Download Planets of the Solar System Section 2 Kepler`s Laws, continued

Planets of the Solar System
Section 2
Section 2: Models of the Solar System
Preview
• Key Ideas
• Early Models
• Kepler’s Laws
• Newton’s Explanation of Kepler’s Laws
Planets of the Solar System
Section 2
Key Ideas
• Compare the models of the universe developed by
Ptolemy and Copernicus.
• Summarize Kepler’s three laws of planetary motion.
• Describe how Newton explained Kepler’s laws of
motion.
Planets of the Solar System
Section 2
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.
Planets of the Solar System
Section 2
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.
Planets of the Solar System
Section 2
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.
Planets of the Solar System
Section 2
Kepler’s Laws, continued
The diagram below demonstrates Kepler’s Law of Equal
Area.
Planets of the Solar System
Section 2
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.
Planets of the Solar System
Section 2
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.