It's spring for the northern hemisphere of Mars and spring on Mars usually means dust storms. This sharp image shows the evolving dust storm (brown swath across polar ice) extending from the large dark region known as Mare Acidalium below the polar cap.

Exam 1: Wednesday, Feb. 17 Review session: Monday, Feb. 15, Jordan Hall 239, 7:00 until everyone has left.

Ptolemy’s Geocentric Model ● Earth is at center (Geocentric) ● Sun orbits Earth ●Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles (this explains retrograde motion)

Geocentric Model  Planet orbits lie in approximately the same plane (this explains why the planets are always near the ecliptic)  Inferior planet epicycles are fixed to the Earth-Sun line (this explained why Mercury & Venus never stray far from the Sun).

Ptolemy’s model fit the data and made fairly accurate predictions. But, it was horribly contrived!

The center moves…

The Revolution Begins!

The Copernican Revolution ● Copernicus, Tycho, Kepler, and Galileo. ● Kepler’s three laws of planetary motion

● Over the years since Ptolemy, astronomers struggled to make his model more accurate, leading to an increasingly complicated model:  moved the earth slightly off the center of the solar system to avoid needing have the planets move at varying speeds along their orbits.  a different type of epicycle was used to explain the motions of Mercury and Venus than that used for Mars, Jupiter, and Saturn  model got extremely complex for Mercury and Mars, e.g., Mercury riding on an epicycle on an epicycle on an epicycle, with constant speed measured from a point well off-center!!

● “If I had been present at the creation, I would have recommended a simpler design for the universe”. ● - Spanish monarch Alphonso X (13th century)

● “Hereafter, when they come to model Heav'n, And calculate the Stars, How will they wield The mighty frame, how build, unbuild, contrive, To save appearances, how grid the Sphere With Centric and Eccentric scribbl'd o'er, Cycle and Epicycle, Orb in Orb”. ● - John Milton, Paradise Lost

Nicolaus Copernicus ( ) He thought Polemy’s model was contrived Yet he believed in circular motion De Revolutionibus Orbium Coelestium

Nicolaus Copernicus ( ) He thought Polemy’s model was contrived Yet he believed in circular motion De Revolutionibus Orbium Coelestium

Copernicus’ Heliocentric Model ●Sun is at center of the Universe ●Earth orbits the Sun like any other planet ●Earth rotates ●Circular orbits for all planets ●Inferior planet orbits are smaller ●Planets move at constant velocities in their orbits ●Retrograde motion occurs when we “lap” Mars & the other superior planets

Copernicus’ Heliocentric Model ●Retrograde motion occurs when we “lap” Mars & the other superior planets

Retrograde Motion (1) Planets, including the Earth, orbit the Sun (2) Planets closer to the Sun have shorter orbital periods than planets farther from the Sun

As we “pass” a planet, it appears to move backwards (as seen from Earth)

Simpler, more “elegant” than the model of Ptolemy BUT  it still required some epicycles in order to make accurate predictions  it was still wedded to Aristotle's circular orbit paradigm  predictions were not much better than those of Ptolemy

Right track? Perhaps, but still not quite there.

Tycho Brahe ( ) ● Greatest observer of his day Charted accurate positions of planets (accurate positions of the planets were not fully available)

Tycho Brahe… was motivated by inadequacy of existing predictions made very accurate observations of positions (this was prior to the development of the telescope) advocated a model in which Sun orbits Earth because he could not observe stellar parallax

The parallax problem troubled the Greeks and Tycho. It led both to reject a heliocentric universe.

The problem was that stars are too distant to produce a parallax large enough to be seen with the technology of those time.

1600 – Tycho brought Johannes Kepler to bear on problem. He assigned him the task of understanding the motions of Mars. Kepler had great faith in Tycho's measurements; they placed strong constraints on model

Suggested webpage to visit for more insight into Tycho Brahe, Johannes Kepler, and the development of Kepler’s Laws:

Johannes Kepler ( ) ● Greatest theorist of his day ● a mystic ● there were no heavenly spheres ● forces made the planets move ● Developed his three laws of planetary motion

Kepler’s First Law 1Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.

Ellipse: defined by points located such that the sum of the distances from the two foci is constant o

Semimajor axis = a Semiminor axis = b y X x 2 /a 2 + y 2 /b 2 = 1 focus Eccentricity e 2 = 1 - b 2 /a 2 The circle is a special form of an ellipse

Kepler’s Second Law ● A planet moves along its orbit with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time. Planet shown at positions equally spaced in time

Consequence - planets move faster when they are closer to the sun and planets spend more time in the more distant parts of their orbits

Kepler’s Third Law The ratio of the cube of a planet’s average distance from the Sun “a” to the square of its orbital period “P” is the same for each planet. a 3 / P 2 = constant

Qualitative Consequence: Planets with larger orbits have longer orbital periods. a 3 / P 2 = constant Earth: a = 1 AU, P = 1 year So, if we use distance in AU and time in years, the constant in the 3rd Law is 1 AU 3 yr -2 Jupiter: a = AU, P = years

 Kepler’s Laws are extremely accurate in their predictions of planetary motions.  They are “empirical”, i.e., they are derived from experiment, experience, and observation rather than from theory or logic  Isaac Newton subsequently demonstrated that Kepler’s laws are the natural outcome of gravity.

Group Activity Assemble into your activity group. Make sure there is an appointed moderator. The moderator job is:  Record the response of the group to the activity  Printed the names of each group member participating (if a member does not participate, omit their name)  Record the group’s number At the end of the activity, each participant should sign their name following their printed name. DO NOT SIGN FOR SOMEONE ELSE!!

Kepler’s laws were determined empirically, i.e., by observation. No theoretical basis existed for these laws. Now, we will determine an A100 analogue: Consider a number of fixed points on a phonograph record that is spinning. Inspired by Kepler’s 3rd Law, determine the relationship between the distance from the center of the record (“a”) and the length of time it takes for that point to make one complete circuit around the center (“P”). Think!!

The “Science” of Astronomy

In the broadest sense, Science refers to any system of knowledge which attempts to model objective reality.

a. Uninfluenced by emotions or personal prejudices. b. Based on observable phenomena; presented factually

“Scientific Thinking” ● a natural part of human behavior. ● We draw conclusions based on our experiences. ● Progress is made through “trial and error.”

● Science seeks explanations for observed phenomena that rely solely on natural causes. ● Science progresses through the creation and testing of models of nature that explain the observations as simply as possible. ● A scientific model must make testable predictions that could force us to revise or abandon the model. The Nature of Science -- a model which survives repeated testing Theory

The word “Theory” has a very different meaning in science than in everyday parlance

A model is only referred to as a theory when it has successfully survived testing to such an extent that it is generally accepted as a valid representation of nature. Even then, testing continues…

Theories  Must be Testable  Must be continuously tested  Should be simple

“Testable” - science, nonscience & pseudoscience Testing separates science from nonscience: e.g., religion is not accessible to experimental verification Testing invalidates pseudosciences : e.g., astrology fails testing.