Today’s APOD

Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due Sept. 26Rooftop Session Tuesday evening,

9PMKirkwood Obs. open Wednesday Eve.,

8:30-10:30IN-CLASS QUIZ ON WEDNESDAY!!

The Sun Today

A100 Solar System

Today: the

Equinox

11:44 AM EDTtoday

http://apod.nasa.gov/apod/ap030923.html

Dr. Phil Plait (Sonoma St. U.) acting as the Bad Astronomer balanced three raw eggs on end in late October 1998

The Problem: Retrograde

Motion

• In a simple geocentric model (with the Earth at the center), planets should drift steadily eastward through the sky against the background of stars

• But sometimes, the motion of the planets against the background stars reverses, and the planets move toward the west against the background stars

Retrograde Motion in a Geocentric

Model• Ptolemy accounted for

retrograde motion by assuming each planet moved on a small circle, which in turn had its center move on a much larger circle centered on the Earth

• The small circles were called epicycles and were incorporated so as to explain retrograde motion

Epicycles get more complexEpicycles did pretty well

at predicting planetary motion, but…

Discrepancies remained Very complex Ptolemaic

models were needed to account for observations

More precise data became available from Tycho Brahe in the 1500s

Epicycles could not account for observations

Astronomy in the Renaissance

Could not reconcile Brahe’s measurements of the position of the planets with Ptolemy’s geocentric model

Reconsidered Aristarchus’s heliocentric model with the Sun at the center of the solar system

Nicolaus Copernicus (1473-1543)

Heliocentric Models with

Circular OrbitsExplain retrograde

motion as a natural consequence of two planets (one being the Earth) passing each other

Copernicus could also derive the relative distances of the planets from the Sun

But a heliocentric model doesn’t

solve all problems

Could not predict planet positions any more accurately than the model of Ptolemy

Could not explain lack of parallax motion of stars

Conflicted with Aristotelian “common sense”

Johannes Kepler (1571-1630)Using Tycho’s

precise observations of the position of Mars in the sky, Kepler showed the orbit to be an ellipse, not a perfect circle

Three laws of planetary motion

Kepler’s 1st Law

Planets move in elliptical orbits with the Sun at one focus of the ellipse

Words to rememberFocus vs. CenterSemi-major axisSemi-minor axisPerihelion, aphelionEccentricity

Definitions

• Planets orbit the Sun in ellipses, with the Sun at one focus

• The eccentricity of the ellipse, e, tells you how elongated it is

• e=0 is a circle, e<1 for all ellipses

e=0.02 e=0.4 e=0.7

Eccentricity of Planets & Dwarf Planets

Mercury 0.206 Saturn 0.054

Venus 0.007 Uranus 0.048

Earth 0.017 Neptune 0.007

Mars 0.094 Pluto 0.253

Jupiter 0.048 Ceres 0.079

Which orbit is closest to a circle?

Kepler’s 2nd

LawPlanets don’t move at constant speedsThe closer a planet is to the Sun, the faster it

moves A planet’s orbital speed varies in such a way

that a line joining the Sun and the planet will sweep out an equal area each month

Each month gets an equal slice of the orbital pie

Kepler’s 2nd Law:

If the planet sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?

Same Areas

Kepler’s 3rd Law

• The amount of time a planet takes to orbit the Sun is mathematically related to the size of its orbit

• The square of the period, P, is proportional to the cube of the semimajor axis, a

P2 = a3

Kepler’s 3rd LawThird law can be used

to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make

P2 = a3

Express the period in years

Express the semi-major axis in AU

Examples of Kepler’s 3rd Law

Express the period in yearsExpress the semi-major

axis in AU

Body Period (years)

Mercury 0.24

Venus 0.61

Earth 1.0

Mars 1.88

Jupiter 11.86

Saturn 29.6

Pluto 248

For Earth:

P = 1 year, P2 = 1.0

a = 1 AU, a3 = 1.0

P2 = a3

Examples of Kepler’s 3rd Law

Express the period in years Express the semi-major axis in AU

Body Period (years)

Mercury 0.2409

Venus 0.61

Earth 1.0

Mars 1.88

Jupiter 11.86

Saturn 29.6

Pluto 248

For Mercury:

P = 0.2409 yearsP2 = 5.8 x 10-2

a = 0.387 AUa3 = 5.8 x 10-2

P2 = a3

Examples of Kepler’s 3rd Law

Express the period in years Express the semi-major axis in AU

Body Period (years)

Mercury 0.2409

Venus 0.6152

Earth 1.0

Mars 1.88

Jupiter 11.86

Saturn 29.6

Pluto 248

For Venus:

P = 0.6152 yearsP2 = 3.785 x 10-1

What is the semi-major axis

of Venus?

P2 = a3

a = 0.723 AU

Examples of Kepler’s 3rd Law

Express the period in years Express the semi-major axis in AU

Body Period (years)

Mercury 0.2409

Venus 0.6152

Earth 1.0

Mars 1.88

Jupiter 11.86

Saturn 29.6

Pluto 248

For Pluto:

P = 248 yearsP2 = 6.15 x 104

What is the semi-major axis

of Pluto?

P2 = a3

a = 39.5 AU

Examples of Kepler’s 3rd Law

Express the period in years Express the semi-major axis in AU

Body Period (years)

Mercury 0.2409

Venus 0.6152

Earth 1.0

Mars 1.88

Jupiter 11.86

Saturn 29.6

Pluto 248

The Asteroid Pilachowski (1999 ES5):

P = 4.11 years

What is the semi-major axis of Pilachowski?

P2 = a3

a = ??? AU

Fill in the Table

Express the period in yearsExpress the semi-major axis in AU

Planet/Dwarf Planet

Period (years)

Semi-Major Axis (AU)

P2 a3

Mercury 0.2409 0.39 5.8 x 10-2 5.9 x 10-2

Venus 0.6152 0.72

Earth 1.0 1 1.0 1.0

Mars 1.8809 1.52

Jupiter 11.8622

5.2

Saturn 29.4577

9.54

Pluto 247.7 39.5

Comparing Heliocentric Models

Geocentric > HeliocentricThe importance of observations!

When theory does not explain measurements, a new hypothesis must be developed; this may require a whole new model (a way of thinking about something)

Why was the geocentric view abandoned?

What experiments verified the heliocentric view?

ASSIGNMENTSthis week

Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due Sept. 26Rooftop Session Tuesday evening,

9PMKirkwood Obs. open Wednesday Eve.,

8:30-10:30IN-CLASS QUIZ ON WEDNESDAY!!