Explaining the Universe

Pioneer and Voyager missions

• Pioneer 10 and 11

• Voyager 1 and 2

• Portrait of Solar System

Ancient Greeks• Aristotle (384-322 BCE)

– Things on Earth made of four basic elements and things in heavens made of a fifth element, the aether

– Objects on Earth follow one set of rules while objects in the heavens follow another.

– Heavenly objects are perfect and unchanging. And move in perfect circles (the “natural motion” of aether).

– The Lyceum

Ancient Greeks

• Ptolemy (85-165 AD)• Made model of universe which explained

positions of planets and stars using only perfect circles and with Earth at center

• Published in 13 volumes (The Almagest) which was THE text for about 1400 years!

Ptolemy’s Model

Ptlolemy had to use epicycles (circles upon circles) to make a model which matched his data

Epicycles

For the next 1500 years, astronomers worked within this model. They changed the speeds and radii of the orbits and epicycles to perfect the model.

To write:

1. Aristotle thought that there was one set of rules for the heavens and another for the Earth. Everything in the heavens was made of aether—perfect, unchanging, moved in circles.

2. Ptolemy made a model of the universe using Aristotle’s ideas. It was geocentric & had to use epicycles to match what was observed. It was THE idea for 1400 years!

Why didn’t Ptolemy’s model work without all of those epicycles?

• The orbits of the planets are not perfect circles.

• Our solar system is NOT geocentric!

Nicolaus Copernicus (1473-1543)

• Worked his whole life to construct a planetary system with the fewest possible uniform circular motions

• Put SUN at center—a heliocentric model

Copernicus’ Model

This is an illustration from Copernicus’ book, The Revolutionibus. Actually, his model still required epicycles and the Sun was not the center of revolution for all the planets.

Copernicus’ Model

•Although Copernicus’ model was not correct, it is responsible for moving the Sun to the center of the universe!

•Published just before he died—heresy!

To write:

3. Copernicus made a heliocentric model of the universe. It was revolutionary, but it still used circles and epicycles.

Tycho Brahe (1546-1601)

• Danish eccentric• Discovered Ptolemy

and Copernicus had relied on inaccurate table of data

• Convinced King Frederick II to finance huge observatory (cost a ton of gold)

Uraniborg, Brahe’s island observatory

Tycho’s Instruments

Tycho’s Model

Tycho was a great technician. His data was by far the most accurate ever gathered. His model of the universe, however, was geocentric (Ptolemaic). It DID show that comets were in the heavens (no crystal spheres).

To write:

4. Brahe collected extremely accurate data on the positions of the planets that was used by later scientists.

Johannes Kepler (1571-1630)

• Assistant to Brahe from 1600-1601. Inherited Brahe’s data when he died

• An excellent mathematician!

Kepler’s Early Model• Dreamed of

perfecting heliocentric model.

• Looked for reasons there are just 6 planets and why they are spaced as they are

• Thought geometric order would offer clues to “God’s mind”

Kepler’s Laws

• Kepler worked with Brahe’s data for 20 YEARS!

• Assumed that motions of planets must be due to actions of forces on them (Galileo’s influence—revolutionary!)

• Came up with three laws to describe planetary motion

To write:

5. Kepler used Brahe’s data to make his three laws of planetary motion.

Kepler’s First Law

The orbits of the planets are ellipses with the Sun at one focus

Kepler’s Second Law

A line drawn between the sun and a planet sweeps out equal areas in equal times.

Kepler’s Third Law

The orbital radius of a planet cubed divided by its orbital period squared is the same for all planets.

T12 / T2

2 = R13 / R2

3

OR

R3/T2 = K

Try it! Find R3/T2

Planet Orbital Radius

(AU)

Orbital Period

(days)

Earth 1 365

Mars 1.524 687

Venus 0.723 224.7

Jupiter 5.203 4328.9

Galileo Galilei (1564-1642)

Used his telescope to look at heavens and found:

1. Moons of Jupiter

2. Phases of Venus

3. Moon has craters and mountains

Isaac Newton (1643-1727)

• Used his knowledge of circular motion and Kepler’s third law to develop the Law of Universal Gravitation

• Reasoned that just as apples fall to the earth, the Moon falls “around” the earth— THE SAME FORCE CAUSES BOTH!!!

The Law of Universal GravitationNewton: F ~m1m2 / d2

Cavendish measured the constant of proportionality, “G”, in 1798, almost 100

years after Newton published his paper on gravity.

F = G m1m2 / d2

Where G = 6.67 x 10-11N m2 kg-2

The Cavendish Experiment

Determined “G” by measuring the twist of a thin, glass thread due to the force between known masses

Example 1

Find the force of gravity between Venus (mass=4.87 x 1024 kg) and the Sun (m=2 x 1030 kg) if the average distance between them is 1.08 x 1011 m.

Example 2

Use the law of universal gravitation to find a 100-kg man’s weight on Venus whose mass is 4.87 x 1024 kg and radius is 6.05 x 106 m. Find the acceleration of gravity on Venus.