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| Adam Schall (汤若望 [湯若望], Tāng Rùowàng, 1591-1666), Imperial Astronomer in Beijing. Designed the current Chinese calendar | Astronomers at the Istanbul Observatory |
| Lecture Notes | Homework and Tutorials | Old Exams | Summary |
| Past Homework | Past Projects | References | Good-bye! |
| Helmer Aslaksen's home page |
The goal of this course is to study astronomy in a cultural context. We will look at questions like: How is the date of Chinese New Year determined? Why do the Muslim and Chinese months start on different days? Will the Moon ever look like it does on the Singapore flag? What date of the year is the earliest sunrise in Singapore? How did ancient sailors navigate?
After taking this course you will become conscious of the motion of the Sun and the Moon and notice and question things you have earlier taken for granted. You will appreciate mankind's struggle through the ages and throughout the world to understand the mathematics of the heavens.
This course is one of the General Education Modules at the NUS.
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| Astronomical instruments in the Imperial Observatory in Beijing made by the Jesuit missionary Ferdinand Verbiest, 1670 |
We start by discussing the motion of the Sun and the Moon. Most astronomy books are written from a high northern latitude point of view, but in this course we will take a "hemispherically correct", tropical point of view. We then look at applications with a cultural flavor. In Singapore we use the Gregorian, Chinese, Islamic and Indian calendars for determining the public holidays and you will learn the rules for these calendars. Most people expect the time of sunrise and sunset in Singapore to stay fixed throughout the year, but we will study the equation of time and the analemma to see why there is a half hour variation. Navigation has been important to people all over the world throughout history, and people at different latitudes developed fundamentally different methods. If we have time, we will look at ancient astronomical instruments, astrology, cartography, archaeoastronomy (the use of astronomy in archaeology), cultural astronomy and astronomy in nature.
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| Brian Greig's astronomical instruments for sale at the Melbourne Arts Centre Sunday Market |
There will be three hours of lectures and one hour of large group tutorial each week. The time slots in 2009/2010 Semester 1 are Tuesday and Friday 8-10 a.m. in LT23. I take a 10 minutes break in the middle, and aim to finnish by 10 to the hour.
I'm only supposed to give three hours of lectures so on Friday I will use the last hour (9 to 10) as a tutorial starting in Week 3. Alternatively, there will be a small group tutorial, too. (Wednesday 11-12 in LT23, starting in Week 3.) The first two weeks I use all four hours for lectures because there is so much practical stuff to cover.
I use a cordless microphone and walk around in class and ask questions. But don't worry, I only ask easy questions! I also like to create physical demonstrations to illustrate the concepts, and I often need “volunteers” for this. I am not afraid of looking silly, and I hope you are not either!
The lectures will be NUScast. The goal of the webcast if to give you a chance to take another look at things you didn't catch, or to help you if arrive a couple of minutes late. They are not meant as a substitute for going to lectures. I'm afraid my lecturing style is not very suitable for webcast. I move around a lot, and I rely on physical demonstrations that probably will not show up in the webcast. Webcast is great for lecturers who read aloud from their lecture notes, which is not my style.
The final exam counts 50% of your grade. There will be a midterm that that counts 30%. There will also be a homework that counts 20% and is done in groups of four to six students.
There will be a midterm test on Tuesday 29/9/2009 during the last hour of lectures at 9 am. The homework is due at the beginning of class on Tuesday 27/10/2009. The exam will be on Monday 30/11/2009, 5 pm.
Please submit to the IVLE workbin. However, I don't want to get 50 files called Homework.doc. Please use the number of your group as the first two characters in the file name. For example “04 Homework.doc”.
I have a special system for group assessment. Each group can either choose to have everybody get the same grade (the default), or you can choose to grade the others in your group, by saying how many percent of the final mark the others deserve. If you manage to agree, I will follow what you agree on! Just gather everybody and come and see me. If you cannot agree, come and see me (separately, if necessary), and I will take the average. But I will not let that average count 100%. I will give it a weight of x%, and the uniform distribution will get weight (100-x)%. I will not tell you what x is, and I may even use different x for different groups. I encourage you to discuss this in a polite, friendly, reasonable, generous and compassionate way, and make every effort to reach a unanimous decision. My weightage may not be fair, so try to sort it out yourselves. At the same time, I want to have a way to protect people from unreasonable group mates. To sum up:
Please do the homework in a group of four to six people.
