NATS 1745 Study Guide Answers Unit 1-4 PDF

NATS1745 - History of Astronomy Ancient Skywatching of the Sun Study Guide Unit 1 1. Introduction to archaeoastronomy: a. List the cycles of the sky described in the lecture videos that have been obvious to skywatchers since ancient times. Apparent motion of the stars, rising and se...

NATS1745 - History of Astronomy Ancient Skywatching of the Sun Study Guide Unit 1 1. Introduction to archaeoastronomy: a. List the cycles of the sky described in the lecture videos that have been obvious to skywatchers since ancient times. Apparent motion of the stars, rising and setting patterns of the Sun and Moon, apparent motion motion plants, solstice and equinox b. What is archaeoastronomy? Archeoastronomy: the study of ancient sites and artefacts and their connections to the patterns in the day and night sky 2. Newgrange: a. What celestial event is Newgrange aligned to? What is special about this day of the year, and the days that follow it? Describe what happens at Newgrange on this day. Newgrange is aligned to the rising sun on Winter solstice (Dec 21st). This is the shortest day of the year with the least amount of sunlight. The winter solstice can be known to represent rebirth, and guarding the Sun’s power. The significance of aligning Newgrange with the Winter solstice is that the people of the culture may have wished rebirth or reincarnation of their dead. A beam of light shines through the roof box through the chamber and hits a tomb at the end of the chamber marked with a Triskele (a common symbol throughout Celtic History), which could represent life-death-rebirth. The light remains momentarily for a period of 17 minutes. 3. The Sundagger of Chaco Canyon: a. What days and times of the year can the Sundagger be used to indicate? Describe what happens to the Sundagger on these days and times. The Sun dagger can be used to indicate the solstice and equinox Equinox: daggers are shown on the large and small petroglyphs, there is one on each Summer Solstice: one sun dagger splitting the middle of the large petroglyph Winter Solstice: one sun dagger on each side of the petroglyph 4. Stonehenge: a. What celestial event is Stonehenge aligned to? Describe what happens at Stonehenge on this day, in the 21st century. The stonehenge is aligned with the rising sun on summer solstice. On June 21st, you are able to see the sunrise behind the heelstone if you are inside the circular ditch of the central region of stonehenge, looking towards the heelstone b. Why do archaeoastronomers suspect that Stonehenge's Heel Stone had a missing partner stone? The archaeoastronomers suspect that stonehenge heel stone had a partner because when stonehenge was built, the rising sun on Summer solstice rose slightly to the left. They believe that there were two stones so that the light would go in between and reach the center region of Stonehenge 5. The Sun’s daily cycle: a. What causes the Sun to rise in the east and set in the west every day? The Sun rises in the east and sets in the west because of the Earth’s rotation towards the East; this is called diurnal motion. The Earth spins on its North-South axis. b. Describe the Sun’s height & approximate direction (N, E, S or W) in the sky at noon, sunset, midnight & sunrise, as seen from both the northern and southern hemisphere. Noon (Day) In the northern hemisphere, people perceive the Sun at its highest point in the Southern direction In the southern hemisphere, people perceive the Sun at its highest point in the Northern Hemisphere Sunset In the northern hemisphere, the sun is at its lowest point and near the horizon. It sets at the Northwest direction In the southern hemisphere, the sun is at its highest point and near the horizon. It sets in the Southwest direction Midnight In the northern hemisphere, people face towards the midnight sun and the sun does not set below the horizon. It is in the Northern direction In the southern hemisphere, people face away from the midnight sun and the Sun does not set below the horizon. It is in the Southern direction Sunrise  In the northern hemisphere, the Sun is low at the horizon. The sun rises in the Northeast in the summer and rises southeast in the winter In the southern hemisphere, the Sun is low at the horizon. The sun rises in the southeast in the summer and rises northeast in the winter 6. The Sun’s annual cycle: a. What does the word "solstice" mean? How does it describe what happens to the Sun's rising and setting positions on the summer and winter solstices? Solstice means for the sun to stand still for a day. It comes from the latin word, sol= sun, sister=to stand still. Winter solstice/solar standstill (Dec 21st): south most-rise and set, shortest day, lowest noon sun Summer solstice (June 21st): north most rise and set, longest day, highest noon sun b. Which day is the longest day of the year? Which day is the shortest day of the year? Describe the difference between the Sun’s path through the sky on these 2 days. Use this to explain the 2 reasons that summertime is warmer than wintertime. The longest day of the year is the Summer solstice. The shortest day of the year is the Winter Solstice. The difference between both days is the tilt that the Earth has. During the summer, it is tilted towards the Earth meaning the energy/light has to spread less of a distance. While during the winter, the Earth is tilted away from the sun, the amount of energy/light has to spread over a large area. As well as the amount of light, each day during winter, the sun is the lowest in the sky, that means not a lot of direct light while during the summer, there is a lot of direct light because the sun is the highest in the sky. c. What are the lengths of day time and night time on the equinoxes? The lengths of day time and night time on the equinoxes is equal, about the same 12 hours each. d. On the two diagrams below, you should be able to determine: the hemisphere of the Earth (north or south) that each diagram represents which daily path of the Sun (A, B, or C) corresponds to the summer solstice, winter solstice & equinoxes, and the months in which they occur. the Sun’s rising, setting, & noon position on each path the direction the Sun is travelling on each of the daily pathways Diagram 1 (southern hemisphere): A. Summer solstice (December 21st) a. Summer solstice rising: south of east, setting south of west. Noon: North B. Autumnal (March 19th) and Vernal (Sept 23rd) Equinox a. Rising due about East, and setting due west. Noon= North C. Winter Solstice (June 21st) a. Winter solstice rising: north of east, setting due north of west. Noon=north D. East to West Diagram 2 (northern hemisphere): A. Summer solstice (June 21st) a. Summer solstice rising: north of east, setting north of west. Noon=South B. Autumnal (Sept 23rd) and Vernal (March 19th) equinox a. Rising due about east, and setting due west. Noon=South C. Winter solstice (Dec 21st) a. Winter solstice rising: south of east, setting south of west. Noon= South D. East to West e. For each position in the diagram below, you should be able to determine: The solstice or equinox that each position of the Earth corresponds to, both in the northern and southern hemisphere The local time at the position of each observer  1. Northern Hemisphere: a. Summer Solstice b. Fall equinox c. Winter solstice d. Spring equinox 2. Southern Hemisphere: a. Winter solstice b. Spring equinox c. Summer solstice d. Fall equinox 3. Local Time: a. Midnight b. Rise c. Noon d. Set 7. The cause of seasons: a. What causes the seasons? Describe the orientation of the Earth relative to the Sun on the solstices and equinoxes. Earth’s tilted axis causes the seasons Orientation of the Earth relative to the Sun on the Solstice: ○ The summer solstice occurs at the moment the earth’s tilt toward the sun is at a maximum. Therefore, on the day of the summer solstice, the sun appears at its highest elevation with a noontime position that changes very little for several days before and after the summer solstice. The summer solstice occurs when the sun is directly over the Tropic of Cancer. For every place north of the Tropic of Cancer, the sun is at its highest point in the sky and this is the longest day of the year ○ The winter solstice marks the shortest day and longest night of the year. In the northern hemisphere, it occurs when the sun is directly over the Tropic of Capricorn Orientation of the Earth relative to the sun on the equinox: ○ There are only two times of the year when the Earth’s axis is neither tilted toward or away from the sun, resulting in a “nearly” equal amount of daylight and darkness at all latitudes. These events are referred to as Equinoxes (Vernal and Autumnal). At the equator, the sun is directly overhead at noon on these two equinoxes  ○ The “nearly” equal hours of day and night is due to refraction of sunlight or a bending of the light’s rays that causes the sun to appear above the horizon when the actual position of the sun is below the horizon ○ Additionally, the days become a little longer at the higher latitude (Those at a distance from the equator) because it takes the sun longer to rise and set b. Why does direct light feel warmer than indirect light? Direct light feels warmer because it covers a small surface area, heat is concentrated and warmer, and the sun is high in the sky. Indirect sunlight feels less warm because it covers a large surface are, head it spread out and colder, and the sun is low in the sky c. What season does the Southern Hemisphere experience during Northern summer, and why? The Southern hemisphere experiences winter during the summer in the Northern Hemisphere.This is because the southern hemisphere is tilted away from the sun and therefore receives the sun’s rays at an angle. This also means that the North pole is tilted towards the SUn, which results in summer in the northern hemisphere. 