Homework #2  Due Monday, February 1, 11:59 PM  Covers Chapters 1, 2, and 3  Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) – can stop and start as you wish  Read chapters, review notes before starting  Some questions have multiple parts – do not skip them  For some of the drag-and-drop ordering questions, two or more of the answers might be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other.  Note: Incorrect guesses will count against you from now on.  Due Monday, February 1, 11:59 PM  Covers Chapters 1, 2, and 3  Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) – can stop and start as you wish  Read chapters, review notes before starting  Some questions have multiple parts – do not skip them  For some of the drag-and-drop ordering questions, two or more of the answers might be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other.  Note: Incorrect guesses will count against you from now on.

We see apparent retrograde motion when we pass by a planet in its orbit.

Explaining Apparent Retrograde Motion  Easy for us to explain: occurs when we “lap” another planet (or when Mercury or Venus laps us).  But very difficult to explain if you think that Earth is the center of the universe!  In fact, ancients (Greeks) considered but rejected the correct (Sun-centered) explanation for our Solar System – more on this in Chapter 3.  Easy for us to explain: occurs when we “lap” another planet (or when Mercury or Venus laps us).  But very difficult to explain if you think that Earth is the center of the universe!  In fact, ancients (Greeks) considered but rejected the correct (Sun-centered) explanation for our Solar System – more on this in Chapter 3.

Why did the ancient Greeks reject the real explanation for retrograde motion? Their inability to observe stellar parallax was a major factor. Highly exaggerated, but you get the point With the naked eye, stars would have to be at a distance of ~0.05 light years or closer for parallax to be detectable (almost 100 times closer than the closest star) Parallax: apparent shifting of position of a foreground object relative to background objects (think: finger in front of clock)

The Greeks knew that the lack of observable parallax could mean one of two things: 1.Stars are so far away that stellar parallax is too small to notice with the naked eye.  correct OR 2. Earth does not orbit the Sun; it is the center of the universe.  incorrect With rare exceptions such as Aristarchus, the Greeks rejected the correct explanation (1.) because they did not think the stars could be that far away. Thus, the stage was set for the long, historical showdown between Earth-centered and Sun-centered systems. 1.Stars are so far away that stellar parallax is too small to notice with the naked eye.  correct OR 2. Earth does not orbit the Sun; it is the center of the universe.  incorrect With rare exceptions such as Aristarchus, the Greeks rejected the correct explanation (1.) because they did not think the stars could be that far away. Thus, the stage was set for the long, historical showdown between Earth-centered and Sun-centered systems.

Ultimately, why didn’t the ancient Greeks accept that the Earth went around the Sun? A)It violated their religious beliefs. B)If they did, they would no longer have an explanation for planetary retrograde motion. C)They were unaware of the concept of stellar parallax. D)They were aware of stellar parallax but were unable to measure it.

Ultimately, why didn’t the ancient Greeks accept that the Earth went around the Sun? A)It violated their religious beliefs. B)If they did, they would no longer have an explanation for planetary retrograde motion. C)They were unaware of the concept of stellar parallax. D)They were aware of stellar parallax but were unable to measure it.

Chapter 2 Study Guide 1)88 constellations have no real physical significance (just used to divide up the sky) 2)The celestial sphere is the projection of the Earth’s surface onto the sky – poles and equator 3)Ecliptic – the path the Sun takes eastward through the sky relative to the background stars degree per day) – caused by Earth’s motion around Sun 4)Altitude of Polaris gives your latitude on Earth 5)Earth’s 23.5 degree tilt causes seasons and different lengths of daylight throughout the year 1)88 constellations have no real physical significance (just used to divide up the sky) 2)The celestial sphere is the projection of the Earth’s surface onto the sky – poles and equator 3)Ecliptic – the path the Sun takes eastward through the sky relative to the background stars degree per day) – caused by Earth’s motion around Sun 4)Altitude of Polaris gives your latitude on Earth 5)Earth’s 23.5 degree tilt causes seasons and different lengths of daylight throughout the year

Chapter 2 Study Guide 6) Know meaning of solstice, equinox and when they occur 7) Earth’s spin precesses (wobbles) over 26,000 year period  Polaris will not be the Pole Star in a few thousand years 8) Know lunar phases, and understand geometry of Sun-Earth-Moon system (picture in your mind, don’t memorize) – Earth shadow does not cause Moon phases! 9) The Moon DOES rotate (once every 29.5 days) so that we never see the back side of the Moon 6) Know meaning of solstice, equinox and when they occur 7) Earth’s spin precesses (wobbles) over 26,000 year period  Polaris will not be the Pole Star in a few thousand years 8) Know lunar phases, and understand geometry of Sun-Earth-Moon system (picture in your mind, don’t memorize) – Earth shadow does not cause Moon phases! 9) The Moon DOES rotate (once every 29.5 days) so that we never see the back side of the Moon

