EARTH & SPACE SCIENCE Chapter 27 Planets of the Solar System 27.2 Models of the Solar System

27.2 Models of the Solar System Objectives  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.

Early Models of the Solar System  Aristotle suggested a geocentric (Earth- centered) model of the solar system that describes the sun, stars, and other planets revolving around Earth.  Aristotle’s model failed to explain retrograde motion where some planets appear to be moving backward in the sky relative to stars.  Ptolemy proposed that planets moved in small circles, called epicycles, as they revolved in larger circles around Earth.

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Early Models of the Solar System  Copernicus proposed a heliocentric (sun-centered) model of the solar system in which the planets revolved around the sun in the same direction, but at different speeds and distances from the sun.  In this model, planets that are slower than Earth appear to move backward.  Galileo Galilei observed four moons orbiting Jupiter. on/Physics/NSCI1000/Pseudo- science/Copernicus_vs_Ptolemy.html

Kepler’s Laws  Tycho Brahe made many detailed observations of the solar system.  After his death, one of his assistants, Johannes Kepler, discovered patterns in Brahe’s observations.  The law of ellipses states that each planet orbits the sun in a path called an ellipse – not in a circle (Kepler’s First Law).  An ellipse is a closed curve whose shape is determined by two points (foci) within the ellipse.

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Kepler’s Laws  In planetary orbits, one focus is located within the sun.  Elliptical orbits vary in shape.  The eccentricity is determined by dividing the distance between the foci of the ellipse by the length of the major axis.  The law of equal areas (Kepler’s second law) states that equal areas are covered in equal amounts of time as an object orbits the sun.  This second law addresses the speed at which objects travel at different points in their orbit.

Kepler’s Laws  An orbital period is the time required for a body to complete a single orbit.  The law of periods (Kepler’s third law) describes the relationship between the average distance of a planet from the sun and the orbital period of the planet.  The mathematical equation is K x a 3 = p 2  K is one when the distance is measured in astronomical units and the period is measured in Earth years.  Average distance of the planet from the sun is a.  The period is noted as p.  For example, if astronomers note that Jupiter’s orbital period is 11.9 Earth years, the square of 11.9 is 142 – the cubed number of 5.2 – therefore Jupiter is 5.2 AU from the sun.