8. The Sun and latitude: a. What is the latitude of the equator? What is the latitude of the North and South Pole? The latitude of the equator is 0 degrees. The latitude of the North pole is 90 degrees North, while the latitude for the South pole is 90 degrees South b. Within what latitudes can an observer see the Sun directly overhead? How did these latitudes get their names? Within 23.5 degrees of the equator called the tropics. Tropic of Cancer 23.5 degrees north, Tropic of Capricorn 23.5 degrees South. They got their names from the Greek/Babylonian constellations c. What are polar nights and polar days? Within what latitudes do these occur? What happens to the number of polar days and nights as you get closer to one of Earth’s poles? During the summer solstice at 70 degrees North latitude (within the Arctic Circle), the sun climbs higher due to the tilt of the Earth towards the sun, preventing the sun from setting. This creates a 24-hour period where the sun continuously moves around the sky, known as a Polar Day. On the other hand, during the winter solstice at the same latitude, the sun is so low on the horizon, because of the Earth's tilt, that it sets and remains below the horizon for several days. This period, when the sun appears to orbit halfway below the horizon, is known as a Polar Night, lasting more than 24 hours. 9. The celestial sphere: a. Where is the zenith and what is its altitude? Where is the horizon and what is its Altitude? Zenith: the point on the sky directly above the observer, it has a 90 deg altitude Horizon: the circle that divides a person’s visible sky from invisible sky, it has a 0 degrees altitude b. What is the altitude of the Sun when it is halfway up the sky? Does the Sun’s altitude and azimuth depend on the observer's location? Explain. The altitude of the Sun when it's halfway up the sky is 45 deg altitude. Yes, the altitude and azimuth depends on the observer’s location because altitude depends on the horizon 10. Describing lengths in the sky: a. What is the Sun’s altitude if you can fit 3 fists in between the horizon and the Sun’s position in the sky? The sun’s altitude is 30 deg altitude b. Given that the Moon’s angular length is 0.5°, what fraction of the width of your finger would span the length of the Moon? 1 It would be 2 of the width of finger NATS1745 - History of Astronomy Study Guide Unit 2 1. Introduction to Mayan Astronomy: a. What 2 features of the Pyramid of Kukulkan tell us that the Maya had deciphered the solar cycle? The Mayans built 91 steps from the bottom to the top of the pyramid, which represented the seasons (e.g. 91 days from equinox to the solstice). The pyramid had 4 stairs with 91 steps and a top step which added to 365 days, which equals the sun’s cycle. This shows the mayans were of the sun’s annual cycle. Also the annual serpent-pattern of light and shade tracks the time of year (e.g. on the equinoxes, the full serpent ends at Kukulkan’s head).  b. What was El Caracol likely used for, and how do we know this? El Caracol is a round building that was used like an observatory and to get a view of the entire horizon. The windows in the observation room alignes to the N-most and S-most setting positions of planet Venus (allowed the Mayans to measure the duration of Venus’ full path in the sky). 2. Mayan Record Keeping: a. Briefly describe the origin of the belief that the world was going to end on Dec 21, 2012. The Mayan’s long calendar was finite (had an ending) and to prove that the Monument 6 contained information referring to the “end of the 13th Baktun.” The Mayan’s calendar maxed out the number and reached the end in counting which gave us Dec 21, 2012. The next calendar would have been 13.0.0.0.0 but the 13th Baktun is a non-repeating straight count of days. It originally meant the amount of cycles that they were counting stopped and a new cycle would start b. What physical proof do we have that the Maya tracked eclipses and the planet Venus? The Dresden Codex was the Mayan’s bark book that contains 30 years with of tracking of Venus and 100 years of predictions of eclipses c. What was it about the Mayan number system that facilitated their ability to find patterns in their numeric records of the events in the sky? The Mayan’s numeral system is a series of dots and lines that is a very easy visual system to represent numbers. It made it easy to represent larger numbers and add and subtract them when tracking cycles in the sky 3. The Moon’s Phases: a. What causes the Moon's phases? Refers to the changing shape of the moon’s sunlit portion (waxing half-lit side is increasing from crescent to full moon, Waning half- from full moon to crescent). Causes= our view of the sunlit side visible to us (the side facing the sun) which changes the moon’s appearance for us on Earth. b. What is a lunation? A lunation is one complete cycle of moon phases (29.5 days long) c. State the 8 phases of the Moon, in order of appearance, starting from New Moon. 8 phases of the moon:  1. New moon (about 15 days after full moon)- the moon is completely dark to us, the unlit portion is facing earth 2. Waxing crescent- lit portion starting to increase towards a full moon, lit up on the right side (based on our relative position on earth) 3. 1st Quarter moon- seen after a new moon, a sunlit portion lit up on the right 4. Waxing gibbous- sunlit portion increasing towards full on the right side of moon towards full moon 5. Full moon- directly whole sunlit side facing us 6. Waning gibbous- moon sunlit side (on left side) is decreasing from a full moon 7. 3rd Quarter moon- seen after a full moon, sunlit portion lit up on the left side 8. Waning crescent moon- lit up portion starting decrease towards a new moon, lit up on the left side d. What is the difference between a waxing and waning moon? If we look at the moon on a given night, how can we tell if it is waxing or waning? A waxing moon refers to the phase of the moon where the portion of the moon we can see from Earth is getting larger each day, moving from a new moon (no visible moon) to a full moon. On the other hand, a waning moon is the phase where the visible portion is getting smaller each day, moving from a full moon back to a new moon. If you're in the northern hemisphere and the right side of the moon is lit, then the moon is waxing. If the left side is lit, then the moon is waning. If you're in the southern hemisphere, the sides are reversed: the moon is waxing if the left side is lit and waning if the right side is lit. e. Why are crescent moons seen primarily during the day? Why are gibbous and full moons seen primarily at night? The crescent moons are always on the side of the sky where the sun is which places it above the horizon. The closer the moon is to the new phase, the more daytime the moon is. Quarter moons are at midpoints and can be seen half during the day and half at night. The larger the moon’s visible sunlit portion (closer it is to full), the more night hours the moon is visible (full moon only be seen at night). A crescent moon is seen primarily during the day because it rises and sets around the same time as the sun. When the moon is in its crescent phase, it is closer to the sun in the sky and is often lost in the sun's glare. That's why we can often see a crescent moon during the day, especially in the hours just after sunrise or before sunset. On the other hand, a full moon rises at sunset and sets at sunrise, so it is visible primarily at night. A gibbous moon, which is when the moon is more than half illuminated but not full, also tends to rise before sunset and set after sunrise, making it visible mostly at night as well.  f. On the diagram below, you should be able to determine the moon’s phases at each of the 4 positions of Earth (A, B, C, D) A. New Moon B. 1st Quarter C. Full Moon D. 3rd Quarter g. In the diagram above, what is the Earth’s phase at positions A and C, as seen from an astronaut on the Moon? Describe how the Earth would appear to an astronaut on the Moon at positions B and D. A. The Earth has a whole sunlit side like full moon B. The earth is completely dark like new moon C. A quarter side of Earth is sunlit like 1st quarter moon D. A quarter side of Earth is sunlit like 1st quarter moon 4. Solar and Lunar Eclipses: a. Why did many ancient civilizations believe that eclipses are bad omens as well  as unpredictable? Eclipses are unpredictable because their cycles span over such a large period of time (18 years). They are seen as a bad omen because it doesn't feel natural. The moon is red, an unnatural colour, during a lunar eclipse. During a solar eclipse it’s hard to see and everything goes dark when it should be light. Light is the source of life essentially, which makes it scary when the light goes out seemingly unexpectedly. b. What is the cause of a solar eclipse? What is the Moon's phase when this happens? A solar eclipse happens when a new moon casts its shadow on earth. The moon must be in it’s new moon phase and the shadow must reach the Earth’s surface c. Describe the appearance of a total solar eclipse and a partial solar eclipse. In a total solar eclipse, the Moon passes in front of the Sun and all that can be observed is a small ring on the outside of light In a partial solar eclipse, the Sun appears to have a bite out of it that increases, but never completely covers it. How much is covered depends on how close you are to the umbra d. If an observer sees a total solar eclipse, where is this observer standing? Where is an observer standing if they see a partial solar eclipse? What will the Sun look like if you are standing outside the umbra and penumbra during a solar eclipse Total: in the umbra Partial: in the penumbra Outside umbra and penumbra: there is nothing; you can see no difference, no eclipse e. What is the cause of a lunar eclipse? What is the Moon's phase when this happens? Describe the appearance of a total lunar eclipse, a partial lunar eclipse and a penumbral lunar eclipse. A lunar eclipse occurs when a Full moon falls onto Earth’s shadow. The moon has to be in its Full Moon phase. Total lunar eclipse: is when the moon goes completely red after slowly disappearing throughout the night as it is covered by the Earth’s shadow. Partial Lunar eclipse: bites appear to be taken out of the moon, but it is not as drastic as a total lunar eclipse. What you see depends on how partial it is Penumbral lunar eclipse: doesn’t really look much different than a normal moon. It is a little fainter/dimmer if you really look, but it’s mostly the same in appearance.  