a Radeon X1650 512mb graphics card (Which I only upgraded last week from a Radeon 9250 128mb card
)