Chapter 2 Study Guide 10) Know geometry of solar, lunar eclipses, and why they do not happen at every new/full Moon 11) Go see the August 2017 total solar eclipse! 12) Planets undergo retrograde motion, where they move backwards (westward) in their path among the stars  natural consequence of Earth lapping them/being lapped 13) Retrograde motion easy to explain in Sun-centered systems, difficult in Earth-centered systems 14) Greeks considered this, but rejected Sun-centered solar system because they could not measure the parallax of any of the stars  thought stars could not be that distant 10) Know geometry of solar, lunar eclipses, and why they do not happen at every new/full Moon 11) Go see the August 2017 total solar eclipse! 12) Planets undergo retrograde motion, where they move backwards (westward) in their path among the stars  natural consequence of Earth lapping them/being lapped 13) Retrograde motion easy to explain in Sun-centered systems, difficult in Earth-centered systems 14) Greeks considered this, but rejected Sun-centered solar system because they could not measure the parallax of any of the stars  thought stars could not be that distant

Chapter 3 The Science (and History) of Astronomy

How did astronomical observations benefit ancient societies? Keeping track of time and seasons for practical purposes, including agriculture for religious and ceremonial purposes aid to navigation However, few cultures used the scientific method to learn about the nature of the Universe (Greeks were an exception), thus they were not truly studying astronomy.

Ancient people of central Africa (6500 BC) could predict seasons from the orientation of the crescent Moon.

England: Stonehenge (completed around 1550 B.C.)

England: Stonehenge (1550 B.C.)

Southwest United States: “Sun Dagger” marks summer solstice

Scotland: 4,000-year-old stone circle; Moon rises as shown here every 18.6 years.

Macchu Pichu, Peru: Structures aligned with solstices.

South Pacific: Polynesians were very skilled in art of celestial navigation.

France: Cave paintings from 18,000 B.C. may suggest knowledge of lunar phases (29 dots)

"On the Xinwei day the new star dwindled." "On the Jisi day, the 7th day of the month, a big new star appeared in the company of the Ho star." China: Earliest known records of supernova explosions (1400 B.C.) Bone or tortoiseshell inscription from the 14th century B.C.

Days of week were named for the Sun, Moon, and visible planets.

Greeks were the first people known to make models of nature. They tried to explain patterns in nature without resorting to myth or the supernatural. Greek geocentric model (c. 400 B.C.) Why does modern science trace its roots to the Greeks?

Eratosthenes Measures Earth (c. 240 B.C.) Calculate circumference of Earth: 7/360 = (Alexandria-Syene distance)/(circum. Earth)  circum. Earth = 5000  360/7 stadia ≈ 250,000 stadia Measurements: Syene (modern day Aswan) to Alexandria distance ≈ 5000 stadia angle = 7° Compare to modern value (≈ 40,100 km): Greek stadium ≈ 1/6 km  250,000 stadia ≈ 42,000 km First day of summer at noon: Sun shone directly into a well in Syene, but missed the well in Alexandria by 7°. Greeks were quite well aware that the Earth was round.

Underpinnings of the Greek geocentric model: How did the Greeks explain planetary motion? Earth at the center of the universe (since no detected parallax) Heavens must be “perfect”: Objects move on perfect spheres or in perfect circles. Aristotle Plato

The most sophisticated geocentric (Earth-centered) model was that of Ptolemy (A.D ) — the Ptolemaic model: Sufficiently accurate to remain in use for 1,500 years. Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”) Ptolemy Extremely contrived…..

But this model made it difficult to explain apparent retrograde motion of planets… Review: Over a period of 10 weeks, Mars appears to stop, back up, then go forward again.

So how does the Ptolemaic model explain retrograde motion? Planets really do go backward in this (wrong) model… Epicycles (circles upon circles) This system predicts the orbits reasonably well if you add enough epicycles to the system…. Mercury eventually required 11 epicycles in Ptolemaic model to remain sufficiently accurate! Needed to mimic retrograde motion Extremely contrived!

Ptolemy’s Geocentric Model Earth is at center Sun orbits Earth Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles This view of the Solar System held for 1500 years….

Which of the following was not a feature of the Ptolemaic model? A)Epicycles were used to explain planetary retrograde motion. B)The Earth was at the center of the Solar System. C)The Earth orbited the Sun. D)The orbits of planets were perfect circles.

Which of the following was not a feature of the Ptolemaic model? A)Epicycles were used to explain planetary retrograde motion. B)The Earth was at the center of the Solar System. C)The Earth orbited the Sun. D)The orbits of planets were perfect circles. Greeks thought the Earth did not move because they could not measure stellar parallax.

How was Greek knowledge preserved through history? The Muslim world preserved and enhanced the knowledge they received from the Greeks. Al-Mamun’s House of Wisdom in Baghdad was a great center of learning around A.D With the fall of Constantinople (Istanbul) in 1453, Eastern scholars headed west to Europe, carrying knowledge that helped ignite the European Renaissance.

How did Copernicus, Tycho, and Kepler challenge the Earth-centered model? Copernicus ( ) Nicolas Copernicus proposed a Sun- centered model (published 1543) Used model to determine layout of solar system (planetary distances in AU) But... The model was no more accurate and not any simpler than the Ptolemaic model in predicting planetary positions, because it still assumed perfectly circular orbits (and therefore still had to use epicycles ).

Tycho Brahe ( ) Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions. Still could not detect stellar parallax, and thus still thought Earth must be at center of solar system (but recognized that other planets go around Sun). Hired Johannes Kepler, who used Tycho’s observations to discover the truth about planetary motion. Tycho Brahe

Kepler first tried to match Tycho’s observations with circular orbits -- no success An 8-arcminute discrepancy led him eventually to use ellipses rather than circles “If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.” Johannes Kepler ( ) Good scientist! Johannes Kepler