Chapter 2 The Copernican Revolution

Chapter 2 Learning Objectives  Know the differences and similarities between the geocentric and heliocentric models of the universe proposed by Ptolemy and Copernicus, respectively.  State Brahe’s contributions to astronomy.  Describe Kepler’s three laws of planetary motion.  Be familiar with Galileo’s contributions to astronomy, especially those to the heliocentric model.  Know Newton’s Law of Universal Gravitation and how it can be used to explain an orbiting body around another.  Be able to state the Scientific Method.  Explain what causes stellar parallax.  Define the astronomical unit (AU) and the light year (ly) and state their size in miles.  Know why planetary retrograde motion is observed.

Distance  What unit is used to measure depends on the scale of the object or distance.  For example:  Use miles or kilometers to measure distances between cities.  Use inches or centimeters to measure the size of family photographs.

Astronomical Unit  Astronomical Unit (AU) -- the average distance between the sun and the earth (93 million miles ≈ 150 million km).  Use the Astronomical Unit (AU) to measure distances to planets in the solar system.

Light-year Light-year (ly)- the distance that light travels in one year (about 63,000 AU or about 6x10 12 miles). Use light-years to measure distances between stars. The nearest star system to the sun (Alpha Centauri) is about 4.4 ly away. The Sun is about 28,000 ly from the center of the galaxy.

Light-year About 100,000 ly

Parallax  The apparent change in the location of an object due to the difference in location of the observer is called parallax.

Parsec Another way to measure distance is parallax. distance (in parsec) = 1/parallax d = 1/p 1 parsec = 206,265 AU = 3.26 ly. For Proxima Centauri p =0.76 sec of arc, d = 1.3 ps = 4.3 ly.

Parsec 1 A.U. d = 1 ps 1 arcsec Can only determine distance for “nearby” stars because AU is “small”.

Scientific Method  The scientific method is used to develop new scientific theories. Scientific theories are accepted when they make testable predictions that can be verified using new observations and experiments.

Scientific Method  Observations are made.  Theories and models are constructed.  They are tested.  Replaced if found inadequate.

Ancient Greeks  Aristotle( BC), Plato ( BC), Ptolemy(140 AD) …  Believed that the universe can be understood.  The heavens are perfect.  All celestial motion is uniform and circular.  Geocentric (Earth-centered) model. The Earth did not move. Lasted for over 2000 years.

Ptolemy’s Geocentric Model

Retrograde Motion  The planets don’t always appear to move in uniform motion with respect to the stars. They appear to move backwards at times. Retrograde motion

Retrograde Motion  Any model of the universe must include planetary retrograde motion.  Ptolemy explained this motion by placing the planets on epicycles which in turn orbited the Earth.

Copernican Revolution  Nicolaus Copernicus ( ).  Heliocentric (Sun-centered) model.  Model went against the church.  His work was published after he died.  Explained retrograde motion.  Kept stars on a sphere.  Some inaccuracies--orbits were circular.

Heliocentric Model

Retrograde Motion  In the sun- centered model, the retrograde motion of Mars is seen when the Earth passes Mars in its orbit around the Sun.

Tycho Brahe ( )  Best known for compiling careful observations of stellar and planetary positions.  In 1572, he saw a new “ star” that displayed no parallax.  New “ star” must lie on the starry sphere of the geocentric model. A contradiction to Aristotle’s perfect heavens.

Tycho’s New “Star”

Question  Do the planets orbit the Sun at constant speeds?  No. The closer a planet is to the Sun in its orbit, the faster it is moving. It moves fastest at perihelion and slowest at aphelion.

Johannes Kepler ( )  Believed in heliocentric model.  Used Brahe’s data to abandon circular orbits.  Planets orbit the Sun in elliptical orbits.  Derived three laws of planetary motion.

KEPLER’S 1 st LAW OF PLANETARY MOTION  The orbit of a planet around the Sun is an ellipse with the Sun at one focus.

Elliptical Orbits  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 2 nd LAW OF PLANETARY MOTION  A line joining the planet and the Sun sweeps out equal areas in equal intervals of time. Planet moves faster in its orbit when closer to the Sun. Planet moves slower in its orbit when farther away from the Sun.

KEPLER’S 3 rd LAW OF PLANETARY MOTION  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 P 2 = a 3.

KEPLER’S 3 rd LAW OF PLANETARY MOTION

Galileo Galilei ( )  First to use the telescope.  Discovered: the Moon has mountains and craters, Sun spots, Sun rotates, moons of Jupiter, Venus has phases, …  Phases of Venus disproved geocentric model over heliocentric model.

Phases of Venus  In the Ptolemaic (geocentric) model, Venus would be seen in only new or crescent phases.

Phases of Venus  However, as Galileo observed, Venus is seen in all phases, which agrees with the Copernican model as shown.

Galileo also discovered moons in orbit around the planet Jupiter. This was further evidence that the Earth was not the center of the universe. Jupiter’s Moons – Galilean Moons

Isaac Newton ( )  Three Laws of Motion.  Linked falling objects to the motion of the Moon.  Both experience Earth’s force due to gravity.  Law of Universal Gravitation.

Question  How much force does it take to keep an object moving in a straight line at a constant speed?  Unless an object is subject to an outside force, it takes no force at all to keep it moving in a straight line at a constant speed.

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. Gravity stops it Goes on forever

NEWTON’S THREE LAWS OF MOTION  LAW #2: The acceleration of an object is proportional to the force acting on it.  Force = (mass)( acceleration) m M F F Easier to move Harder to move

NEWTON’S THREE LAWS OF MOTION  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. I push on you, you push on me.

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.

Orbits

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.

Question  Why was the discovery of Neptune a major confirmation of Newton’s universal law of gravitation?

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.

WHAT DID YOU THINK?  What makes a theory scientific?  If it makes predictions that can be objectively tested and potentially disproved.  What is the shape of the Earth’s orbit around the Sun?  Elliptical

WHAT DID YOU THINK?  Do all the planets orbit the Sun at the same speed?  No. A planet’s speed depends on its average distance from the Sun.  How does an object’s mass differ when measured on the Earth and on the Moon?  Its mass remains constant.