Key Concepts: Kepler’s Laws

Kepler's Three Laws of Planetary Motion

1. Law of Ellipses

• Every planet orbits the Sun in an ellipse, with the Sun at one focus.
• Most planetary orbits are nearly circular (low eccentricity).

2. Law of Equal Areas

• A line from the Sun to a planet sweeps out equal areas in equal times.
• Planets move faster when closer to the Sun (perihelion) and slower when farther (aphelion).

3. Law of Periods (Harmonic Law)

• T² ∝ r³ — the square of the orbital period is proportional to the cube of the semi-major axis.
• T² = (4π²/GM) r³. This allows calculating one quantity from the other.

Applications: Kepler's third law is used to determine the masses of stars and planets, and to predict orbital parameters of satellites.