Don't worry if you have a hard time finding a group, you're probably not alone! Post a message on the discussion forum and you'll probably find other people in the same situation who you can form a group with.
I used to have two homework, but many students complained that it was too much work and too dependent on good weather, so I have simplified into one homework.
I get a lot of e-mail, so it would be helpful if you try to observe the following.
Many of the questions involve geometry, and it is hard to discuss it by e-mail. If you want to make an appointment to see me, just mail me and tell me when you are free.
| Week 1 | First week of lectures |
| Week 2 | Signing up for groups |
| Week 3 | Tutorial 1 |
| Week 4 | Tutorial 2 |
| Week 5 | Tutorial 3 |
| Week 6 | Tutorial 4 |
| Mid-semester Break | Yippee!!! :-) |
| Week 7 | Midterm test Tuesday 29/9/2009, Tutorial 5 |
| Week 8 | Tutorial 6 |
| Week 9 | Tutorial 7 |
| Week 10 | Tutorial 8 |
| Week 11 | Homework due Tuesday 27/10/2009, Tutorial 9 |
| Week 12 | Tutorial 10 |
| Week 13 | Last lecture Friday 13/11/2009, Tutorial 11 |
| Reading Week | Don't panic! Stay cool! |
| Exam | Exam Monday 30/11/2009 5 pm. Good luck! |
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| Royal Observatory Greenwich |
I have a course page at IVLE, the Integrated Virtual Learning Environment. It contains several useful tools.
Otherwise, the current page is the main source of information.
Unfortunately, there's no textbook for this course. Maybe I'll try to write one myself? The closest is The Ever-Changing Sky, A Guide to the Celestial Sphere by James B. Kaler. However, it goes into a lot more detail about astronomy than we will cover. The level of astronomy I expect you to learn is comparable to the first chapter and the appendix of The Copernican Revolution, Planetary Astronomy in the Development of Western Thought by Thomas S. Kuhn. For convenience, the main reference for the first part will be Strobel's Astronomy Notes on the web.
I have compiled a list of additional references. In addition to the books by Kaler and Kuhn, I've also placed The History and Practice of Ancient Astronomy by James Evans and Calendrical Calculations: The Millennium Edition by Nachum Dershowitz and Edward M. Reingold on RBR in the Science Library.
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| Orrery by Brian Greig |
Together with Tey Meng Khoon and Frederick H. Willeboordse of CITA (Centre for Information Technology and Applications), I have developed interactive Java applets that I hope will help you understand the motion of the Earth, the Sun and the Moon.
You will notice that a lot of the applets are somewhat similar. They show the same thing, but we're trying to emphasis different aspects or points of view in each one.
You can get the Java Runtime Environment (JRE) at java.com. If you prefer to view the applets off-line, you can download them. Just unzip astro-applets.zip, and open astro-applets.html in your browser.
The last two applets are related to What Does the Waxing or Waning Moon Look Like in Different Parts of the World?
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| Equatorial (left) and ecliptic (right) armillary spheres in the Imperial Observatory in Beijing made by the Jesuit missionary Ferdinand Verbiest, 1670 | |
Together with Keith Phua Kuan Wee of CITA (Centre for Information Technology and Applications), I have recorded video clips to help you understand the material. The clips are available in three formats:
I have recorded video clips to explain the Java applets and Strobel's Astronomy Notes.
Nick Strobel of Bakersfield College has written a wonderful set of Astronomy Notes for his introductory astronomy course. His chapter on Astronomy Without a Telescope is very relevant background for this module. I have recorded video clips with annotations to some of the sections of the first chapter of Strobel's notes.
Here is the table of content for the first chapter of Strobel's Astronomy Notes with links to my video clips.
RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime. RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime. RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime. RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime. RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime. RealVideo
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SureStream, RealVideo
LAN/150Kbps, QuickTime. |
I recommend the wonderful freeware Stellarium Astronomy Software (or from Sourceforge) available for Windows, Linux/Unix and MacOSX. I have written a Help Page.
How can we use the celestial sphere to understand the movement of the Sun, Moon and stars across the sky? Observing the sky has always been an important part of human civilization. We give a summary of some basic facts from spherical astronomy. One of my students, Viduranga Yashasui Waisundara, has written a beautiful poem about this, called If I were God.
There are a lot of Myths about the Copernican Revolution. Many people whose main interest is philosophy of science, but with little knowledge of astronomy or history of science, have written extensively about it. Unfortunately, much of what they say is incorrect.