f. If a total lunar eclipse is seen, what is the Moon passing through? How about if a partial lunar eclipse is seen? How about if a penumbral lunar eclipse is seen? If a total lunar eclipse is seen, the moon is passing through the Earth;s umbra. If a penumbral lunar eclipse is seen, the moon is only passing through the penumbra If a partial lunar eclipse is seen, the moon is passing partially through the umbra, but not completely, so it spends a lot of time in the penumbra g. If an observer on the night side of Earth witnesses a total lunar eclipse, will all observers on the night side of Earth see a total lunar eclipse at the same time? Yes they will because Earth is casting the shadow on the moon and everyone will be able to see this on the night side since it is not location dependent, you just to be in the night 5. The Eclipse Cycle and the Mayan Eclipse Records: a. Why don’t eclipses occur every New and Full moon? The orbit of the moon is slightly tilted at 5 degrees. Hence a new moon may be slightly below the Earth so that its shadow is not cast on Earth. Likewise, a full moon may be slightly above the Earth so that the Earth’s shadow is not cast on the moon. So unless the new moon is directly in line with the sun and the full moon is directly in line with Earth, an eclipse will not occur. They have to be coplanar. Eclipses don't occur every New and Full moon due to the tilt of the Moon's orbit. The Moon's orbit around the Earth is tilted about 5 degrees relative to the Earth's orbit around the Sun. As a result, the Earth, Moon, and Sun only align perfectly (which is required for an eclipse) about two to five times a year, rather than during every New and Full moon. b. What do we call the time period when eclipses can occur? On average, how many lunations are there between these time periods? Why are there always at least 1 (or 2) solar eclipses and 1 (or 2) lunar eclipses during these time periods? An eclipse season is when the Sun, Earth, and the Moon are coplanar and eclipses can occur. There may be 6 lunations between the eclipse seasons. Further, there are 29.5 days in a lunation period whereas there are 31-38 days in an eclipse season. Hence, eclipses may occur at least twice a year c. Why are lunar eclipses seen more frequently than solar eclipses? It is because to see a solar eclipse one must be within the umbra or penumbra but to see a lunar eclipse you only need to be on the night side of the Earth d. On the diagram in question 3, you should be able to identify the position(s) (A, B, C and/or D) at which either a solar eclipse or lunar eclipse is possible A solar eclipse is possible at Position A, a lunar eclipse is possible at position C e. Describe the evidence in the Mayan Dresden codex that tells us that the Maya understood the eclipse cycle and were able to predict, for eternity, the dates on which eclipses could occur. The number 177 and 148 are found at the bottom of all 8 pages. These numbers represent the approximate time between eclipse seasons (1 lunation= 29.5 days, 6 lunation=177, 5 lunations=148). Their understanding was so broad that they could also predict when there would be 2 eclipses or 3. The Tzolk’in dates predicted precisely the dates when the Mayans expected to see an eclipse. Further, they also had cumulative days since the eclipse started being recorded all the way up to 11,960 days, where the table would repeat itself f. Why did the Maya believe that they had occasionally prevented an eclipse by worshiping the Sun and Moon god? If the Mayns had not seen an eclipse during the Tzolk’in dates, they would attribute their prayers appeasing the Sun and Moon gods. This is due to the fact that the Mayns believed eclipses occurred as the Sun and Moon gods were angry or fighting. 6. The Cycle of Planet Venus and the Mayan Venus Records: a. What 2 characteristics of the planet Venus caused the Mayans to identify it as a special kind of star? It was the brightest star in the night sky visible to the Mayans. It was also a wandering star in that it changed its position against the background stars b. What is a heliacal rise of Venus, and how does Venus appear when this occurs? According to Mayan legend, why was this event an important day of Mayan worship? Heliacal rise of Venus is when it reappears in our morning sky, is at its brightest and rises with the sun, i.e. sunrise. It was important because the Mayans depicted god Kukulkan as the planet Venus.  c. When is Venus seen (morning or evening) during the ~8-month period after its bright heliacal rise? Is it getting brighter or dimmer, and why? Why does it disappear after this period? When it finally reappears, is it a morning or evening star? For the next ~8 months, is it getting brighter or dimmer? Why does it disappear again after this period, before its next heliacal rise? Can be seen every morning. Gets dimmer because Venus gets further away from Earth in its orbit. After this period, Venus is hidden behind the Sun (hence it disappears). Reappears as an evening star, gets brighter then. It disappears for a week after because of inferior conjunction (Venus’s dark side faces the Earth). d. Look up the date of the most recent heliacal rise of Venus, and use this to figure out Venus' current appearance. Is it visible or invisible? If it's visible, is it a morning or evening star? Is it getting brighter or dimmer? If it's invisible, why is this? June 10, 202, the last helical rise. Hence, Venus can be seen every morning before sunrise, but ist slowly getting dimmer e. Describe the evidence in the Mayan Dresden codex that tells us that the Maya understood the Venus cycle and were able to predict, for eternity, the dates on which the appearances and disappearances of Venus would occur. The Dresden codex has in it the number of days that Venus spends in a particular cycle. For example, the number 236 can be found on the codex which depicts the number of days Venus spends after its heliacal rise and then the number 90 which is the number of days it disappears. Row 4 of the Tzolk’in dates contains exact dates of theVenus’s cycle 7. Babylonian Astronomy: a. According to historians, what was it about climate conditions in the region of Ancient Babylon that motivated the Babylonians to study the sky? The region of Babylon didn't have a reliable source of rainfall, which made it harder to grow crops. Hence, Babylonians studied the sky in hoped that they could predict the weather b. Why are there so many ‘60s’ in our units for time and angle? Babylonaisn used a base 60 in their numeric system as 60 has many factors, and has less fractions. We inherited that from the Babylonaisn and that is evident in how we measure time and a full circle. 8. The Naming of the Visible Planets: a. For each of the 5 visible planets, what aspect of their appearance was used to choose the Babylonian/Greek god to name them for? Mercury: Roman- Mercury, Messenger god Greek- Hermes, Messenger god Babylonian- Nabu, the scribe, the god of wisdom and writing Mercury is close to the sun that it is difficult to see for most of its orbit Mercury is fact moving across the sky in comparison to the other planets Venus: Venus is the brightest object after the moon. ○ Roman - Venus, goddess of love. ○ Greek - Aphrodite, Goddess of love. Babylonian - Ishtar, goddess of love. Mars: ○ Mars appears very red in the sky. Roman - Mars, god of war. Greek - Aries, god of war. ○ Babylonian - Nergal, god of war. Mars' soil contains a lot of iron, which has oxidized into rust. Jupiter: ○ Roman - Jupiter, king of gods. ○ Greek - Zeus, father of gods and humans. ○ Babylonian, supreme god. ○ Jupiter is bright but also has a measure and stoic motion from night to night. Saturn: ○ Roman - Saturn, god of harvest/old age. ○ Greek- Kronos, God of harvest/old age. ○ Babylonian = Ninurta, farmer god. ○ Saturn is faint and weak and is much slower moving in the sky. 9. Daily Cycle of the Stars: a. Why do the stars move across the sky throughout the night? As the Earth spins, the stars appear to rotate around the North celestial pole. From the southern hemisphere, the star appears to rotate around the South celestial pole. b. Suppose we are standing on Earth’s North pole, what are the stars moving around, and where in the sky is their centre of rotation? What happens to this point if we travel toward the equator? The stars are moving around the North Celestial Pole (NCP). Centre of rotation is Polaris- the north star if you're in the Northern Hemisphere, NCP gets lower and lower to the sky if we travel towards the equator. c. When standing on the equator, how will the stars appear to move if we face north? How about if we face south? What will happen to the centre of the Southern stars’ rotation if we travel south of the equator? When standing at the equator the stars appear to be towards the horizon and setting west. For the South it will be the same image as the north but upside down as things are flipped. If you travel towards the south of the equator, everything will start to rise higher and higher in the sky. d. What objects (if any) mark the North and South Celestial Poles? The north pole has polaris known as the north star and sits almost where the north pole sits in space. The south pole does not have a star that sits by the south pole, to find the south celestial pole, but they use magellanic clouds to find the south celestial pole. e. In the Northern hemisphere, how can we use a star to determine our latitude on Earth? Higher by the exact amount of latitude that you've increased across the earth. An observer's latitude is equal to the altitude of the visible celestial pole. The higher the latitude, the higher in the sky the celestial pole will appear. Polaris altitude= your latitude, you can determine your latitude on earth by sticking your fist out at arms length and stack your dist on top of another. A fist equals 10 degrees. In the Northern Hemisphere, we can use the North Star, or Polaris, to determine our latitude. This is because the angle between the horizon and Polaris approximately equals your latitude. For example, if Polaris is directly overhead, you are at the North Pole (90 degrees north). If Polaris is on the horizon, you are at the equator (0 degrees). Anywhere in between, your latitude is roughly equal to the degree of the angle between the horizon and Polaris. 10. Annual Cycle of the Stars: a. Why do we see different stars and constellations at different times of the year? We see different constellations and stars at different times of the year due to the Earth’s annual orbit around the sun b. How is it possible to use a star to determine when 1 year has elapsed? When a star/ constellation returns to its normal position, we know that 1 year has elapsed. 11. Astronomy in Ancient Egypt: a. What was the primary motivation for studying the sky in Ancient Egypt? The primary reason the Ancient Egyptians studied the sky was to predict When the Nile river was going to flood. b. Why was the star Sirius used to mark the beginning of a new year? Sirius' heliacal rise was marked as the beginning of the new year because as a coincidence it aligned with the annual flooding for the Nile River. The Ancient Egyptians saw Sirius above the horizon before sunrise, before the flooding would happen. c. Why did the Ancient Egyptians divide the day into 24 hours? The Ancient Egyptians divided the day into 24 hours because they noticed that there were 12 constellations that rose at night after the sun set and would set before the sun rose. Also, there were 12 constellations that rose in the day and set when the sun set. These constellations would rise and set which gave them a 24 hour clock. 