Exam Wednesday September 21 PHYS 3380 - Astronomy Exam Wednesday September 21 The exam will cover anything that was covered in the notes The exam will be closed book. You will be allowed to have one 8/12 X 11 sheet of notes for the exam. Good Luck!

placed Earth away from center of perfect spheres PHYS 3380 - Astronomy Hipparchus (c. 190 - 120 B.C.) placed Earth away from center of perfect spheres developed a star catalog - method to predict positions of sun and moon - discovered precession of earth’s axis of rotation - estimated precession of equinoxes at 46”/year - actually 50.26” Ptolemy (c. A.D. 100 - 170) combined all available astronomical information into 13 volume work, the Almagest - a geometrical model of solar system with Earth in center that predicted positions of Sun, Moon and planets - used for 1,500 years used idea of Apollonius (c. 240 - 190 B.C.) that planets move on small circle that turns upon larger circle around the Earth explained retrograde motion of planets - fully developed by Hipparchus - accurately predicted planetary positions within a few degrees of arc

Retrograde Motion of Planets PHYS 3380 - Astronomy Retrograde Motion of Planets Apparent retrograde motion - reversal of planetary motion through the zodiac from eastward to westward Apparent retrograde motion of Jupiter

Ptolemaic Model Deferent - main circle of planet path PHYS 3380 - Astronomy Ptolemaic Model Deferent - main circle of planet path Epicycle - small circles on deferent along which planet moved

Ptolemaic Model Animation PHYS 3380 - Astronomy Ptolemaic Model Animation

PHYS 3380 - Astronomy Ptolemy's model of the motions of the Sun, Moon, and planets around Earth.

Mars Retrograde Motion PHYS 3380 - Astronomy Mars Retrograde Motion Earth’s orbital speed is faster than Mars’. When Earth catches up with Mars, Mars appears to move backwards against the background of the stars

Mars Retrograde Motion Animation PHYS 3380 - Astronomy Mars Retrograde Motion Animation

Heliocentric World View - The Copernican Revolution PHYS 3380 - Astronomy Heliocentric World View - The Copernican Revolution Nicholas Copernicus (1473-1543) - wanted better way to predict planetary positions - adopted Sun-centered planetary system suggested by Aristarchus - worked out simple geometric relationships that allowed calculation of planet’s true orbital period and distance from Sun in terms of Earth-Sun distance (AU) - still believed that heavenly motion must be perfect circles - had to add circles upon circles as in the Ptolemaic model - did not make substantially better predictions and was not accepted for another 50 years

- observed comet - proved was in the heavens PHYS 3380 - Astronomy Tycho Brahe (1546 - 1601) - observed alignment of Jupiter and Saturn in 1563 - occurred two days later than Copernicus prediction - decided to compile precise measurements of stellar and planetary positions - compiled best set of naked-eye observation ever made - to within 1 arcminute (thickness of a fingernail at arm’s length) - observed supernova of 1572 - proved it was farther away than the Sun - called it a nova (“new star”) - observed comet - proved was in the heavens - believed planets must orbit Sun but never succeeded in explaining planetary motion. Inability to detect stellar parallax led him to believe that Sun orbited Earth while all other planets orbited Sun

A Complete Reformation of Astronomy PHYS 3380 - Astronomy A Complete Reformation of Astronomy Johannes Kepler (1571 - 1630) - hired by Tycho Brahe to explain observations - years of calculations trying to find circular orbit for Mars that matched Tycho’s observations - succeeded in matching Mars’ position in ecliptic - could not match position north or south of ecliptic - finally realized planetary orbits were not circular but elliptical - developed three laws of orbital motion - accurately predicted planetary motions and matched Tycho’s data

Kepler’s Laws of Planetary Motion PHYS 3380 - Astronomy Kepler’s Laws of Planetary Motion : Law 1: Law of elliptical orbits Each planet moves in an elliptical orbit. Law 2: Law of areas The imaginary line connecting any planet to the sun sweeps over equal areas of the ellipse in equal intervals of time. Law 3: Law of periods The square of any planet's period of orbital revolution is proportional to the cube of its mean distance from the sun.

PHYS 3380 - Astronomy Kepler’s First Law The orbit of each planet around the Sun is an ellipse with the Sun at one focus

Drawing a circle. (b) Drawing an ellipse. (c) Eccentricity PHYS 3380 - Astronomy Drawing a circle. (b) Drawing an ellipse. (c) Eccentricity describes how much an ellipse deviates from a perfect circle -ratio between distance from the center of the ellipse to the focus of the ellipse and the semi-major axis.

PHYS 3380 - Astronomy

PHYS 3380 - Astronomy Kepler’s Second Law As a planet moves around its orbit, it sweeps out equal areas in equal times.

