3-to-2 Spin-Orbit Coupling

Mercury undergoes three sidereal rotations every 2 years. You
can see this by following the flag on Mercury (a) from
timestep 1 to timestep 15 and then (b) from timestep 15 to
timestep 29. The flag points to the right four times during this
interval (at times 1, 10, 20, and, finally, at 29). This means that
Mercury has rotated three times in exactly 2 sidereal Mercurian
years. Because a sidereal year is 88 Earth days long, a sidereal
day on Mercury is 58.7 Earth days long. During the same
interval, however, the Sun is at noon as seen from the flag’s
location only twice: at timestep 1 and timestep 29. Therefore, a
solar day is 176 Earth days long.