12. Origin of the Modern Calendar: a. Why do we add a leap day every 4 years? Who incorporated this rule into our calendar, and from what civilization did he learn this rule? We add a leap year every 4 years to add up to 365 days for the year. Pope Gregory XII incorporated this rule because too much time was being added. It came from the Roman civilization. We add a leap day every four years to align our calendar year with the solar year. The Earth's orbit around the Sun takes approximately 365.2425 days, not exactly 365. Therefore, if we didn't add a leap day approximately every four years, our calendar year would gradually drift apart from the solar year, causing our seasons to shift over time. b. Why do we now use the Gregorian calendar instead of the Julian calendar? We use the Gregorian calendar instead because there was too much time in the Julian calendar. Also, the Gregorian calendar would stop a leap year or a leap day from happening and would keep things on track 13. The Zodiac: a. Where are the zodiac constellations? Why were they significant to the Babylonian astrologers? Babyloanians associated constellations into groupings, Greeks borrowed it and transferred to Latin. They are Capricorn(us), Aquarius, Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio(us), Ophiuchus, Sagittarius Zodiac: The constellation along the ecliptic (path of sun, moon and planets)(; used for making astrological predictions The zodiac constellations were significant to the Babylonian because the wonders known as goods would take a path that went through the zodiac constellation. They assign importance to the grouping of stars the gods would pass through. These are significant to Babylonian beliefs because associating the sun, moon, and planets with their gods shaped the way the Babylonians lived their lives and viewed the world around them. b. Why can we not see our astrological constellation in the month we were born? The constellation related to your astrological sign won’t necessarily be visible in the sky on the month you are born in. If you are born under a particular constellation, that constellation it's named for it not visible at night. Instead the sun is passing through it around that time of year, making it a daytime constellation that can't be seen. The reason we cannot see our astrological constellation in the month we were born is because during that time, the sun is "in" that constellation. In other words, the sun is between the Earth and that constellation. So the sun's glare washes out the stars of the constellation, making it impossible to see from Earth. c. Why have our zodiac signs changed since their original definitions by the Ancient Greeks? Due to the procession of the equinox, the zodiac constellation rotates in the sky and will align again in 26,000 years. NATS1745 - History of Astronomy Ancient Greek Astronomy: Study Guide Unit 3 1. Introduction to Ancient Greek Astronomy: a. According to historians, what was it about the ancient Greek empire that made it possible for theories about natural science, and astronomy in particular, to progress further than in other ancient civilizations? The Ancient Greek Empire progressed because of the region’s fragmented geography and decentralized rule. They had more ability and time to think and intellectual freedom. They established higher places for learning and argued to understand the universe. b. What does a geocentric cosmology refer to? How about a heliocentric  cosmology? How would each cosmology explain the daily cycle of the Sun and the stars? Geocentric cosmology refers to all celestial bodies orbiting around the fixed Earth at the center. Heliocentric cosmology refers to all celestial bodies including Earth revolving around the Sun at the center. Geocentric cosmology explains how the Sun revolves around the Earth once a day and stars orbit the Earth once every year. Heliocentric cosmology explains how the Earth revolves around the Sun and stars or all celestial bodies revolve around the Sun annually. 2. The Ionian Philosophers: a. Why is Thales called one of the "original scientists"? According to legend, what celestial event did Thales successfully predict in order to prove his philosophy? Thales sought explanations for natural phenomena that didn’t involve the gods and took a scientific approach. Thales successfully predicted the eclipse in order to prove his philosophy, b. Describe (very generally) the features of Anaximander’s cosmology and how it explained some of the cycles of the sky. Anaximander’s cosmology placed the Earth floating in space (first person to do that they thought the Earth never ended), it was a cylinder surrounded by rings that contained the Moon and Sun/ He should show people why there was daytime or night-time because the Sun and Moon are orbiting around the Earth/ There was a cylinder of stars as well that moved around the Earth. 3. The Pythagoreans: a. What was Pythagoras proposing when he called the Universe a "cosmos"? When he called the universe the “cosmos,” he was proposing that the universe follows comprehensible mathematical laws and all cycles of nature could be predicted by mathematical equations. It was a harmonies and ordered system. b. What did Pythagoras propose about the shape of planetary orbits? What did he propose about the shape of the Earth? Pythagoras proposed that all planetary orbits including Earth were perfectly circular and believed that circle was the purest geometric shape. c. Describe 3 observations that support the Pythagorean hypothesis about the shape of the Earth. Ships gradually disappear on the horizon- bottom first Earth’s shadow on the eclipse moon is always round When you travel North of South, the constellations rise and set rapidly than they would have if the Earth was flat 4. Philolaus, Herakleides and Aristarchus: a. What did Philolaus believe about the Earth? What did this belief explain about the sky? He believed that the Earth rotates once a day around a central fire that’s not the Sun. This belief explained the daily motion of celestial bodies in the sky. b. What did Herakleides believe about the Earth, and what caused him to propose a different theory than Philolaus’? What did Herakleides believe about the motion of Mercury and Venus, and why? Herakleides believed that there is no evidence of “central fire,” the earth spins once a day around its own axis which would explain the daily motion of the sky. Herakleides believed that Mercury and Venus orbited around the sun; he used this explanation as an answer as to why their motion and brightness changes. c. What two measurements are Aristarchus famous for? Combining these measurements, what did he correctly conclude about the relative sizes and distances of the Sun and Moon? What did these conclusions lead Aristarchus to propose about the known Universe? Aristarchus was famous for methods of measuring the distance and size of the Moon and Sun. He correctly concluded that the Sun is 10 times larger than Earth and used geometry to determine the Moon is smaller than Earth. He also concluded that the Sun is at the center and all celestial objects including Earth revolve around the Sun. 5. Apparent Planetary Motion: a. What is meant by apparent planetary motion? Apparent planetary motion is the motion of the planets we see across the sky from night to night b. Describe the 3 features of apparent planetary motion discussed in the lecture. Changing direction/ motion: Temporary retrograde motion and direction motion Changing apparent speed: Planets don’t maintain a constant speed across the sky Changing apparent brightness: It gets brighter or dimmer according to the cycles 6. Plato and Eudoxus: a. What was Plato’s view on the scientific method? Plato’s view was what you observe is not necessarily a reality, all that matters is if the theories themselves make sense. Theories do not have to be proven by observations as it can be accepted by faith. b. What were the two beliefs of Plato’s about the celestial bodies that directed the objectives of the next generations of ancient Greek astronomers? Platos’ two beliefs were: All celestial bodies are perfect spheres with constant circular motion (CCM) Appearances of celestial bodies don’t matter c. According to Eudoxus, what do the planets reside on in space? Explain why a planet required 4 rotating spheres to explain its motion. Eudoxus placed the planets on a system of invisible nested spheres, known as ‘crystal orbs’ each of which had Constant Circular Motion (CCM) around the Earth. The purpose is having two orbs to induce the appearance of retrograde motion by having 1 thing spinning inside of another allows appearance on the sky of non-spherical motion- retrograde motion even though physically the motion is CCM. Sphere 1: the 24 hours spheres Sphere 2: The 687 cycle the night to night cycle or direct motion Sphere 3 and 4: crete retrograde motion All planets require 4 spinning glass orbs each and net motion of orbs accounted for daily, night and retrograde motion. Eudoxus's model of celestial spheres aimed to explain the observed behavior of planets from our perspective here on Earth. The first sphere is attributed to the daily rotation of the sky. This sphere is like an outer shell that encapsulates everything else and rotates once every 24 hours. This rotation is what makes heavenly bodies, including the planets, appear to rise in the east and set in the west, similar to the Sun's daily motion. The second and third spheres are responsible for what we observe as retrograde motion. From our vantage point on Earth, planets sometimes appear to pause, move backward (or in "retrograde"), then move forward again along their path in the sky. This is caused by the relative speeds and positions of Earth and the other planet in their orbits around the Sun. These two spheres in Eudoxus's model, each rotating at different speeds and in slightly different orientations, were proposed to explain this complex motion. The fourth sphere deals with the perceived change in a planet's size. As planets orbit the Sun, their distance from Earth changes, causing them to appear larger when they are closer to us and smaller when they are farther away. According to Eudoxus, a fourth sphere, moving in a way that aligns with the planet's orbit around the Sun, could account for these changes. 