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For solar orbits in years and AU, what is Kepler's third-law relation?

P squared equals a cubed.

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  1. P equals a
  2. P cubed equals a squared
  3. P squared equals a cubed ✔

Why: For a small body orbiting the Sun, the square of period P in years equals the cube of semimajor axis a in AU. More distant planets therefore have much longer periods.

Huh, didn't know that: An object at 4 AU has an 8-year period because 4 cubed is 64 and its square root is 8.

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Kepler's third law has a square relationship with a cubic personality.
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References

Answer: P squared equals a cubed. For a small body orbiting the Sun, the square of period P in years equals the cube of semimajor axis a in AU. More distant planets therefore have much longer periods.

  1. Orbits and Kepler's Laws science.nasa.gov/solar-system/orbits-and-keplers-laws
    The orbital period of a planet, squared, is directly proportional to the semi-major axes of its orbit, cubed.
    Checked 2026-10-10.

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