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.

Homework #3 is due Monday, Feb. 15, 2:30 pm. Exam 1: Wednesday, Feb. 17 Review session: Monday, Feb. 15, 7 pm til ?, Location to be announced

1.Which planets are visible at 9 pm? At 3 am? 2. Mercury and Venus appear in the sky only shortly after sunset, at which time they are called “evening stars”, OR shortly before sunrise (“morning stars”). What are these two planets currently? 3.The orbit planes of all of the planets are near a plane for which we have already discussed. What is the name of this plane? What defines it? 4. Do we expect to ever see either the inferior planets (Venus & Mercury) or the inferior planets (all the rest) close to the North Celestial Pole? At southern celestial latitudes? Explain.

Saturn Jupiter Outer solar system Inner solar system Venus Earth Mars Mercury

Planets in the Sky

There are five “naked eye” planets 1. Mercury 2. Venus 3. Mars 4. Jupiter 5. Saturn They are all quite bright. They have been well known to throughout human existence

Where are these seen relative to the sun?

“Naked eye” planets in the sky  Mercury: always close to Sun in sky  Venus: always close to Sun in sky  Mars: no restrictions on distance from Sun in sky  Jupiter: no restrictions on distance from Sun in sky  Saturn: no restrictions on distance from Sun in sky What causes these differences?

Where are these seen on the celestial sphere?

 Planets are always close to the “ecliptic”, the apparent annual path of the sun through the sky. This is a consequence of the planets orbiting in planes that are near each other.

How do the planets move on the Celestial Sphere?

 On short term (diurnal motion), planets appear to move with the stars, east to west, making a full circuit around the sky (meridian to meridian) in approximately one day  Most of the time, planets move slowly eastward each day relative to the stars: different planets at different rates Motions of the planets What causes these motions?

Some planets occasionally reverse their motion relative to the stars, moving slowly westward relative to the stars, for a few days apparent retrograde motion What causes this?

We have now set the stage for discussing the historical development of astronomy

What causes the observed motions of the stars, sun, moon, and planets in the sky? The Greeks developed a model for the Universe that lasted for nearly 15 centuries. It did a reasonably good job explaining these motions.

Claudius Ptolemy ( CE) Developed a model of the universe designed to fit the observational data.

Ptolemy and later scientists were strongly influenced by the belief of Plato that … “all natural motion is circular”

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)

Apparent retrograde motion in geocentric model

Geocentric Model  Planet orbits lie in approximately the same plane (this explains why the planets are always near the ecliptic)  Inferior planet epicycles were 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 accurate predictions, but was horribly contrived!

● Although the geocentric model of Ptolemy gained dominance, Aristarchus of Samos actually proposed that the earth rotated daily and revolved around the sun

Ptolemy’s Geocentric Model ●Relied upon circles upon circles (epicycles & defferents) to explain the motions of planets and the sun. ●Tied to Plato & Aristotle’s belief that “all natural motion is circular” ●With modifications (e.g., additions of epicycles upon epicycles), remained the standard through the middle-ages.

The ancient Greeks rejected the notion that the Earth orbits the sun. Why? ● It ran contrary to their senses. ● If the Earth revolved about the Sun, then there should be a “great wind” as we moved through the air. ● Greeks knew that we should see stellar parallax if we orbited the Sun – but they could not detect it.

Parallax Angle Apparent shift of a star’s position due to the Earth’s orbiting of the Sun

Possible reasons why stellar parallax was undetectable: 1.Stars are so far away that stellar parallax is too small for naked eye to notice 2.Earth does not orbit Sun; it is the center of the universe Unfortunately, with notable exceptions like Aristarchus, the Greeks did not think the stars could be that far away, and therefore rejected the correct explanation (1)… Thus setting the stage for the long, historical showdown between Earth-centered and Sun-centered systems.

Plato proposed that the orbits of the planets have what shape? conical circular elliptical equal-angular epicycles

Plato proposed that the orbits of the planets have what shape? conical circular elliptical equal-angular epicycles

The diurnal (daily) motion of stars is due to the motion of the earth around the sun the rotation of the earth the epicyclic nature of the celestial sphere the rotation of the celestial sphere

The diurnal (daily) motion of stars is due to the motion of the earth around the sun the rotation of the earth the epicyclic nature of the celestial sphere the rotation of the celestial sphere

What is the ecliptic? when the Moon passes in front of the Sun the constellations commonly used in astrology to predict the future the Sun's daily path across the sky the Sun's apparent path across the celestial sphere

What is the ecliptic? when the Moon passes in front of the Sun the constellations commonly used in astrology to predict the future the Sun's daily path across the sky the Sun's apparent path across the celestial sphere

About how long does it take the Sun to complete one “trip” around along the ecliptic around the entire sky? One day One month One year The time varies from one trip to the next This never happens

About how long does it take the Sun to complete one “trip” around along the ecliptic around the entire sky? One day One month One year The time varies from one trip to the next This never happens

The Revolution Begins!

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

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” But, it still required some epicycles in order to make accurate predictions because It was still wedded to Aristotle's circular orbit paradigm Predictions were not much better than those of Ptolemy

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.

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

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.