7. Aristotle: a. Explain the thought experiment, attributed to Aristotle, that was taken as “proof” that the Earth is fixed. He claimed that if the Earth spins and you shoot an arrow into the sky, then it would land behind you. Since the arrow comes directly back down on the person shooting it, he believed it was evident enough to prove the Earth was fixed in place. b. In Aristotle's cosmology, what body is at the centre? Aristotle believed that the universe is geocentric, meaning that the Earth is fixed in place at the center. c. According to Aristotle, what is everything in the terrestrial realm composed of? How did Aristotle explain the cause of motion in the terrestrial realm? According to Aristotle, everything in the terrestrial realm is made up of the four natural elements- earth, wind, fire and water. These were also known as the Greek classical elements, which Aristotle adopted into his cosmology. He explained the cause of motion is due to these elements returning to their natural layer (a landslide trying to return to the earth layer, rain falling from the sky to reach the water layer, air bubbles and fire falting up to reach the wind and fire layers). He believed wind was above Earth and water and fire was above wind. Aristotle, a renowned philosopher and scientist in ancient Greece, had a particular understanding of the natural world, which he called the 'terrestrial realm'. He proposed that this realm was made up of four essential elements: earth, water, air, and fire. In Aristotle's model, each of these elements had a 'natural place' within the universe. Earth and water, considered heavier elements, naturally moved or 'strived' towards the center of the universe. This striving is what we perceive as the downward force of gravity in our day-to-day experience. On the other hand, air and fire, being lighter, strived in the opposite direction, upwards, away from the center of the universe. This upward striving is less immediately apparent to us but can be seen in phenomena like smoke rising or the tendency of flames to reach upwards. According to Aristotle, this striving to reach their natural place is what causes all motion in the terrestrial realm. Therefore, the movement or change we observe in the natural world is, in Aristotle's view, a result of these four elements striving to reach their natural place in the universe. d. According to Aristotle, what is everything in the celestial realm composed of? What are the qualities of this material? According to Aristotle, there was a fifth element that makes up the heavens and realm of celestial bodies. He later taught that everything beyond the fire was composed of this fifth element called “aether/either” or “quintessence.” Unlike the four elements of the terrestrial realm, aether isn't subject to change or decay. It inherently moves in perfect eternal circles, mirroring the observed movements of celestial bodies. e. Whose model did Aristotle use to explain the motion of the planets? In this model, what are the shapes of the planetary orbits, and do the planets have constant or non-constant speed through space? Aristotle used Eudoxus’ CCM model. Each crystal orb is composed of 4 individual nested spheres to create: nightly direct motion, 24 hours daily east to west motion and two for retrograde motion. All planets have CCM. f. How did Aristotle explain the daily motion of the sky? Aristotle took out the 24 hour orb and surrounded the entire universe with 1 single orb that spins once a day, to give daily spin to inner orbs. According to Aristotle, the apparent daily motion of the sky is a result of the rotation of the outermost celestial sphere. This sphere encapsulates all other celestial spheres and rotates once every 24 hours. This rotation is in the direction from east to west, mirroring the observed daily path of the Sun. As a result of this rotation, all celestial bodies, including the stars and the planets, appear to rise in the east, move across the sky, and then set in the west. This perceived motion is simply an effect of the rotation of the outermost celestial sphere, according to Aristotle's interpretation of Eudoxus's celestial spheres model. g. What was Aristotle's explanation for the source of all motion in the celestial realm? Aristotle explained that motion of the orbs were driven by a “prime mover” ( a spiritual entity residing in the outermost orb) h. Why did Aristotle believe that comets are atmospheric phenomena? Aristotle believed that if it is transient, it can't be celestial because only eternal phenomena happen in the celestial realm. Transient bodies in the sky must be atmospheric. He thought that comets were not celestial bodies, like stars or planets, but were instead phenomena occurring within Earth's atmosphere. Two key observations supported Aristotle's belief. Firstly, comets appeared lower in the sky than the moon. For Aristotle, this was evidence that comets were closer to the Earth, existing within its atmospheric boundary rather than in the celestial realm beyond. Secondly, comets did not display the regular, predictable motion that was characteristic of celestial bodies. Stars, planets, and the moon followed consistent paths and cycles in the sky, a pattern that comets did not adhere to. This irregularity further convinced Aristotle that comets were atmospheric phenomena, not celestial bodies. Therefore, Aristotle's belief that comets were atmospheric phenomena was based on his understanding of the natural world and observations of comets' appearances and behaviors in the sky. 8. Apollonius and Hipparchus: a. Describe the components of Apollonius' epicycle model. Is this model geocentric or heliocentric? Is all motion constant and circular in this model? Apollonius model is a geocentriC CCM. He placed each planet on an epicycle, then set the epicycle on a deferent circle. The deferent carries the epicycle around the Earth. This was developed to explain the apparent irregular movements of the planets as seen from Earth. In this model, each planet is thought to move in two ways: 1. It moves in a small circle called an "epicycle". 2. The center of this epicycle, in turn, moves in a larger circle around the Earth. This larger circle is known as the "deferent". These combined circular motions were used to explain the observed changes in a planet's speed and direction of movement in the sky. However, the motion in this model is not uniform. The speed of a planet on its epicycle can change, and the speed of the center of the epicycle on the deferent can also change. This allowed the model to better match the observed motions of the planets. But even though the motion is not uniform, it is still circular. Both the small epicycle and the larger deferent are circular paths. b. How does Apollonius' epicycle model explain retrograde motion, the planets’ changing brightness and their changing apparent speed? Changing brightness- planet is dim due to distance, appears brighter when closer/proximity Changing apparent speed- planet motion appears direct and fast when planet and epicycles move in the same direction Changing direction- planet motion appears retrograde and slow when the planet and epicycle are moving in opposite directions c. Which feature of the Antikythera Mechanism suggests that it was constructed to predict the motion of the celestial bodies using Hipparchus' model? Part of the device looked like the model of motion developed by Hipparchus. The Antikythera Mechanism's use of differential gears is a key feature suggesting that it was constructed to predict the motion of celestial bodies using Hipparchus' model. These gears allow the mechanism to reproduce the irregular motion of the Moon, as per Hipparchus' theories, which state that the Moon's motion is elliptical rather than circular, and therefore its velocity changes depending on its position in the sky. d. What is the difference between a sidereal year and a solar year? What observation led Hipparchus to discover the precession of the equinoxes? A sidereal year is 365.26 days and a solar year is 365.24 days. The solar year is shorter than the sidereal year. Hipparchu observed a difference between the solar year and the sidereal year in which he discovered the precession of the equinoxes. Shifting of the Earth’s position at a rate of 1/100 degree every year. e. How does precession affect our view of the Sun relative to the stars? Use this to explain why our zodiac signs are gradually changing. Due to precession, this causes the sun’s coordinates to shift by 0.014 degrees/year. Knowledge of precision is now used to determine precise positions of the sun and the stars in the past (for example, the stonehenge). E.g. Sun was in Pisces in Spring Equinox but 1000 years ago it was in Aries. The Earth doesn't just spin on its axis; it also wobbles like a spinning top. This wobble causes the direction that the Earth's axis is pointing to change slowly over time, completing one full cycle approximately every 26,000 years. This is referred to as axial precession. This gradual shift affects our view of the stars and constellations. As the Earth's axis wobbles, the position of the stars shifts slightly. More specifically, the apparent position of the Sun against the backdrop of constellations at the time of the equinoxes also changes. This means that, over thousands of years, the Sun appears to be in a different constellation on the equinox than it was in previous years. Astrology and Zodiac signs are based on the position of the Sun relative to certain constellations at the time of one's birth. For example, if you were born at a time of the year when the Sun appeared to be in the constellation of Aries, then Aries is your astrological sign. However, because of precession, these positions are gradually changing. The Sun now appears in a different constellation during a specific date range than it did 2000 years ago when the Zodiac was first established. f. How does precession affect our pole star? Use this to explain why the Ancient Egyptians constructed a shaft in one of their pyramids which pointed to the star  Thuban. The star coordinates on a given date shift eastward which is why we are losing our pole star. It was constructed to mark the North celestial pole and the narrow shaft of the pyramid points out to the North celestial pole. g. Explain (briefly) how it was determined that the Farnese status of Atlas is holding a celestial globe constructed using Hipparchus' lost star catalogue. The Farnese Atlas is a 2nd-century Roman marble copy of a Greek statue of Atlas kneeling with the celestial spheres, not a globe, on his shoulders. It is the oldest surviving statue of the Titan Atlas, along with the globe. This statue has been used to identify and reconstruct the celestial globe that the Greeks used in antiquity. The unique constellation figures carved on the statue's globe enable scientists to determine that it was based on the star catalogue of the Greek astronomer Hipparchus. The constellations on the Farnese Atlas are positioned according to this catalogue, which was otherwise lost in history. This theory was confirmed by studying the measured positions of the constellations on the globe, which matched Hipparchus' time around 125 BC. The celestial sphere has carvings of the zodiac constellation on it. And there was a grid that referenced how they measured everything. The star located on the celestial sphere matches the start position from 140 BCE and the only person that travelled at that constellation would have been Hipparchus. 