Area and Time Animation PHYS 3380 - Astronomy Area and Time Animation

PHYS 3380 - Astronomy Kepler’s Third Law The square of any planet's period, P, of orbital revolution is proportional to the cube of its mean distance, r, from the sun. I.e., the more distant a planet, the slower it moves on average. Example: For earth, r E= 1 AU, PE = 1 year. For Mars, r M= 1.52 AU, PM = 1.88 years

A plot of the cube of the average planetary distance vs the square PHYS 3380 - Astronomy A plot of the cube of the average planetary distance vs the square of the orbital period is a straight line The average orbital speed is inversely proportional to the average distance from the sun

Planet Semimajor Axis (1010 m) Period (T yr) T2/a3 (10-34 y2/m3) PHYS 3380 - Astronomy Planet Semimajor Axis (1010 m) Period (T yr) T2/a3 (10-34 y2/m3) Mercury 5.79 0.241 2.99 Venus 10.8 0.615 3.00 Earth 15.0 1 2.96 Mars 22.8 1.88 2.98 Jupiter 77.8 11.9 3.01 Saturn 143 29.5 Uranus 287 84 Neptune 450 165 Pluto 590 248

PHYS 3380 - Astronomy Note: - Kepler's third law needs to be modified when the orbiting body's mass is not negligible compared to the mass of the body being orbited. - Kepler's laws assume a two-body system - particularly bad approximation in the case of the Earth-Sun-Moon system for calculations of the Moon's orbit, Kepler's laws are far less accurate than the empirical method invented by Ptolemy. - Kepler's laws do not consider the emission of radiation or relativity - Because electrical forces, like gravity, obey an inverse square law, Kepler's laws also apply to bodies interacting electrically. Kepler did not understand why his laws were correct - Isaac Newton discovered the answer more than fifty years later. For instance, the second law also a statement of conservation of angular momentum.

The Death of the Earth Centered Universe PHYS 3380 - Astronomy The Death of the Earth Centered Universe Galileo Galilei (1564 - 1642) - demonstrated that a moving object remains in motion unless acted on by an outside force (Newton’s 1st law) - contradicted Aristotle’s claim that the natural tendency of any moving object is to come to rest. Birds, falling stones, clouds, etc.. would stay with the Earth unless knocked away by some force - used telescope that he built (invented by Hans Lippershey) - - saw sunspots on the Sun, craters and valleys on the moon - proved that the heavens were not perfect and unchanging - observed moons orbiting Jupiter - observed the phases of Venus - showed that Milky Way resolved into countless individual stars - argued stars far more numerous and distant than imagined - reason stellar parallax not observed - recanted before Church inquisition in Rome in 1633 - formerly vindicated by the Church in 1992

Major Discoveries of Galileo PHYS 3380 - Astronomy Major Discoveries of Galileo Moons of Jupiter (4 Galilean moons) (What he really saw) Rings of Saturn (What he really saw)

PHYS 3380 - Astronomy Surface structures on the moon - shadows; first estimates of the height of mountains on the moon

Sun spots (proving that the sun is not perfect!) PHYS 3380 - Astronomy Sun spots (proving that the sun is not perfect!)

PHYS 3380 - Astronomy Phases of Venus (including “full Venus”) - In the Ptolemaic system, phases would only range from new to crescent. Proved that Venus orbits the sun, not the Earth!

Phases of Venus Animation PHYS 3380 - Astronomy Phases of Venus Animation

A New View of Nature Sir Isaac Newton (1642 - 1727) PHYS 3380 - Astronomy A New View of Nature Sir Isaac Newton (1642 - 1727) - followed Galileo’s lead - developed fundamental laws of motion - revolutionized mathematics and science - experienced moment of inspiration at 24 years old - saw apple fall from tree and suddenly understood gravity - published most famous book in science in 1687 - Philosophiae Naturalis Principia Mathematica - Principia for short - built first reflecting telescope - invented calculus - discovered three laws of motion - discovered universal law of mutual gravitation

Newton's Three Laws of Motion PHYS 3380 - Astronomy Newton's Three Laws of Motion First law: A body remains at rest or moves along a straight line with constant velocity so long as no external force acts upon it. Second law: A body (m) acted upon by a force (f) will accelerate (a) in the direction of the applied force. The greater the force or the smaller the mass, the greater will be the acceleration . F =ma Third law: A body subjected to a force reacts with an equal counter force to the applied force: That is, action and reaction are equal and oppositely directed, but never act on the same body.

For every force, there is an equal and opposite force 2nd Law PHYS 3380 - Astronomy 1st Law A body moves along a straight line with constant velocity so long as no external force acts upon it. 3rd Law For every force, there is an equal and opposite force 2nd Law Force equals mass times acceleration

Velocity and Acceleration PHYS 3380 - Astronomy Velocity and Acceleration Newton showed that acceleration (a) is the change of a body’s velocity (v) with time (t): a a = Dv/Dt Differential calculus! Velocity and acceleration are vectors. v Different cases of acceleration: Acceleration in the conventional sense (i.e. increasing speed) Deceleration (i.e. decreasing speed) Change of the direction of motion (e.g., in circular motion)

Feather and Hammer Movie PHYS 3380 - Astronomy Galileo demonstrated that acceleration of gravity is independent of the mass of the falling object - supposedly dropped balls of different mass from Leaning Tower of Pisa - Newton showed why. Feather and Hammer Movie