Planetary Orbits and Kepler's Laws

Planetary Orbits and Kepler's Laws

Overview

This lecture covers the transition from geocentric to heliocentric models of the solar system, focusing on Kepler's First Law and key definitions related to planetary orbits.

The Shift to Heliocentrism

• For centuries, people believed in a geocentric (Earth-centered) model of the solar system.
• Copernicus reintroduced the heliocentric (Sun-centered) model, with planets orbiting the Sun in circles.
• Kepler supported the heliocentric model using improved star charts and discovered it needed adjustment.

Kepler’s First Law of Orbits

• Kepler’s First Law: The orbit of each planet is an ellipse with the Sun at one focus.
• An ellipse is an oval shape, not a perfect circle.
• The Sun is not at the center of a planet’s orbit but at one focus of the ellipse.
• Orbits vary in distance from the Sun; planets are sometimes closer or farther at different times.
• The other focus of the ellipse is empty—nothing is located there.

Ellipses, Foci, and Orbital Properties

• A perfect circle is a special case of an ellipse with both foci at the center.
• The more stretched the ellipse, the farther apart the foci are.
• Most planetary orbits in our solar system are close to circles (low eccentricity).
• Comets have orbits with high eccentricity—much more stretched out.
• The semi-major axis ("a") is the average distance from the planet to the Sun and is important for describing orbit size.
• Eccentricity measures how stretched an orbit is (0 = circle, close to 1 = highly elongated ellipse).

Key Orbital Terms

• Perihelion: The closest point in a planet’s orbit to the Sun.
• Aphelion: The farthest point in a planet’s orbit from the Sun.

Key Terms & Definitions

• Heliocentric — Model with the Sun at the center of the solar system.
• Geocentric — Model with the Earth at the center of the solar system.
• Ellipse — An oval-shaped curve; not a perfect circle.
• Focus (plural: Foci) — Points inside an ellipse; the Sun is at one focus.
• Semi-major axis (a) — The average distance from the planet to the Sun, running from the center through a focus to the edge.
• Eccentricity — A value (0 to 1) describing how stretched an ellipse is.
• Perihelion — Closest orbital point to the Sun.
• Aphelion — Farthest orbital point from the Sun.

Action Items / Next Steps

• Review Chapter 3 for details on Kepler’s laws and orbital elements.
• Prepare for discussion of Kepler’s Second and Third Laws in the next class.