What does the Bible say about how the solar system revolves?

The Bible makes no claims regarding the orbital dynamics of the solar system, so there is no case to be made from scripture in the matter you mentioned. The Bible describes the working of our universe from the perspective of a human being standing on earth (e.g., seeing the sun “rising” or “setting” etc.), but these descriptions were never offered in the Bible as a literal, scientific explanation of our universe’s functioning. Therefore proper biblical exegesis prevents us from misapplying such descriptions to arrive at foolish, pseudo-scientific notions. 

Moreover, we caution every Christian against becoming deceived by false teaching that opposes plain truths and promotes novel and sensationalistic myths. Paul said such interests would be evidence of the end times, when believers are swept away by false teaching:

2Tim. 4:3 For the time will come when they will not endure sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires,
2Tim. 4:4 and will turn away their ears from the truth and will turn aside to myths.

1Tim. 6:20 O Timothy, guard what has been entrusted to you, avoiding worldly and empty chatter and the opposing arguments of what is falsely called “knowledge” —
1Tim. 6:21 which some have professed and thus gone astray from the faith.  Grace be with you.

Therefore, we exhort believers to set aside concern over these matters entirely. Do not waste time in endless and unprofitable arguments on one side or the other of these myths. Return to scripture seeking a meaningful understanding of Christ and your walk with Him that will profit you into eternity.

Scripture quotations taken from the (NASB®) New American Standard Bible®, Copyright © 1995, 2020 by The Lockman Foundation. Used by permission. All rights reserved. www.lockman.org