Why outer planets take so long to orbit

Lesson notes

Key points

• Kepler's third law states that a planet's orbital period squared is proportional to its orbit's semi-major axis cubed.
• The semi-major axis is half the longest diameter of an elliptical orbit, effectively the average orbital distance.
• Newton later derived it from gravity, showing T² equals four pi squared a³ divided by G times the total mass.
• Astronomers use this to weigh stars and black holes, by measuring how fast objects orbit them.

Takeaway: T² ∝ a³: farther orbits are slower and longer.

Kepler's third lawSemi-major axisNewton's formWeighing masses