Why Mercury's year is 88 days.
Mercury is close to the Sun, so one trip around takes only 88 days. Neptune is about 78 times farther out and takes almost 165 years. Double a planet’s distance from its star and its orbital year becomes 2.83 times longer.
Central star mass M
the Sun
Distance from the Sun a
T ∝ a1.5
0.2 AUlog scale · 2× a → 2.83× T35 AU
Orbiting body’s mass m
~Marslog scale · selected star at 1 M☉= the Sun
Orbital period around the Sun
Ticks mark all eight planets; labels show four landmarks.
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Kepler’s third law says T² ∝ a³: a planet farther from its star has a longer orbital year. The full two-body form is T = 2π√(a³/(G(M+m))), where M and m are the central and orbiting masses. It applies to any two-body orbit; in AU, Julian years, and solar masses, T/yr = (a/AU)1.5/√((M+m)/M☉), because GM☉ = 4π² AU³/yr². The star pills show that a heavier star makes the same orbit faster; the mass slider shows why a planet’s own mass barely matters until it approaches a star’s mass. TRAPPIST-1 (0.09 M☉), Proxima Centauri (~0.125 M☉), and Sirius A (~2 M☉) are rounded from NASA references; the simplified map still uses Solar-System distances. Planet distances and orbital years are rounded from NASA/JPL’s planetary orbital elements and physical-parameters table. See NASA on TRAPPIST-1, Proxima Centauri, and Sirius. See the Wikipedia article on Kepler’s laws of planetary motion for the full derivation.
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