Section 2: Models of the Solar System Preview Key Ideas Early Models Kepler’s Laws Newton’s Explanation of Kepler’s Laws

Early Models Aristotle suggested an Earth-centered, or geocentric, model of the solar system. In this model, the sun, the stars, and the planets revolved around Earth. Ptolemy proposed changes to Aristotle’s model. He thought that planets moved in small circles, called epicycles, as they revolved in larger circles around Earth. Copernicus proposed a sun-centered, or heliocentric, model of the solar system. In this model, the planets revolved around the sun in the same direction, but at different speeds and distances from the sun.

Kepler’s Laws Law of Ellipses Kepler’s first law, the law of ellipses, states that each planet orbits the sun in a path called an ellipse, not in a circle. An ellipse is a closed curve whose shape is determined by two points, or foci, within the ellipse. In planetary orbits, one focus is located within the sun. eccentricity the degree of elongation of an elliptical orbit (symbol, e) Elliptical orbits vary in shape. Its eccentricity is determined by dividing the distance between the foci of the ellipse by the length of the major axis.

Reading check Define and describe an ellipse. An ellipse is a closed curve whose shape is defined by two points inside the curve. An ellipse looks like an oval.

Kepler’s Laws, continued Law of Equal Areas Kepler’s second law, the law of equal areas, describes the speed at which objects travel at different points in their orbit. When the object is near the sun, it moves relatively rapidly. When the object is far from the sun, it moves relatively slowly. Equal areas are covered in equal amounts of time as an object orbits the sun.

Kepler’s Laws, continued The diagram below demonstrates Kepler’s Law of Equal Area.

Kepler’s Laws, continued Law of Periods Kepler’s third law, the law of periods, describes the relationship between the average distance of a planet from the sun and the orbital period of the planet. orbital period the time required for a body to complete a single orbit The mathematical equation, K x a3 = p2, where K is a constant, describes this relationship. The cube of the average distance (a) of a planet from the sun is always proportional to the square of the period (p). When distance is measured in astronomical units (AU) and the period is measured in Earth years, K = 1 and a3 = p2.

Newton’s Explanation of Kepler’s Laws inertia the tendency of an object to resist a change in motion unless an outside force acts on the object Newton’s Model of Orbits Newton discovered the force gravity. Gravity is an attractive force that exists between any two objects in the universe. While gravity pulls an object towards the sun, inertia keeps the object moving forward in a straight line. The sum of these two motions forms the ellipse of a stable orbit. The farther from the sun a planet is, the weaker the sun’s gravitational pull on the planet is.