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| Tycho Brahe (1546-1601) |
video clips with
annotations to some of the sections of the first chapter of Strobel's notes. |
| The Meridian Line at Greenwich |
How is the date for Chinese New Year, Eid ul-Fitr (Hari Raya Puasa) and Deepavali determined? Singapore is unique in that we use four different calendars for determining the date of the public holidays. Seven of our eleven public holidays move, and we study the rules for Chinese New Year, the two Eid's (Hari Raya's), Deepavali, Vesak Day and Good Friday. The exact rules are very complex, but the basic ideas are simple. We give two simple rules of thumb that determine the date for Chinese New Year with a margin of error of one day. I have written a set of lecture notes on The Mathematics of the Public Holidays of Singapore.
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You will also see why both Eid ul-Fitrs (Hari Raya Puasas) in 2000 were celebrated one day earlier than they would have been if MUIS had relied on sightings or scientific criteria.
Why is it difficult to determine the Islamic prayer times in Northern Europe? This is an interesting astronomical problem, which very few people understand.
What are leap seconds? This requires understanding some delicate points in the definition of atomic time.
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| Chinese astronomers determining the summer solstice |
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| Chinese sundials from the Adler Planetarium | |
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| MoonCalc image |
Determining the direction to Mecca was together with determining the first visibility of the lunar crescent and computing prayer times one of the central problems in Islamic astronomy. It requires a clear understanding of spherical trigonometry and knowing how to find longitude. However, you would think that at the moment it would be a trivial computation. I was therefore quite surprised when I received e-mails from Muslims in the US and Canada who started asking me about it. I realized that it is a major controversy among Muslims in North America. All the famous Muslim astronomers and mathematicians in the past, like al-Khwarizmi (780-850), al-Battani (858-929) and al-Tusi (1201-1274) agreed that qibla should be measured by great circle. However, some people who are used to looking at Mercator maps and don't understand great circles argue that you should draw straight lines on a Mercator map, i.e., follow rhumb lines. They strongly attack people who follow the traditional method of great circles. For examples of this, see Direction of Al-Qiblah and Qiblah.us. For a scientifically correct discussion, please see moonsighting.com.
This is one of my favorite topics. I have some lecture notes about this, which I'm trying to expand on. Most astronomy books are written from a “high-northern-latitude-centric” point of view. I will discuss the motion of the Sun and the Moon from a “hemispherically-correct” point of view, with special emphasis on the needs of “latitudinally-challenged” observers.
I have a number of web pages about astronomical topics from a Singaporean point of view.
Some of my students have contributed greatly to this. One of my favorites is the following e-mail from one of my students, LIEW Wen Hwee.
Subject: The theory of hanging clothes to dry
Date: Wed, 18 Dec 2002 12:44:51
Hi Sir,
Ohh my. I just discovered the theory behind my mum's “theory of hanging clothes to dry”.
My mum have been telling me since I was a kid that for half of the year that she will have to hang the clothes out in the kitchen and the other half of the year in the corridor for them to dry. I was perplexed by her “theory” for a long time. I thought “wasn't the sun suppose to rise East always?”
And your lesson cleared my doubts!!! My flat lies exactly (ermmm maybe not that exact. didn't notice tat until I used the compass. Was almost scared by a faulty compass that points “west” in the direction where the sun rises!!!) in the East- west plane. And so for half of the year, the sun be in the South-east and the other half in the North-east. MY MUM IS AN ASTRONOMER !!!(ha.).
Sir, what u have taught is of practical purpose!!! (Maybe u could tell the next batch of students abt tat and they could advise their mum on how to better dry their clothes. =))
Thanks a lot, Sir!!!
I have a separate web page on Which Day Does the Sun Rise Earliest in Singapore? Singapore lies almost on the equator, so most people would expect the Sun to rise at more or less the same time each day of the year. In fact, the sunrise time varies between 6:46 a.m. and 7:17 a.m., with the earliest sunrise on November 1 and the latest on February 9. In the same way, the sunset time varies between 6:50 p.m. and 7:21 p.m., with the earliest sunset on November 5 and the latest on February 13. The difference between the earliest and latest sunrise in 30 minutes, but the difference between the longest and shortest day is only 8 minutes. The key to understanding this is the analemma, which is a graphical representation of the equation of time.