9. Claudius Ptolemy: a. What was the Latin name of the definitive Astronomy textbook written by Ptolemy in roughly 150 CE? The Latin name was “The Greatest Treatise” written by Ptolemy b. Is the Ptolemaic model geocentric or heliocentric? What was the purpose of Ptolemy’s ‘equant point’, and where is it located? Why does the equant point conflict with the Aristotelian view of planetary motion? Why did the Ptolemaic model become widely accepted, despite having violated one of Aristotle’s fundamental principles? The Ptolemaic model is geocentric, an epicycle with circular orbits. The purpose of the “Equant point” is to find where the planet’s apparent speed is constant, located in a spot out in the universe. The equant point conflicted with Aristotle’s cosmology of constant circular motion (CCM) because the Ptolemaic model epicycle is forced to speed up and slow down. The Ptolemaic model was accepted because it made the best predictions for the planet’s path. The Ptolemaic model is geocentric, meaning it places Earth at the center of the universe with all celestial bodies, including the sun, revolving around it. Ptolemy introduced the concept of the 'equant point' to account for the irregular motion of the planets. This point, located off-center from the Earth, is the point from which each planet's motion, along its deferent (the circle along which it revolves), would appear constant to an observer. This concept, however, conflicted with Aristotle's view of planetary motion, which asserted that the heavenly bodies moved in perfect circles and at a constant speed. Despite this contradiction, the Ptolemaic model was widely accepted because it provided a relatively accurate predictive model for planetary positions, which was particularly useful for astrological purposes and navigation. c. What was Ptolemy able to explain by establishing 2 different rules that attached the motion of the planets to the Sun? 1st rule: The center of Venus and Mercury epicycle must align with the Earth through the Sun line 2nd rule: The line connecting the center of the epicycle of Jupinter to planet Jupiter and etc/ so on Mars, the line that connects the veneer of the epicycle is always parallel d. What wrong assumption about space led Ptolemy to underestimate the size of our visible planetary system (i.e. out to Saturn)? What was the importance of his measurement, despite being an underestimate? Ptolemy believed that there’s no space between the orbits of the planets. Saturn is not the last planet in the solar system. The importance of his measurements was the first time the enormity of the universe was revealed. This included the Sun, which was thought to revolve around the Earth along with the planets. The planets were assumed to move in smaller circular paths, or epicycles, whose centers, in turn, moved in larger circles around the Earth, known as deferents. This geocentric model was a flawed assumption that led Ptolemy to underestimate the size of our visible planetary system, which extends out to Saturn. The model failed to accurately represent the actual distances of the planets from the Sun, as it would be in a heliocentric (Sun-centered) system. Therefore, it significantly underestimated the true vastness of our solar system. NATS1745 - History of Astronomy Medieval and Renaissance Astronomy: Study Guide Unit 4 1. The Dark Ages: a. Explain why the knowledge of the Ancient Greeks gradually became inaccessible to scholars during the Dark Ages. The church rejected the knowledge and theories of Ancient Greek because they believed in multiple gods and the Christian church believed in one god. Therefore, christian scholars were less able to speak Greek so knowledge of Ancient Greek became inaccessible and lost. Everything had also been translated into Latin so they couldn't read about the Greek’s discoveries.  b. What is the example provided in the lecture which demonstrates the lack of knowledge about the sky during this time period? The sky is seen as a dome, night and day were created by god (light created by god as sun to rule day and moon to rule night) and that’s all god wants us to know about astronomy. 2. The Rise of Islamic Astronomy: a. Describe how the knowledge of the Ancient Greeks was preserved during the Dark Ages. Why were Islamic scholars interested in the astronomical knowledge of the Ancient Greeks? Qu’an encourages knowledge of the sky for time-keeping (Islam founded in 7th century). Knowledge of the sky was important for observing the sky for religious observances. Interactions between Islamic scholars & Greek refugees led to translation of Greek texts into Arabic. The Islamic world kept Ancient Greek knowledge alive during the dark ages because the knowledge of the sky was important for religious observations. Islamic calendar is a lunar calendar (12 lunations 354 days). There was an increasing interaction between the Islamic scholars and the Ancient Greeks who fled and brought their knowledge to the attention of the Islamic leaders. b. Why is Ptolemy's astronomy textbook known as "The Almagest"? Ptolemy’s book was interesting and helpful for the Islamic world as it was about how to predict the patterns in the sky. The Islamic scholars renamed the book as “The Almagest” meaning the greatest book because it was used for predictions. c. What can we tell about the star “Alpha Centauri” based on its name, and who named the stars in this format? It is the brightest star in its constellation. Ptolemy named the stars (the name we use today is the western pronunciation of the Arabic name of the stars). d. Why are the names of bright stars typically Arabic in origin? Describe one of the examples provided in the lecture or reading material. The names of bright stars are typically Arabic in origin due to the fact that in the Dark Ages, the Arabic world safeguarded information from the Greeks which consisted of how some of the things were named. E.g. objects in the night sky. Most of the star names we use today came from a star catalogue procured and procured by an Islamic and Persian astronomer named Al-Sufi in the 1900’s in the 10th century roughly. Al-sufi used Ptolemy’s star catalogue and identified all the stars in that star catalogue and then observed each one of them himself. He then recorded the coordinates of each star and took record of the star. Instead of using the Ptolemaic names for the stars, he renamed each of the stars after Arabic expressions more descriptive than the Ptolemaic names. Ptolemy would name them first based on the brightness to dimmest of each star in each constellation. 3. Early Renaissance Astronomy: a. What was the importance of Regiomontanus’ translation of The Almagest? It was the most readable and comprehensive translation of Ptolemy’s The Almagest (directly translated from Greek). He included useful commentaries on the translation which summarize the main ideas of each topic. It allowed readers to grasp the general features of the Ptolemaic model. b. Whose cosmology did the medieval Church adopt, and why? Was it geocentric or Heliocentric? The epitome of the Almagest led to Christian scholars to adopt Aristotelian-Ptolemaic Cosmology due to the consistency with scripture. It was geocentric. c. How did Buridan's thought experiments about moving objects on Earth pave the way for heliocentrics like Copernicus? Buridan theorized that thrown/projected objects have impetus (in addition to their natural motion towards Earth), and therefore, if Earth moves, projected objects inherit Earth’s impetus. A fixed Earth and a moving Earth appear equivalent from our perspective. Whether the Earth is moving or not, the motion that we observe on Earth doesn’t change. He said that once something starts moving, it will keep going until something stops it. Before Buridan, people thought that you would need to keep pushing something to make it move. But Buridan's idea was different. He said that things keep moving all on their own unless something stops them. This idea is called inertia. This was a big deal because it helped people like Copernicus and Galileo understand why planets, like Earth, keep moving around the Sun. They realized that once the planets started moving, they kept going all by themselves. 4. The Copernican Model: a. What 2 features of the Ptolemaic model led Copernicus to suspect that the model was incorrect? The two features of the Ptolemaic model were the equant point with forced non-constant motion and a forced connection between the motion of the planets with sun (inner vs outer). 1. The Geocentric Foundation: The Ptolemaic model is geocentric, meaning it places Earth at the center of the universe, with all celestial bodies revolving around it. This contradicted the observations and calculations made by Copernicus, leading him to propose a heliocentric model instead, where the Sun is at the center and the Earth and other planets revolve around it. 2. The Concept of Epicycles: Ptolemy used the concept of epicycles, smaller circular paths that the planets move along, whose centers, in turn, move in larger circles around the Earth (deferents). This was to account for the apparent retrograde motion of the planets. However, Copernicus found this concept overly complicated and not reflective of his observations and calculations. b. According to Copernicus, what do the planets orbit around, what is the shape of their orbits, and do they move at constant or non-constant speeds through space? According to Copernicus, the planets orbit around the Sun. The shape of their orbits is circular, and they move at non-constant speeds through space. This model, in which the Sun is at the center and the Earth and other planets revolve around it, is known as a heliocentric model. c. In the Copernican model, what are the 3 components of Earth's motion? In the Copernican model, the three components of Earth's motion are: 1. Rotation: The Earth spins on its axis, which is responsible for the cycle of day and night. 