Follow up on the Earth stopping rotation question.
What if instead of stopping, the Earth simply slowed down or sped up its rotation rate (as it has, historically)?
Do we halachically count a single calendar day as passing using A) a fixed length of time, e.g. 24 hours or B) using the Sun's apparent position in a certain location [e.g. Jerusalem] to make a full cycle. or C) some other possibility.
To illustrate, let's say the Earth starts rotating 2x as fast. If A is true, then we'd still be counting seven 24-hour periods between one Shabbos and the next, but we'd have 14 sunsets during that time. If B is true, then from one Shabbos to the next would be seven 12-hour periods.