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| Analemma picture by Dennis di Cicco |
The famous picture by Sky & Telescope's Dennis di Cicco records the Sun's position in the sky at the same time of day on 45 different dates throughout the year.
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This is also related to the concept of time zones. As you can see from the map, Singapore and West Malaysia are in the “wrong” time zone! For more details, please see my page Why is Singapore in the “wrong” time zone?
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| Sundial in Enschede, Netherlands, 1836, photo by Fer J. de Vries. |
RealVideo
SureStream, RealVideo
LAN/150Kbps, QuickTime.Why do sundials look different in Singapore and Beijing? We study the theory behind sundials and show how to construct an accurate sundial for any latitude. There are several nice sundials in Singapore. There is one in the Botanic Gardens and one in Marina City Park. As part of their Science is everywhere program, The Singapore Science Centre together with the National Parks Board recently put up a series of sundials representing the planets. With Science Centre representing the sun, unique sculptures are placed at various locations around Singapore. The relative distance of these sculptures from the Science Centre represents the distances of each planet from the Sun. Please check out the map!
Four common types of sundials are the equatorial, armillary, horizontal and vertical sundials.
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| Equatorial sundial | Armillary Sundial at City Hall, Ruurlo, photo by Frans W. Maes. |
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| Horizontal sundial by Harriet James | Vertical sundial by Harriet James |
For telling the time at night, you can use a nocturnal.
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| Nocturnal | Nocturnal |
The quadrant is a simple tool for determining latitude.
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| Quadrant |
The astrolabe was made famous by Arab astronomers, and can be thought of as an analog astronomical computer. We discuss the difference between an astrolabe and a mariner's astrolabe.
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| Astrolabe by Norman Greene | Mariner's astrolabe by Norman Greene |
There's a lovely Persian astrolabe from 17th century at the Asian Civilisations Museum in Singapore.
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| Brass astrolabe, 17th century, Persia, Asian Civilisations Museum's collection, Singapore |
One of the most fascinating of all astronomical instruments is the Antikythera mechanism. The Antikythera Mechanism is the name given to an astronomical calculating device, measuring about 32 by 16 by 10 cm, which was discovered in 1900 in a sunken ship just off the coast of Antikythera, an island between Crete and the Greek mainland. Several kinds of evidence point incontrovertibly to around 80 B.C. for the date of the shipwreck.
Geoffrey Chaucer, the author of Canterbury Tales wrote a Treatise on the Astrolabe in 1391.
We then look at the cross-staff and the back staff.
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| Cross-staff | Backstaff |
We will compare the relative advantages of the quadrant, mariner's astrolabe and cross-staff.
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| Quadrant | Mariner's astrolabe | Cross-staff |
The Chinese astronomer Guō Shǒujìng (郭守敬,1231-1314) designed many outstanding instruments. We will look at some of the famous observatories in China and India.
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| Dengfeng Observatory, designed by Guō Shǒujìng (郭守敬,1231-1314) in 1276 | Armillary spheres at the Purple Mountain Observatory in Nanjing designed by Guō Shǒujìng (郭守敬,1231-1314) | |
We study the armillary spheres made by the Danish astronomer Tycho Brahe (1546-1601). (My second cousin lives in a castle built by a nephew of Tycho Brahe!) You will learn the difference between an ecliptic armillary sphere and an equatorial armillary sphere. I also have a separate page about “Fake” Armillary Spheres.
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| Ecliptic armillary sphere | Equatorial armillary sphere |
How were cathedrals used as solar observatories? We study meridian lines in European churches. I have created a separate page on meridian lines, A Guide to “The Sun in the Church” by J.L. Heilbron.
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| Meridian Line. S. Petronio, Bologna, Calter Photo | Solar eclipse at the Meridian line at S.Maria degli Angeli in Rome by Mario Catamo |
The Ambassadors by Holbein is a famous example of Anamorphosis. Do you see the strange object on the floor? Close your left eye, put your face close to the computer screen near the right side of the picture. You will then see a skull! If you can't get it to work, you can cheat and look at a picture of it.
The reason why I include this painting on this page, is because it contains an incredible collection of astronomical and mathematical instruments! Please check out my page about The Ambassadors by Holbein.
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| The Ambassadors (1533), by Hans Holbein the Younger (1497/8 - 1543) |
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| Celestial globe made for the Beijing Observatory by Ferdinand Verbiest (1673) | Celestial Star Globe |
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| The large Samyat Yantra, equatorial sundial, at Jaipur | Drawing of the small equatorial sundial showing the shadow, quadrants, gnomon, and Sun rays |
Does astrology make sense? I'm personally skeptical. In the past, however, there was a close relationship between astronomy and astrology, and astronomy has great historical interest. We look at the mathematical foundation of some of the key concepts in both Western and Chinese astrology.
