The Motion of Planets

Birth of Modern AstronomyOR

How Nerds Changed the World!!!

Theory?Hypothesis?Law?Scientific Method?

How is science done?

Observations

Experiments

Explanations

Theories

Laws

Repeat

Assumptions of Early Models

• Geocentric - Earth in the middle

• Everything orbits the Earth

• Stars are located on the Celestial Sphere

• Everything moves in uniform circular motions

The Greeks• Anaximander

– Celestial sphere rotates around the earth

• Pythagoras– Earth is a sphere

• Eudoxus– Planet motion accounted for by separate spheres

• Aristotle– Complete model of the universe (4 elements)

– Perfect heavens

• Apollonius– epicycles

The Time of Aristotle

Model of the Universe

All things in the universe go to their Natural Place

Element Natural Motion Properties

Earth Falls down Dry, Cold

Air Rises up Wet, Hot

Water Falls down Cold, Wet

Fire Rises up Hot, Dry

Hellenistic (Greek)Periodic Table

Retrograde Motion

The problem of Retrograde Motion: Apollonius

• The motion of these spheres did not account for retrograde motion.

• Apollonius introduces ‘epicycles’– Roughly meaning ‘cycles within’

What is an epicycle?

• The Center of of epicycle revolves around the earth

• The planet spins along the epicycle at the same time.

Earth Deferent

EpicycleMars

Enter the Roman: Ptolemy

• Brought it all together• Added the equant to adjust the model to match

observations• Wrote “The Mathematical Compilation”• Destruction of Library of Alexandria

– (Europe lost almost all it’s written knowledge)• The Arab Scholars called it “Almagest” (“the

greatest”)• This is how they came to know it once the work

returned to Europe.

Earth

Deferent

Epicycle

Mars

EquantClaudius Ptolemy (87-165)

The Dark Ages

Nicolaus Copernicus (1473-1543)

Errors building up

Must be a better way!

Let’s try a Heliocentric system!

Not any better though

Tycho Brahe (1546-1601)

Comet – beyond the Moon

Supernova – far away

Naked eye observations of planets

Accuracy through repetition

Best observations of planetary positions

Hired “nerd” to help calculate model

Died….

Johannes Kepler (1571-1630)

Worked for Brahe

Took data after his death

Spent years figuring out the motions of the planets

Came up with…

Three Laws of Planetary Motion

1. Planets move in elliptical orbits with the Sun at one foci

Sun

Foci (sing. Focus)

Perihelion Aphelion

Average distance from the Sun = 1 Astronomical Unit (1 A.U.)

2. Planets move faster at perihelion than at aphelion.

1 Month

1 Month

3. Period is related to average distance

P = period of the orbit

a= average distance

P2 = k a3

Longer orbits - greater average distance

Need the value of k to use the formula

k depends upon the situation

Can be used for anything orbiting anything else

Special version of Kepler’s third Law –

If the object is orbiting the Sun

P – measured in years,

a – measured in A. U., then….

P2 = a3

Galileo Galilei (1564-1642)

Knew of Copernicus’s & Kepler’s work

Used a telescope to look at the sky

What did he see?

The Moon was an imperfect object

Venus has phases

Jupiter has objects around it

Saturn is imperfect

The Sun is imperfect

Isaac Newton (1642-1727)

The ultimate “nerd”

Able to explain Kepler’s laws

Had to start with the basics -

The Three Laws of Motion

1. Law of Inertia - Objects do whatever they are currently doing unless something messes around with them.

2. Force defined

F=ma

F=forcem=massa=acceleration (change in motion)

3. For every action there is an equal and opposite reaction.

The three laws of motion form the basis for the most important law of all (astronomically speaking)

Newton’s Universal Law of Gravitation

221

R

MGMF

F=force of gravity

G=constant

M1, M2 = masses

R=distance from “centers”

Gravity is the most important force in the Universe

Newton’s Revisions to Kepler’s Laws of Planetary Motion:•Kepler’s 1st and 2nd Laws apply to all objects (not just planets)•3rd Law rewritten:

3

21

22

32

)(

4

became...

was...

aMMG

P

kaP

•4π2 and G are just constant #s (they don’t change)

•M1 and M2 are any two celestial bodies (could be a planet and Sun)

•Importance: if you know period and average distance of a planet, you can find mass of Sun (2 x 1030 kg)

or any planet!

Mass of Sun is 2 000 000 000 000 000 000 000 000 000 000 kg

Mass of Earth is 6 000 000 000 000 000 000 000 000 kg

Mass of Mr. J is 100 kg! WOW!