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 6x1012 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-yearAbout 100,000 ly

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

Scientific MethodObservations

are made.Theories and

models are constructed.

They are tested.

Replaced if found inadequate.

Ancient Greeks

Aristotle(384-322BC), Plato (427-347BC), 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 MotionThe 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 Any model of the universe must include

planetary retrograde motion.planetary retrograde motion. Ptolemy explained this motion by placing Ptolemy explained this motion by placing

the planets on epicycles which in turn the planets on epicycles which in turn orbited the Earth.orbited the Earth.

Copernican Revolution

Nicolaus Copernicus (1473 - 1543). 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-In the sun-centered centered model, the model, the retrograde retrograde motion of motion of Mars is seen Mars is seen when the when the Earth passes Earth passes Mars in its Mars in its orbit around orbit around the Sun. the Sun.

Tycho Brahe (1546 - 1601) 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 (1571 - 1630)

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.

KEPLERKEPLER’’S 1S 1stst LAW OF PLANETARY LAW OF PLANETARY MOTIONMOTION

The orbit The orbit of a of a planet planet around around the Sun is the Sun is an ellipse an ellipse with the with the Sun at Sun at one focus.one focus.

Elliptical Orbits In an elliptical orbit, the distance from a In an elliptical orbit, the distance from a

planet to the Sun varies. The point in a planet to the Sun varies. The point in a planetplanet’’s orbit closest to the Sun is called s orbit closest to the Sun is called perihelion, perihelion, and the point farthest from and the point farthest from the Sun is called the Sun is called aphelion.aphelion.

KEPLERKEPLER’’S 2S 2ndnd LAW OF LAW OF PLANETARY MOTIONPLANETARY MOTION

A line A line joining the joining the planet and planet and the Sun the Sun sweeps sweeps out equal out equal areas in areas in equal equal intervals intervals of time.of time.

Planet moves Planet moves faster in its orbit faster in its orbit when closer to the when closer to the Sun.Sun.

Planet moves Planet moves slower in its orbit slower in its orbit when farther away when farther away from the Sun.from the Sun.

KEPLERKEPLER’’S 3S 3rdrd LAW OF LAW OF PLANETARY MOTIONPLANETARY MOTION

The square of a planetThe square of a planet’’s sidereal period s sidereal period around the Sun is directly proportional to the around the Sun is directly proportional to the cube of its semi-major axis.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.

KEPLERKEPLER’’S 3S 3rdrd LAW OF LAW OF PLANETARY MOTIONPLANETARY MOTION

Galileo Galilei (1564 - 1642)

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 VenusHowever, 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 (1642 - 1727)

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.

NEWTONNEWTON’’S THREE LAWS S THREE LAWS OF MOTIONOF MOTION

LAW #1: A body remains at rest or LAW #1: A body remains at rest or moves in a straight line at constant moves in a straight line at constant speed unless acted upon by a net speed unless acted upon by a net outside force.outside force.

Gravity stops it

Goes on forever

NEWTONNEWTON’’S THREE LAWS S THREE LAWS OF MOTIONOF MOTION

LAW #2: The acceleration of an LAW #2: The acceleration of an object is proportional to the force object is proportional to the force acting on it. acting on it.

Force = (mass)( acceleration)

mMF

F

Easier to move Harder to move

NEWTONNEWTON’’S THREE LAWS S THREE LAWS OF MOTIONOF MOTION

LAW #3: LAW #3: Whenever one Whenever one body exerts a body exerts a force on a second force on a second body, the second body, the second body exerts an body exerts an equal and equal and opposite force on opposite force on the first body.the first body.

I push on you, you push on me.

Gravity, the force that causes Gravity, the force that causes objects to fall to the ground on objects to fall to the ground on Earth, is the same force that Earth, is the same force that keeps the Moon in its orbit keeps the Moon in its orbit around the Earth.around the Earth.

Orbits

NEWTONNEWTON’’S LAW OF S LAW OF UNIVERSAL GRAVITATIONUNIVERSAL 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?

NewtonNewton’’s laws were applied to other objects in our s laws were applied to other objects in our solar system.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.