Kepler's laws describe how planets move around the Sun with remarkable accuracy. They replaced the older idea of perfect circular motion with ellipses, changing astronomy into a quantitative science. These laws matter because they let us predict planetary positions, compare orbits, and understand the motion of moons, comets, satellites, and exoplanets.
They also connect observation to deeper physical causes.
Key Facts
- Kepler's first law: planets move in ellipses with the Sun at one focus.
- For an ellipse, the semi-major axis a is half the longest diameter of the orbit.
- Kepler's second law: a line from the Sun to a planet sweeps out equal areas in equal times.
- A planet moves faster near perihelion and slower near aphelion.
- Kepler's third law for objects orbiting the Sun: T^2 proportional to a^3.
- Newton explained Kepler's laws using gravity: F = Gm1m2/r^2 and centripetal acceleration.
Vocabulary
- Ellipse
- An ellipse is an oval-shaped curve with two fixed points called foci, where the sum of the distances to the foci is constant.
- Focus
- A focus is one of two special points inside an ellipse, and in a planetary orbit the Sun lies at one focus.
- Semi-major axis
- The semi-major axis is half the longest width of an elliptical orbit and is often used as the orbit's average size.
- Perihelion
- Perihelion is the point in a planet's orbit where it is closest to the Sun.
- Aphelion
- Aphelion is the point in a planet's orbit where it is farthest from the Sun.
Common Mistakes to Avoid
- Putting the Sun at the center of the ellipse, which is wrong because Kepler's first law places the Sun at one focus, not usually at the center.
- Assuming planets move at constant speed, which is wrong because Kepler's second law means they speed up near the Sun and slow down far from it.
- Using diameter instead of semi-major axis in T^2 proportional to a^3, which gives incorrect comparisons because a is half the long axis of the orbit.
- Thinking Kepler's laws apply only to planets, which is wrong because they also describe moons, artificial satellites, comets, and many binary systems when gravity dominates.
Practice Questions
- 1 A planet has a semi-major axis of 4 AU. Using T^2 = a^3 for orbits around the Sun, find its orbital period in Earth years.
- 2 Planet A has a semi-major axis of 1 AU and Planet B has a semi-major axis of 9 AU. How many times longer is Planet B's orbital period than Planet A's?
- 3 A comet travels in a very stretched elliptical orbit around the Sun. Explain where it moves fastest, where it moves slowest, and how Kepler's second law supports your answer.