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| 15th century French woodcut |
What do astrologers mean when they say that somebody has an Aries ascendant? In order to understand this, we study the division of the ecliptic into houses. This is a very difficult issue, especially in high latitudes.
Why is it harder to find your position at sea than at land? We study how ancient sailors in different parts of the world navigated in different ways, and how technological advances opened up new possibilities for discoveries and trade.
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| Cross-staff used for computing lunar distance and height of buildings on the cover of Introductio geographica by Petrus Apianus, Ingolstadt, 1533 |
Why is it harder to determine the longitude than the latitude? In 1714 the British Parliament offered 20,000 pound to anybody who could come up with a practical method to determine the longitude at sea. That was the equivalent of US$12 million in modern money! The Astronomer Royal was only paid 100 pounds a year, and had to pay for his own instruments.
We will watch the movie Longitude, starring Jeremy Irons, which is based on the best-selling book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time by Dava Sobel. The movie is very interesting, and includes famous names like Jeremy Irons, Michael Gambon, Bill Nighy, Ian Hart and Gemma Jones.
Why is it harder to find your position in an air plane than at sea? We look at some modern methods, including GPS.
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| Harrison's 4th Timekeeper and Longitude prize-winner |
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| Danish high school students working on a navigation project |
Most capital cities have a geographical origin of coordinates, which is used when making maps for the country. All cities also have a zero point for road distances from the city center to other points. Why do capital cities need an origin of coordinates? In the past, finding coordinates, especially the longitude, was so hard that the best way was to pick a local origin, do astronomical observations at that point, and then do triangulation for the rest of the country. That's why the origin of coordinates is often at observatories.
In London the origin of coordinates is at Greenwich, while the zero point for road distances is at Trafalgar Square. In Oslo the origin of coordinates is at the Observatory, while the zero point for road distances is at Stortorvet. But what about Singapore? After a bit of detective work, and a lot of help from various people, I found that the origin of coordinates is at Empress Place and the zero point for road distances is at the old General Post Office, now the Fullerton Hotel. For more details, see my page on Where is the Geographical Origin of Coordinates of Singapore?
How big is the Earth? We look at Eratosthenes's solution to this problem.
Did people in the Middle Ages believe that the Earth was flat?
Why is there no perfect map? We define the curvature of a surface and show that the curvature of the Earth is positive while the curvature of the plane is zero.
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| Mercator's 1569 world map | Mercator map of the world attributed to Edward Wright (1599) | Modern Mercator map |
What makes the Mercator projection so important in navigation? We study the geometry of rhumb lines. We also show how it is related to the invention of logarithms.
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| This is NOT a medieval woodcut! |
Was Stonehenge an observatory? When were the pyramids of Egypt built? Archaeoastronomy is a very active area these days. Many ancient monuments reveal an astronomical background.
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| Newgrange | Stonehenge |
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| Winter Solstice Sunrise at Newgrange | Winter Solstice Sunrise at Maeshowe |
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| Astronomical instruments in the Imperial Observatory in Beijing made by the Jesuit missionary Ferdinand Verbiest, 1670 |
What is “wrong” with the Singapore flag? Why is the coat of arms more correct? I have a page on The Mathematics and Astronomy of the Singapore Flag.
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| The Singapore Flag | The Singapore Coat of Arms |
What is a Harvest Moon? What is a Blue Moon? What is Groundhog Day? There are a lot astronomical terms that people use but don't really understand.
What was the Star of Bethlehem? How can eclipses be used to date historical events?
Chaucer wrote a book on the astrolabe, and the Canterbury Tales are filled with astronomical references.
Celestial Navigation Net has a very interesting section on Dante and Celestial Navigation!
Donald Olson and others have championed a new field called forensic astronomy. A nice example of this is Astronomers turn detectives to pinpoint date of Ansel Adams image.
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| Phil the groundhog |
I have a separate page on What Does the Waxing or Waning Moon Look Like in Different Parts of the World? This is a complex question that confuses many people.
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| Moonrise from Sky & Telescope |
What does the orbit of the Moon around the Sun look like? Most people, even almost all mathematicians I've asked this question, tend to believe that it will have loops and look something like the picture below.
