Kepler's three laws describe how planets, moons, comets, and satellites move in orbit around a larger body. This cheat sheet helps students connect orbit shapes, changing speeds, and orbital timing in one clear reference. These laws are essential for understanding the solar system and for solving basic astronomy problems involving periods and distances.
The first law says orbits are ellipses with the central body at one focus. The second law says an orbiting object sweeps out equal areas in equal times, so it moves faster when it is closer to the central body. The third law connects orbital period and average orbital distance using P^2 = a^3 when P is in Earth years and a is in astronomical units for objects orbiting the Sun.
Key Facts
- Kepler's first law states that planets move in elliptical orbits with the Sun at one focus of the ellipse.
- An ellipse has two foci, and the sum of the distances from any point on the ellipse to the two foci is constant.
- The semi-major axis, a, is half the longest width of an ellipse and represents the orbit's average distance from the Sun.
- Kepler's second law states that a line from the Sun to a planet sweeps out equal areas in equal time intervals.
- A planet moves fastest at perihelion, where it is closest to the Sun, and slowest at aphelion, where it is farthest from the Sun.
- Kepler's third law for objects orbiting the Sun is P^2 = a^3, where P is the period in Earth years and a is the semi-major axis in astronomical units.
- If a planet has a = 4 AU, then P^2 = 4^3 = 64, so P = 8 years.
- Kepler's laws describe orbital motion but Newton's law of gravity explains why the motion occurs.
Vocabulary
- Ellipse
- An oval-shaped closed curve with two foci, used to describe the shape of planetary orbits.
- Focus
- One of two fixed points inside an ellipse, with the Sun located at one focus for a planet's orbit.
- Semi-major axis
- Half of the longest diameter of an ellipse, often used as the average orbital distance.
- Perihelion
- The point in a planet's orbit where it is closest to the Sun.
- Aphelion
- The point in a planet's orbit where it is farthest from the Sun.
- Orbital period
- The time an object takes to complete one full orbit around another object.
Common Mistakes to Avoid
- Assuming planetary orbits are perfect circles is wrong because Kepler's first law says they are ellipses, although many are nearly circular.
- Putting the Sun at the center of the ellipse is wrong because the Sun is at one focus, not usually at the exact center.
- Thinking planets move at constant speed is wrong because Kepler's second law shows they move faster near perihelion and slower near aphelion.
- Using P^2 = a^3 with the wrong units is wrong because the simple form works for solar orbits only when P is in Earth years and a is in astronomical units.
- Confusing radius with semi-major axis is wrong because an elliptical orbit does not have one constant radius, so a represents half the longest width of the orbit.
Practice Questions
- 1 A comet orbiting the Sun has a semi-major axis of 9 AU. Using P^2 = a^3, what is its orbital period in Earth years?
- 2 A planet has an orbital period of 27 Earth years. Using P^2 = a^3, what is its semi-major axis in AU?
- 3 Mars has a semi-major axis of about 1.52 AU. Estimate its orbital period using P^2 = a^3.
- 4 Explain why a planet travels faster near perihelion than near aphelion using Kepler's second law.