2. Revolution: The Earth orbits around the Sun once a year. 3. Precession: The Earth's axis slowly wobbles over time, completing one full cycle approximately every 26,000 years. d. What was Copernicus' correct explanation for retrograde motion? Copernicus explained retrograde motion. When Earth 'overtakes' another planet in its path around the Sun, it seems like the other planet is moving backward in the sky. But it's not really going backward. It's an illusion caused by the Earth moving faster. e. In the Copernican model, when do planets appear to slow down and increase their brightness, and why? Does this match what we observe in the sky? In the Copernican model, the Earth and other planets revolve around the Sun. There are moments when the Earth comes between the Sun and another planet, which is known as an "opposition." At this time, the planet is closer to Earth than at other times, causing it to appear brighter and larger in our sky. Additionally, as Earth and this planet continue their respective orbits, there is a period when Earth, moving faster along its smaller orbit, overtakes the planet. This makes it seem to us, from our viewpoint on Earth, like the planet is slowing down and even moving backwards. This apparent backward motion is known as "retrograde motion." So, during opposition, a planet appears to slow down, move backward, and increase in brightness. When they are in retrograde, because the planets are closer in proximity to earth and therefore reflect more sun's light on it to earth. This doesn't match what we observe in the sky because our position is relative to where we are on earth not in reality of the path of earth's and the planets'. This is because our viewing angle of the object is changing as well. Brightness changes due to planets varying distance from earth f. What was Copernicus' correct order of the planets? Mercury, Venus, Earth, Mars, Jupiter, Saturn g. In the Copernican model, what is the explanation for the different motion of Mercury and Venus compared to Mars, Jupiter and Saturn? In Copernicus’ heliocentric model, Mercury and Venus are inner planets that explain their apparent proximity to the Sun In the Copernican model, Mercury and Venus are referred to as inferior planets because their orbits lie closer to the Sun than Earth's orbit. Because of this, they always appear close to the Sun from an Earth observer's perspective and can only be seen shortly after sunset or before sunrise. Their apparent motion in the sky is, therefore, different from that of Mars, Jupiter, and Saturn, the superior planets, whose orbits lie outside of Earth's orbit. The superior planets can be seen at various times throughout the night and can appear in any part of the sky, not just near the Sun. 5. Copernicus’ De Revolutionibus: a. When Copernicus compared the orbital periods of the planets with their orbital radii in his heliocentric model, what did he find? When Copernicus compared the orbital periods of the planets with their orbital radii in his heliocentric model, he found a clear relationship: the farther a planet is from the Sun, the longer it takes to complete one orbit. This observation laid the groundwork for the later formulation of Kepler's Third Law of Planetary Motion, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Mercury takes 88 days to orbit around the Sun. Venus, 225 days. Earth, 1 year. Mars, 2 years. Jupiter, 12 years. Saturn, 30 years. b. What is the (shortened) name of Copernicus' famous book in which he presented his heliocentric cosmology? De Revolutionibus, and the preface negated Copernicus’s conviction by making it merely a mathematical device.  c. What did Copernicus' colleague add to the book in order to make it appear less controversial? What important purpose did this preface serve in the decades following the book’s publication? The colleague added an anonymous preface, “These hypotheses need not be true nor even probable.” It served a very valuable purpose because it prevented the book from being completely rejected. Also, the book became popular and was taught in schools. 6. The Early Observations of Tycho Brahe: a. What planetary event did Tycho Brahe witness in 1563? Describe what causes this event and how it appeared in the sky. What did this event motivate Tycho to do, and why? In 1563, Tycho Brahe observed a conjunction of Jupiter and Saturn. A planetary conjunction occurs when planets align and appear very close to each other in the sky. This event is due to the planets' orbits around the Sun. From our perspective on Earth, the planets seem to move closer together and then drift apart. In Tycho's time, planetary movements were predicted using tables based on the Ptolemaic system. However, the tables incorrectly predicted the date of the Jupiter-Saturn conjunction that Tycho observed. This discrepancy motivated Tycho to improve and refine the existing astronomical observations. He realized that more accurate observations were necessary to advance the field of astronomy and, thus, he dedicated his life to making precise astronomical measurements. b. What discovery did Tycho make about the supernova of 1572 ("Tycho's Star"), and how did it contradict Aristotelian beliefs about celestial bodies? Is "Tycho's Star" still visible without a telescope? How can we tell today that a supernova really did occur in the Cassiopeia constellation? In 1572, Tycho Brahe, an astronomer, saw a new star in a group of stars called Cassiopeia. This was surprising because people at that time, following the ideas of the ancient philosopher Aristotle, thought that the stars never changed. Tycho's accurate measurements showed that this new star was far away, in the region where the stars are, not close to Earth, contradicting Aristotle's belief that the stars always stay the same. Today, we can't see "Tycho's Star" without a telescope because the light faded after about two years. But with powerful telescopes, scientists can see leftovers from the explosion, known as "Tycho's Supernova Remnant". We know that a star really did explode in Cassiopeia because of what Tycho wrote down and from what scientists see today - the expanding remains of the explosion and a faint echo of the original light from the star.  c. What sort of observations did Tycho make from his observatories on the island of Hven, and why were these observations so valuable? At his observatories on the island of Hven, Tycho Brahe made a series of detailed and precise measurements of the positions of stars and planets. His meticulous observations were considered exceptionally accurate for his time. These observations were significant because they provided a wealth of data that greatly improved the existing star catalogues and challenged the established geocentric model of the universe. His detailed record of a supernova in the constellation Cassiopeia, for instance, went against the Aristotelian belief that the celestial realm was unchanging. Similarly, his accurate prediction of a solar eclipse provided valuable evidence supporting the need for a revision of existing astronomical models. His data later served as a crucial foundation for Johannes Kepler's laws of planetary motion. 7. Tycho’s Search for Stellar Parallax: a. What is parallax? Describe how parallax would affect a photograph of a stop sign if you took the photograph from two different locations. Parallax is the perceived shift of an object relative to its background due to the observer’s motion. The stop sign would look different in its positioning due to which location the picture was taken. Parallax is the observed change in the position or direction of an object when viewed from different points of view. In the context of photography, if you took a photograph of a stop sign from two different locations, the sign would appear to be in different positions relative to the background in each photo. For example, if you took a photo of the stop sign with a tree in the background from one location, the tree might appear directly behind the sign. But if you moved a few feet to the right and took another photo, the tree might now appear to the left of the sign. This shift is a result of the change in your viewpoint and is an example of parallax. b. Describe how parallax affects our view of the stars. Can we see stellar parallax with the naked eye? Why/why not? The parallax would make the stars look as if they were changing places but actually we are moving causing them to look like it moves. Stellar Parallax: the shift of stars due to Earth’s motion through space, closer stars shift more than more distant stars. It can’t be seen with the naked eye because they are very far and the shift is very small and can’t be seen. c. Explain (very generally – no calculations necessary) why Tycho’s search for stellar parallax led him to believe that the Earth is motionless. He built a very precise Mural Quadrant that measures angles from 0 degrees to 90 degrees, which is ¼ of a circle hence a quadrant. He used it to track the closest stars locations, but evern with the highest precision instruments available, Tycho couldn’t detect stellar parallax, he determined there were two possibilities for this: 1. The Earth wasn’t moving at all, it was stationary 2. The stars are too far away for him to measure it Tycho then became a firm believer in the geocentric model, believing that the Earth is fixed d. What is the definition of an 'Astronomical Unit'? An 'Astronomical Unit' (AU) is a unit of distance used in astronomy. It is defined as the average distance from the Earth to the Sun. 1 AU= approximately 150 million kilometers. 8. The Tychonic System: a. Describe the motion of the Sun, Moon, stars and planets in the Tychonic system. The Earth is at the center of the universe, the Sun and Moon and the stars revolve around the Earth and the other five planets revolve around the Sun. b. Does the Tychonic system explain the 3 features of apparent planetary motion? Why/why not? Yes because by placing the planet’s orbit around the Sun and having the Sun orbit around the Earth, it basically adopts the geometrically equivalent to the Epicycle model. The Tychonic system does account for the three main features of apparent planetary motion: daily motion, yearly motion, and retrograde motion. 