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PHYS 1411 Introduction to

Origins of Modern Astronomy

Chapter 4

Announcement Topics in Chapter 4 • of the • Midterm Exam – ’s Model – Wednesday October 10 during class – Retrograde Motion of – More on it next week – 's Model: Epicycles th • After Friday 28 September you should be – Model able to see you participation and lab • Heliocentric Model of the Solar System scores on Blackboard – • • Kepler’s Laws of Planetary Motion

Aristotle’s Geocentric Model (350 BC)

Is the Center of Our Solar System?

NASA StarChild

1 First Observational Challenge to Geocentric Model First Observational Challenge to Geocentric Model

Retrograde Motion of Mars http://astro.unl.edu/classaction/animations/renaissance/retrograde.html

Brief Timeline of Astronomy Brief Timeline of Astronomy • ~ 45 BC: A solar called Julian calendar is • ~400 BC: Eudoxus tries introduced for the Roman army to explain retrograde • ~100 AD Ptolemy introduces epicycles in his model of motion the solar system. • The spheres of Eudoxus explain the motions in the heavens by means of nested spheres rotating about various axes at different rates. • Earth is located at the center. In this illustration, only 4 of the 27 spheres are shown.

McGraw Hill Higher Education

Brief Timeline of Astronomy Ptolemy Model of the Solar System

•~140 BC: Ptolemy perfects the geocentric model of the solar system • Uniformly rotating were key elements of ancient astronomy. • Ptolemy created a mathematical model of the Aristotelian in which the followed a small called an epicycle that slid around a larger circle called a deferent. • By adjusting the size and rate of rotation of the circles, he could approximate the retrograde motion of a planet.

2 Brief Timeline of Astronomy Brief Timeline of Astronomy

• 1582 AD: Pope Gregory XIII introduces the Gregorian • ~ 45 BC – 1420 AD: Muslim astronomers invent calendar. and make important contribution to the • 1603 AD: Johann Bayer assigns Greek letters to , knowledge of astronomy. still in use today (Bayer astronomical catalog). • ~ (1394- 1440) was a noted Muslim • 1608 AD: Hans Lippershey invents the . astronomer and built an observatory and published astronomical tables and a catalogue with 1000 stars • 1609 AD: Galileo uses the telescope for astronomical purpose. He discovers the 4 Jovian , the Moons •14th-15th century AD: The period craters and a detailed sketch of the Milky Way. Galileo • 1543 AD: Copernicus present the heliocentric of proposes the law of falling bodies. the Universe. • 1609 AD: Kepler announces the first and second law.

Tycho Brahe Model of Solar System Tycho Brahe (1546 - 1601) • He proposed a model of the solar system. – The and the the earth while the other orbit the Sun. • Invented instruments for planetary motion studies. • Discovered exploding stars and . • Debated the validity of the heliocentric model. Tycho’s model is geocentric with the Sun and Moon revolving • Realized that the Universe is around Earth, but the planets revolved around the Sun. All changing and is complex. motion was along circular paths.

Copernicus’ new (and correct) explanation The Copernican Universe for retrograde motion of the planets

Retrograde (westward) motion of a planet occurs when the Earth passes the planet.

This made Ptolemy’s epicycles unnecessary. Speed of Planet is indicated by length of blue arrow http://astro.unl.edu/classaction/animations/renaissance/retrograde.html

3 Kepler’s Laws of Planetary Motion (1571 – 1630)

• Used the precise observational tables of Tycho Brahe to study planetary motion mathematically c • Found a consistent description of planetary motion by abandoning both: – Eccentricity e = c/a – Uniform motion • Planets move around the sun on elliptical paths, with non-uniform velocities

Kepler’s Laws of Planetary Motion How to find Eccentricity 1.The of the planets are ellipses with the sun at one focus.

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Eccentricities of Ellipses Eccentricities of Planetary Orbits

1) 2) 3) Orbits of planets are virtually indistinguishable from circles: e = 0.02 e = 0.1 e = 0.2 Most extreme example: Earth: e = 0.0167 Pluto: e = 0.248

4) 5) e = 0.4 e = 0.6

4 Kepler’s First Law of Planetary Kepler’s Second Law of Planetary Motion Motion • A line from a planet to the Sun sweeps over equal areas in equal intervals of time

Keplers Third Law Keplers Third Law

• A planet’s (P) squared is proportional to its average distance from the sun (a) cubed:

(Py = period in years; aAU = distance in AU)

2 3 Py = aAU

Schools.wiki.com

Kepler’s Third Law of Planetary The Eye is Inefficient Motion • A planet’s orbital period squared is • The early Greek philosophers believed proportional to its average distance from that the earth did not moved because their the Sun cubed eyes could not see the motion of stars • The telescope was not invented yet. • So they could not decide which model (heliocentric or geocentric) was correct.

5 What is Parallax? Apparent Motion of Stars

• After the invention of the telescope it became known that a foreground appeared to move with respect to background stars during the course of a year. • This let the acceptance of heliocentric model

Geocentric VS Heliocentric Model • https://www.youtube.com/watch?v=UtOEn TiAZlU • https://www.youtube.com/watch?v=khIzr6 610cQ

Acknowledgment

• The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only • Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class.

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