For example, a Chevy Cavalier with a 10 gallon fuel tank and an average fuel efficiency of 25 mpg will not go as far as a Saturn SL2 with a 9 gallon fuel tank and an average fuel efficency of 30 mpg. The Cavalier will get 200 miles of range and the SL2 will get 270 miles of range.

Thus, the Enterprise could visit 10,000 worlds if the engines are efficient, there a decent storage capacity for the matter and antimatter, and if the crew has a lot of time on their hands.

However, the other side to this problem is the number of planets within proximity to the Earth. Are there 10,000 planets within range of Earth given the range of the Enterprise? Possibly. When you count in all of the M class worlds and all of the non-M class worlds and the planetoids and the like, there will be a lot of them. 10,000 though? I don't know, that may be stretching it a good bit.

quote:

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At warp 5, 10,000 inhabited planets are within one year's journey, compared to only 18 at warp 2.

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In any case, the "within range" issue could be modified by tactical considerations. You can't send a starship so far away that it cannot return to take part in an interstellar war you might feel like having. A fast ship can go farther out and still be back by dinnertime. And if you have a greater number of ships, you can spare more of them for long-duration exploration.

Also, early exploration efforts would make use of Vulcan knowledge. Their existing records would reveal which places were not worth a visit, and might thus speed up exploration. Then again, the records might be pessimistic or outright rigged, deliberately slowing down human expansion.

Doing the math, warp 5 in Okudaic-cubic terms ought to be about 15 times faster than warp 2, and the volume covered by a series simple straight-out exploration runs then 15^3 times larger, or about 3500 times. The Bible suggests 5000 times, assuming constant star density (or, rather, constant density of class M planets), so we're in the ballpark. If we assume that Earth was in a low-density region (explaining how we could stay undisturbed so long), we're talking business.

But it's all theoretical business. One ship cannot explore a sphere all at one, just one radius of the sphere at a time. And the bigger your sphere, the more ships you need to fill in the gaps between the radii. Archer wouldn't meet 10,000 alien races in his lifetime (duh - he has, what, fifty years of life to look forward to, so he'd have to meet an alien every second day for the rest of his life), nor would a Starfleet of a hundred Enterprise-like ships.