1. Daily Motion: Since the stars and Sun revolve around the Earth in the Tychonic system, this explains the daily rise and set of celestial bodies. 2. Yearly Motion: The planets revolve around the Sun, which itself orbits the Earth. This explains the yearly motion of the planets through the constellations of the zodiac. 3. Retrograde Motion: The Tychonic system can account for the apparent retrograde motion of the planets. When Earth, on its path around the Sun, overtakes another planet in its orbit, that planet appears to move backwards in the sky with respect to the zodiac. This apparent motion is well explained in the Tychonic system. However, it's worth noting that while the Tychonic system can model these phenomena accurately, it does so with the Earth at the center of the system, which is inconsistent with the modern understanding of the solar system where the Sun is at the center (heliocentric model). c. Explain how Tycho’s observations of the Great Comet of 1577 led him to conclude that the crystal orbs do not exist. Why did this conclusion make the Tychonic system more believable? Tycho’s parallax distance to the Great Comet of 1577 placed it beyond the Moon. This proved: comets are celestial bodies, and the “crystal orbs” do not exist. He was able to conclude that the comets showed no measurable parallax (with his naked-eye instruments) and hence must be greatly beyond the distance to the Moon. In 1577, Tycho Brahe observed a Great Comet. He noticed that the comet's path moved through the area where people believed "crystal orbs" or "celestial spheres" existed. These spheres were thought to be invisible shells where the stars and planets were set. However, Tycho saw that the comet didn't slow down or change direction as if it was hitting these solid orbs. So, he concluded that these crystal orbs didn't exist. This finding made Tycho's own theory, the Tychonic system, seem more believable. In this system, Earth is at the center, the Sun and stars revolve around the Earth, and the other planets revolve around the Sun. This model didn't need the crystal orbs to work, which matched Tycho's observations from the Great Comet. So, people started to believe the Tychonic system could be a good alternative to the old model where Earth was the center of the universe. 9. Kepler’s Cosmographic Mystery: a. What astronomical connection did Kepler make during one of his lectures when he drew a triangle with an inscribed and circumscribed triangle? Describe the model that Kepler published in Cosmographic Mystery as a result of this realization. He believed that the spacing between the planets is defined by a series of geometric shapes around the Sun. In Cosmographic Mystery, Kepler proposed: the 5 perfect solids (3D shapes) define the 5 spaces between the 6 planets. In this model, Kepler proposed that the distances between the planets and the Sun could be described by nesting the five platonic solids within each other, each encased in a sphere. (This model was ultimately incorrect). b. Was Kepler’s model in Cosmographic Mystery heliocentric or geocentric? What were the shapes of the planetary orbits? Kepler’s model was heliocentric. The shapes of the planetary objects were elliptical. c. When Kepler compared his model to the Copernican model, why did Kepler become convinced that his own model was correct? He believed that his own model was correct because his perfect solids matches with the Copernican model and that’s important because it was known at the time that the Copernican model was accurate in able to predict where the planets were. Kepler was convinced that his own model was correct because it provided a geometric explanation for the number of planets, their relative sizes, and their distances from the Sun. In his model, each of the five Platonic solids corresponded to the orbits of the six known planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). This was a mathematical harmony that he believed could not be coincidental and hence, he was convinced that his model was the correct representation of the cosmos. 10. Kepler’s Search for the Driving Force of Planetary Motion: a. What did Tycho hire Kepler in order to prove? Why did Kepler accept Tycho’s offer? Tycho hired Kepler to prove the accuracy of the Tychonic system. The tychonic system suggested that the Earth is fixed at the centre and the Sun, Moon, and the other planets orbit the Earth. Kepler took this offer because it allowed him to prove his own heliocentric model using Tycho’s precise data. b. In Gilbert's book On The Magnet, what was his correct explanation for why compass needles always point to the Earth's North geographic pole? Gilbert showed that the Earth has a magnetic field, similar to a bar magnet. So, the needle itself has a South magnetic field compared to the North Pole. Since the magnets attract the negative pole, the needle always points north. c. After reading On the Magnet, what did Kepler conclude about the cause of planetary motion? After reading “On the magnet” Kepler concluded that the Sun’s magnetic force may be the cause of planetary motion. 11. Kepler’s 1st and 2nd Laws: a. Explain why Kepler’s theory about the driving force of planetary motion led him to conclude that the speeds of planets cannot be constant. They are not constant because the planets move along elliptical orbits (as do moons, etc) and so as a planet “falls towards” the Sun, orbital speed increases. As a planet “moves away” from the Sun, orbital speed decreases. b. What is it about the planet Mars that led Kepler to the true shape of planetary orbits? Tycho gave Kepler the data on Mars because he thought Mars was the planet whose observations would be the most difficult to interpret. Ironically, Mars’ orbit is the one for which Tycho had good data that deviates the most from a circle and hence was the most likely to guide Keplet to the conclusion that Mars’ orbit is elliptical. Kepler's extensive observations of Mars led him to conclude that its orbit was not a perfect circle, as previously thought, but an ellipse. Mars' orbital speed varied, and it moved faster when it was closer to the Sun and slower when it was further away. This observation contradicted the circular orbits of the Ptolemaic and Copernican systems, and led Kepler to formulate his First Law of Planetary Motion, which states that planets move in elliptical orbits with the Sun at one focus. c. What is Kepler's 1st Law? What is location at each of the focus points in a planetary orbit? Kepler’s first law states that planetary orbits are ellipses with the Sun at one focus d. What is the 'semimajor axis' of an ellipse? What does the 'eccentricity' of an ellipse refer to? What is the eccentricity of a perfect circle? A semi-major axis is half of the major axis (which measures eccentricity). Its like the radius of a circle. Eccentricity is how elongated an ellipse is A circle has 0 eccentricity e. What does 'perihelion' and 'aphelion' mean? Perihelion is when the Earth is closest to the Sun in its orbit, it moves fastest there. Aphelion is when the Earth is the furthest away from the Sun in its orbit, it moves slowest there. f. Describe the speed of a planet according to Kepler's 2nd Law. A planet’s speed varies as it moves around its orbit; it moves fastest at perihelion and slowest at aphelion. g. Why does Mars experience a large change in speeds compared to Earth? Mars experiences larger changes in distance from the Sun as a result of its more eccentric orbit. Mars moves in an elongated, oval-shaped path around the Sun, while Earth's path is more like a circle. This means that Mars sometimes gets much closer to the Sun and sometimes much farther away. When Mars is closer to the Sun, it moves faster. When it's farther, it moves slower. Earth's speed also changes a bit, but not as much as Mars, because Earth's path around the Sun is less oval and more circular. 12. Kepler’s 3rd Law: a. Kepler represented the orbit of each planetary in our solar system as an ascending and descending series of music notes. Why is this? Each planet’s song was based on the speed of its orbit because the vibrations caused by its motion through space would create sound waves. Even though we can't actually hear it, he imagined each planet as creating its own 'note' as it traveled around the Sun. When a planet moved closer to the Sun, its note would change, and it would also change when it moved farther away. He believed that the varying speeds of planets as they moved closer to or farther from the Sun could be thought of in terms of musical pitches. When a planet moved closer to the Sun and sped up, its "musical note" would ascend, and when it moved farther and slowed down, its "note" would descend. b. Describe the connection that Kepler made between the spacing of the planetary orbits and musical intervals. Kepler calculated the changing speeds of each planet and converted those speeds into tones. His theory was that the music of the spheres was a continuous and ever changing song. c. What does Kepler's 3rd Law tell us about the relationship between the orbital periods of planets and their distance to the Sun? Kepler’s third law implies that the period for a planet to orbit around the Sun increases rapidly with the radius of its orbit. In simpler terms, it means that the further away a planet is from the Sun, the longer it takes for it to complete one full orbit around the Sun. Conversely, the closer a planet is to the Sun, the shorter its orbital period is. d. What are the Rudolphine Tables, who wrote them, and whose planetary model are they based on? How does their accuracy compare to the tables made using the other available models? Written in 1627, the Rudolphine tables are tables of planetary coordinates of the Sun, moon and planets derived from the laws of planetary motion. Kepler wrote them using his laws and comparing them to the motion of the planets that Tycho had observed. They are based on Kepler’s planetary model with non-constant speed and elliptical orbits not perfect circles. Kepler’s predictions were the most accurate available being only 10 arcseconds off, which likely was from human error and a result from Tycho’s observations or instruments. The most accurate because of the fact that it used the laws of the universe.