Let me just add one more thought on exactness:
The sun lines up in the position that it was at Creation EVERY YEAR. Not every 28. The event that happens once in 28 years is that it lines up on a Tuesday night at sunset (when the sun was created – according to the shitta we follow). In Jerusalem. Yet, you say the bracha at 7 am on Wednesday morning in NYC. So much for exactness – you might give a thought to the time of day that you should say it (and based on the time zone of Jerusalem) at the same time you give thought to the day we select to say it.
If you do the calculation with exactness (and I call on our resident math experts to help out), Bircas Hachama would NEVER take place. In 5769 years the sun has never returned to the place of creation AT sunset on Tuesday evening in Jerusalem (although it returns every year at a different time and/or day of the week). So your choice is to never have bircas hachama or to calculate it imprecisely. So we follow Shmuel for this, whose calculations are easy enough that anyone can work them out (or at least, it is easy to find someone in any locality who can handle his calculations).