Why Mercury's year is 88 days.
Mercury orbits the Sun in 88 days; Neptune takes 165 Earth years — roughly 690 times longer. Yet Neptune sits only about 78 times farther from the Sun than Mercury does. Period grows much faster than distance, because it scales with distance to the 1.5 power.
log-compressed radial scale — not to true linear distance
Semi-major axis a
T ∝ a1.5
0.2 AUlog scale · double a · 2.83× the period50 AU
Try
Kepler's third law states that the square of a body's orbital period is proportional to the cube of its semi-major axis: T² ∝ a³, or precisely T² = 4π²a³/(GM) for a body orbiting a much larger mass M, where G is the gravitational constant. For anything orbiting the Sun, with T measured in Earth years and a in astronomical units (1 AU = Earth's average distance from the Sun), the constants 4π²/(GM☉) collapse to 1 — leaving the tidy special case used above, T = a1.5. That simplification is specific to the Sun's mass and to AU/year units; a moon orbiting a planet, or a planet orbiting a different star, would need the general form rescaled with that body's own GM. The orbit diagram above uses a log-compressed radial scale, not true linear distance, since Mercury (0.39 AU) to Neptune and beyond (30–50 AU) span nearly two orders of magnitude and wouldn't otherwise fit in one honest view. See the Wikipedia article on Kepler's laws of planetary motion for the full derivation.