That two minute mismatch on Mars is not a rounding error; it is a quiet piece of orbital mechanics written into the sky. A Martian sidereal rotation, measured against distant stars, takes about 24 hours 37 minutes, yet the solar day, measured from one noon to the next, stretches to roughly 24 hours 39 minutes.
The key point is blunt. Spin alone does not define a day. Because Mars orbits the Sun in prograde motion, each full rotation leaves the Sun slightly short of its old position in the Martian sky, so the planet must rotate a little farther to bring the Sun back to local noon. That extra angle, added every spin, is the same geometric effect that separates a sidereal day from a solar day on Earth, encoded in angular velocity and orbital period rather than in any atmospheric or surface process.
What this exposes is a constant tug‑of‑war between two motions that never synchronize. Planetary rotation tries to set a clean clock. Orbital revolution keeps hacking it. The Sun appears to drift because Mars advances along its elliptical path, and that apparent drift forces an extra slice of rotation, a small but persistent tax paid every single sol. In that discrepancy, timekeeping quietly admits that gravity, not clocks, is in charge.