CHAPTER 2: Gravitation and the Waltz of the Planets Geocentric Model • • • • Earth centered Aristotle (384 - 322 B.C.) Heavens are fixed Circular orbits Problem with Geocentric Model • Did not explain retrograde motion, • Planets usually move from west to east along ecliptic. Occasionally they would stop and move from east to west Problem “solved” with Ptolemy 140 A.D. • Planets move around earth on epicycles. • Epicycles move around earth on deferents. • Seemed to solve problem of backward motion of planets. • Unchallenged for 1300 years even though it was not perfect Heliocentric Model • Sun in in the center • First proposed by Aristarchus in (310230 B.C) • Not taken seriously until 1500 with Copernicus Nicolaus Copernicus developed the first heliocentric (sun-centered) model of the solar system. In this model, the retrograde motion of Mars is seen when the Earth passes Mars in its orbit around the Sun. Many people disagreed with the Copernican Theory, However, the works of Brahe, Kepler, Galileo, and Newton proved that Copernicus’s heliocentric theory was correct Tycho Brahe • Accurate records of the stars and planets • Observed a supernova with a small parallax angle so is was far away • Inspired Kepler to develop his laws Because the parallax of the “star” was too small to measure, Tycho knew that it had to be among the other stars, thus disproving the ancient belief that the “heavens” were fixed and unchangeable. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus. The amount of elongation in a planet’s orbit is defined as its orbital eccentricity. An orbital eccentricity of 0 is a perfect circle while an eccentricity close to 1.0 is nearly a straight line. In an elliptical orbit, the distance from a planet to the Sun varies. The point in a planet’s orbit closest to the Sun is called perihelion, and the point farthest from the Sun is called aphelion. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #2: A line joining the planet and the Sun sweeps out equal areas in equal intervals of time. Planet moves slower in its orbit when farther away from the Sun. Planet moves faster in its orbit when closer to the Sun. KEPLER’S THREE LAWS OF PLANETARY MOTION LAW #3: The square of a planet’s sidereal period around the Sun is directly proportional to the cube of its semi-major axis. This law relates the amount of time for the planet to complete one orbit around the Sun to the planet’s average distance from the Sun. If we measure the orbital periods (P) in years and distances (a) in astronomical units, then the law mathematically can be written as P2 = a3. Galileo Galilei • Observed celestial motion with telescope • Evidence to support Heliocentric model • Opposed the church’s view of a geocentric model Galileo also discovered moons in orbit around the planet Jupiter. This was further evidence that the Earth was not the center of the universe. Galileo was the first to use a telescope to examine celestial objects. His discoveries supported a heliocentric model of the solar system. Galileo discovered that Venus, like the Moon, undergoes a series of phases as seen from Earth. In the Ptolemaic (geocentric) model, Venus would be seen in only new or crescent phases. However, as Galileo observed, Venus is seen in all phases, which agrees with the Copernican model as shown. Newton • Identified gravity and gave the reason why Kepler’s Laws worked. • Gravity is everwhere! • Sun keeps planets in orbit around it. Isaac Newton formulated three laws to describe the fundamental properties of physical reality. NEWTON’S THREE LAWS OF MOTION LAW #1: A body remains at rest or moves in a straight line at constant speed unless acted upon by a net outside force. LAW #2: The acceleration of an object is proportional to the force acting on it. LAW #3: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. Newton also discovered that gravity, the force that causes objects to fall to the ground on Earth, is the same force that keeps the Moon in its orbit around the Earth. NEWTON’S LAW OF UNIVERSAL GRAVITATION Two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. With his laws, Newton was able to derive Kepler’s three laws, as well as predict other possible orbits. Newton’s laws were applied to other objects in our solar system. Using Newton’s methods, Edmund Halley worked out the details of a comet’s orbit and predicted its return. Deviations from Newton’s Laws in the orbit of the planet Uranus led to the discovery of the eighth planet, Neptune.