Chapter 2 Sections 2.2-2.3

Geocentric Model The geocentric model was the idea that the Earth is the center of the universe and all celestial bodies revolve around it This model was pioneered by the ancient astronomer Ptolemy Ptolemy lived in Alexandria Egypt during the time of the Roman Empire

Ptolemy (90 A.D. – 168A.D.)

Problems with the Geocentric Model The problem of retrograde motion Retrograde motion refers to the motion of the planets with respect to background stars Planets slowly move eastward among the background stars Occasionally, they move back west before moving east again

Retrograde Motion of Mars

Ptolemy’s explanation Each planet revolves around an epicycle Each epicycle revolves around a deferent centered on the Earth

Copernicus and the Heliocentric Model Eventually, problems compounded over the years and it was clear that the geocentric model was not correct This led Copernicus to propose a sun-centered model of the solar system This is known as the Heliocentric Model of the solar system

Copernicus Polish Astronomer who solved the problem of retrograde motion by proposing the Earth revolved around the sun He published a book called On the Revolutions of the Heavenly Bodies (1543), which he received a copy of on his deathbed

Heliocentric Explanation of Retrograde Motion

Galileo Galilei (1564-1642) An Italian who made observations that supported the heliocentric model Also considered the father of modern physics

Phases of Venus Galileo was one of the first to use a telescope to observe the night sky Galileo observed that Venus has phases like the moon He also observed that the apparent size of Venus changes with phase

Galileo’s explanation of the phases of Venus

Moons of Jupiter Galileo also observed several objects orbiting the planet Jupiter This was direct evidence against the Geocentric Model These are now known as the 4 Galilean moons

Galileo’s sketches of Jupiter

Galilean Moons

Galileo published a book , Dialogue Concerning the Two Chief World Systems, supporting the heliocentric model He was punished by the Roman Catholic Church and condemned to house arrest for the last 9 years of his life

Johannes Kepler (1571-1630) The German Johannes Kepler accepted the heliocentric model He used the observations of Tycho Brahe to deduce his 3 laws of planetary motion

Kepler’s First Law The orbit of a planet around the Sun is an ellipse with the Sun at one focus

Conic Sections

An Ellipse

Kepler’s Second Law A line joining a planet and the Sun sweeps out equal areas in equal intervals of time

Kepler’s Third Law Relates the time it takes a planet to revolve around the sun and its average distance from the sun The time to make one complete revolution is called the period (p) The average distance of a planet to the sun is approximately the semi-major axis (a) of the elliptical orbit

The average distance from the Earth to the sun, 93 million miles, is called an Astronomical Unit (AU) If period is measures in Earth years, and semi-major axis in AU’s, then Kepler’s third law can be written as: p2 = a3 The square of a planets sidereal period is equal to the cube of its semi-major axis

Isaac Newton (1642-1727) Born in England Considered one of the greatest mathematicians and physicists of all time One of the most celebrated scientists of all time

Newton’s First Law of Motion Objects at rest will remain at rest until a force acts on them Objects in motion in a straight line moving at a constant speed will continue to do so until a force acts on them

Newton’s Law of Gravitation Every object attracts every other object The more massive the objects are, the larger the force The farther apart the objects are, the weaker the force Mathematically:

The distance, d, is the distance between the center of mass of each object The force is inversely proportional to the distance squared This means if you double the distance between two objects, the force becomes 4 times weaker If you triple the distance between two objects, the force becomes 9 times weaker