In fact it looks like this picture!
It is not a circle, but is close to a 12-gon with rounded corners. It is locally convex in the sense that it has no loops and the curvature never changes sign. I have a page that explains why The Orbit of the Moon around the Sun is Convex!
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| Halls Harbour, Nova Scotia, six hours apart | |
Why are there two high tides each day? This is very frequently asked question! I used to think that the answer was simple, but after looking around in the library and on the web, I discovered several different attempts at explaining it. Newton's equilibrium theory from 1687 used the differential of the gravitational force, but some people (especially oceanographers) also consider a centrifugal force caused by the rotation of the Earth around the Earth-Moon barycenter. Unfortunately, it seems to me that the methods using a centrifugal force are unnecessarily complicated, if not outright wrong! I will describe some of the attempted explanations I found.
How often can we see lunar and solar eclipses in Singapore? It turns out that it is fairly easy to make reasonably accurate eclipse predictions. There are several solar eclipses each year, but at a given place, they occur on average only every 360 years. Solar eclipses, Singapore lists all solar eclipses visible from Singapore between 1700 and 2100. The last total eclipse was in 1821, and there will be annular eclipses in 2019 and 2053, but I'm afraid there will not be any total eclipses in Singapore before 5 July 2168.
How is astronomy related to the ice ages? It turns out that changes in the Earth's movement is related to the ice ages.
Why does the Moon look bigger when it is near the horizon?
Can you balance an egg on the Spring equinox? This turns out to be related to the Chinese calendar!
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In October 1995 I went with Professor John Parkinson to Sabah to watch a total solar eclipse.
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| What's Wrong With This Moon? |
The truth may be out there, but there's a lot of crap, too! I will discuss some common misconceptions and hoaxes. One of my favorites is the “Mars will be as big at the Full Moon” e-mail. It has several variations, but here is a common one.
The Red Planet is about to be spectacular! This month and next, Earth is catching up with Mars in an encounter that will culminate in the closest approach between the two planets in recorded history. The next time Mars may come this close is in 2287. Due to the way Jupiter's gravity tugs on Mars and perturbs its orbit, astronomers can only be certain t! hat Mars has not come this close to Earth in the Last 5,000 years, but it may be as long as 60,000 years before it happens again.
The encounter will culminate on August 27th when Mars comes to within 34,649,589 miles of Earth and will be (next to the moon) the brightest object in the night sky. It will attain a magnitude of -2.9 and will appear 25.11 arc seconds wide. At a modest 75-power magnification Mars will look as large as the full moon to the naked eye.
Mars will be easy to spot. At the beginning of August it will rise in the east at 10p.m. and reach its azimuth at about 3 a.m. By the end of August when the two planets are closest, Mars will rise at nightfall and reach its highest point in the sky at 12:30a.m.
That's pretty convenient to see something that no human being has seen in recorded history. So, mark your calendar at the beginning of August to see Mars grow progressively brighter and brighter throughout the month. Share this with your children and grandchildren. NO ONE ALIVE TODAY WILL EVER SEE THIS AGAIN!
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Does this make you think that Mars will be as big as the Full Moon in the sky? That's NOT what they're saying, but you have to read carefully to not get tricked.
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| Kepler's Mysterium Cosmographicum, 1596 |
The first part of the course gives a basic introduction to spherical astronomy. Here are the slides from the lectures.
The second part of the course is about calendars.
The last part of the course is about time and navigation.
A brief summary of some of the main points.
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| Armillary sphere at the Purple Mountain Observatory in Nanjing designed by Guō Shǒujìng (郭守敬,1231-1314) | Armillary sphere at the Purple Mountain Observatory in Nanjing designed by Guō Shǒujìng (郭守敬,1231-1314) |
I have a separate page for past homework.
Before 2009, students did a project. I have a separate page for past projects.
I have a separate web page with references.
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| Adam Schall (1591-1666), Imperial Astronomer in Beijing | Armillary sphere |
Congratulations! You've made it to the end of my page! Thanks for your patience! But before you go, it's time for a little quiz. In the picture of Adam Schall above, can you name the five astronomical and three geometrical instruments in the picture? Can you tell what is wrong with one of them? Hint: Look at the picture on the right. I have included answers.
I hope you have found something of interest. That makes my efforts worthwhile. Feel free to send me a message.
And remember, if life is hard, do like the sundial: Count only the bright hours!
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