Today’s APODAPOD  Review Chapter 1, Kepler’s Laws  Read Chapter 2: Gravity & Motion  2 nd Homework due Sept. 26  Rooftop Session Tuesday evening, 9PM  Kirkwood Obs. open Wednesday Eve., 8:30-10:30  IN-CLASS QUIZ ON WEDNESDAY!! The Sun Today A100 Solar System

Today: the Equinox 11:44 AM EDT today Dr. Phil Plait (Sonoma St. U.) acting as the Bad Astronomer balanced three raw eggs on end in late October 1998Phil PlaitSonoma St. U.Bad Astronomer

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 complex  Epicycles 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 ( )

Heliocentric Models with Circular Orbits  Explain 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 ( )  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 1 st Law  Planets move in elliptical orbits with the Sun at one focus of the ellipse  Words to remember  Focus vs. Center  Semi-major axis  Semi-minor axis  Perihelion, aphelion  Eccentricity

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=0.4e=0.7

Eccentricity of Planets & Dwarf Planets Mercury0.206Saturn0.054 Venus0.007Uranus0.048 Earth0.017Neptune0.007 Mars0.094Pluto0.253 Jupiter0.048Ceres0.079 Which orbit is closest to a circle?

Kepler’s 2nd Law  Planets don’t move at constant speeds  The 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 2 nd 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 3 rd 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 P 2 = a 3

Kepler’s 3 rd Law  Third law can be used to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make P 2 = a 3  Express the period in years  Express the semi-major axis in AU

Examples of Kepler’s 3 rd Law  Express the period in years  Express the semi-major axis in AU BodyPeriod (years) Mercury0.24 Venus0.61 Earth1.0 Mars1.88 Jupiter11.86 Saturn29.6 Pluto248 For Earth: P = 1 year, P 2 = 1.0 a = 1 AU, a 3 = 1.0 P 2 = a 3

Examples of Kepler’s 3 rd Law  Express the period in years  Express the semi-major axis in AU BodyPeriod (years) Mercury Venus0.61 Earth1.0 Mars1.88 Jupiter11.86 Saturn29.6 Pluto248 For Mercury: P = years P 2 = 5.8 x a = AU a 3 = 5.8 x P 2 = a 3

Examples of Kepler’s 3 rd Law  Express the period in years  Express the semi-major axis in AU BodyPeriod (years) Mercury Venus Earth1.0 Mars1.88 Jupiter11.86 Saturn29.6 Pluto248 For Venus: P = years P 2 = x What is the semi-major axis of Venus? P 2 = a 3 a = AU

Examples of Kepler’s 3 rd Law  Express the period in years  Express the semi-major axis in AU BodyPeriod (years) Mercury Venus Earth1.0 Mars1.88 Jupiter11.86 Saturn29.6 Pluto248 For Pluto: P = 248 years P 2 = 6.15 x 10 4 What is the semi-major axis of Pluto? P 2 = a 3 a = 39.5 AU

Examples of Kepler’s 3 rd Law  Express the period in years  Express the semi-major axis in AU BodyPeriod (years) Mercury Venus Earth1.0 Mars1.88 Jupiter11.86 Saturn29.6 Pluto248 The Asteroid Pilachowski (1999 ES5): P = 4.11 years What is the semi-major axis of Pilachowski? P 2 = a 3 a = ??? AU

Fill in the Table  Express the period in years  Express the semi-major axis in AU Planet/ Dwarf Planet Period (years) Semi- Major Axis (AU) P2P2 a3a3 Mercury x x Venus Earth1.01 Mars Jupiter Saturn Pluto

Comparing Heliocentric Models

Geocentric > Heliocentric  The 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?

ASSIGNMENTS this week  Review Chapter 1, Kepler’s Laws  Read Chapter 2: Gravity & Motion  2 nd Homework due Sept. 26  Rooftop Session Tuesday evening, 9PM  Kirkwood Obs. open Wednesday Eve., 8:30-10:30  IN-CLASS QUIZ ON WEDNESDAY!!