As far as I know this account CANNOT be reconciled with the ROUND EARTH. From David Wardlaw Scott's TERRA FIRMA
Joshua 10:13
So the sun stood still,
and the moon stopped,
till the nation triumphed over its enemies,
as it is written in the Book of Jashar.
The sun stopped in the middle of the sky and delayed going down about a full day.
I do believe that this happened but wonder about the mechanism of such (I am a religious person but believe that Jehovah rarely intervenes physically in the world and thus what we read in the ancient texts, including the Bible, did happen but with a natural explanation. What worries me most about NASA and the other agencies poking around in the celestial sphere (and this is where I disagree with many of my compatriots- they are doing SOMETHING up there, just not what they are telling us) is that they may damage the delicate mechanism of this creation. My own view (and I have nothing to back this up other than my own intuition and thoughts) is that NASA, ESA and Roscosmos are in a race to breach the firmament. In addition I think there are efforts to tap the suns energy. All of this could lead to catastrophic and unforeseen results.