On the eve of a new academic year of teaching and as usual I'm worried about getting the balance right. It's the usual conflict. Students are required to know the subject well enough to pass exams at various points during the next 8 months. There are various methods and techniques I can employ to ensure this happens. But if that was was the only focus of the course then I'd be guilty of "teaching to the test". Students would probably pass the exams but they'd be ill-equipped to handle new material or cope with even small variations on what they've already seen.
As a maths teacher I want my students to be independent learners. For me that means they are able learn from their mistakes and that they have strategies for thinking about and solving mathematics problems in a very general way. The intensity of my course - the amount of time allocated and the material that the students are expected to know - means that I definitely won't get enough sessions emphasising skills required to be an independent learner.
In practice what will probably happen is that I build some kind of activity into most classes where I get the students thinking about how to solve a problem that isn't textbook. There are plenty of teachers blogging about how to do this and lots of real world scientific examples to draw on.
Anyway, I'll record the best examples of my strategies here!
Fomalhaut is a tough star to see from these northerly latitudes. You can find it using the popular "Square of Pegasus" stars shown above. Follow a line from the two right-hand stars down to the horizon. It's typically only visible for just a few hours each night and it climbs just 6 degrees above the southern horizon at most. The further north you are, the harder it gets! Way up past 61 degrees north it doesn't rise at all.
In Northumberland on late on autumn evenings there's a bright, lonely star near the southern horizon. It often goes unnoticed - perhaps hidden by nearby (or even distant) buildings or trees. The name of the star is Fomalhaut (pronounced "fum-al-hort").
The planet Uranus was the first to be discovered after the invention of the telescope (William Herschel, 1781). At more than double the distance of Saturn and less than half the diameter, the planet Uranus is on fringe of naked eye visibility.
I've tried to spot Uranus without binoculars or telescope in the past. But for many years the planet was either lost among the stars of the southern Milky Way or just too far south of the celestial equator and so never very high my local sky.
Uranus is now north of the celestial equator (for the first time in decades) and in a part of the sky with very few stars. Last night I was able to see this distant ice giant world for the first time by naked eye. It looked like a tiny star - visible with averted vision.
I took a 30 second exposure on the camera; the original and labelled versions are shown below.
The dashed yellow line shows my method of star-hopping to the planet. Starting at the lower-left corner of the Square of Pegasus, jump to the two stars in Pisces (named epsilon and delta). At the moment Uranus makes an approximate equilateral triangle with these two.
Zooming in on the image.....the camera picked up the green-blue colour of Uranus' atmosphere:Not bad f
Not bad for a DSLR 2.8 billion km away from the subject!
It should become easier to find the planet Uranus during the next few years - at least until it enters the richer starfields of Aries and Taurus in the 2020s.
Just one more thing. I took another look at my 30 second image to see if I'd managed to pick up Neptune. I thought it unlikely but after checking - I definitely registered some light from the outermost planet of the solar system:
I've labelled the brighter stars (in Aquarius). You can find those three brighter stars in the original image near the top of the page: look down the RHS of the picture - almost two-thirds of the way down. I stretched the image a bit but Neptune is definitely there! I verified the position using SkyMap Pro - there are no stars at that position brighter than Neptune. Neptune was about magnitude +7.8 and 4.3 billion km from Earth when I took the picture. It was invisible to the naked eye.
Before you get the wrong idea Uranography is the art of making making high quality star charts. Celestial cartography is another way to describe it. I've just finished a substantial first attempt to make maps of the entire night sky - including all the stars visible to the unaided eye and lots of star clusters, nebulae and galaxies.
Click here to go to the page with my star charts and more details.
Here's one of the charts.
Setting up the star charts was a great way to become familiar with parts of the sky not visible from Northumberland. These charts are based on the code from open source PP3 Star Charts. I learned a lot of stuff along the way - namely modifying the C++ code to do things slightly differently and compiling it to work on Windows 7. I also modified the original constellation definitions (there are errors in the original). It's not perfect but I'm happy there are no big errors.
Course notes from my session called "Astrometry" at NASTRO are available by clicking the link.
The PDF has Flash animations from University of Nebraska-Lincoln embedded in it. When you open it, you'll have to enable them to run. It usually means clicking a little toolbar at the top of the talk. For best results press ctrl-L to view in full screen after you've done that.
You can view the Flash animations online if you prefer. These are the ones I showed during the talk:
Altitude/Azimuth (Horizon coordinates)
Right Ascension / Declination (Equatorial coordinates)
Coordinate Systems Comparison
There are loads more at the UNL website on other topics. Enjoy!
At NASTRO outreach sessions I usually begin constellation tours with some advice about how to get started in learning the night sky. Given that there's an app for just about anything you might think the days when you had to learn star patterns to enjoy astronomy is long gone. But It is possible to navigate the night sky by starting with simple star patterns. Over time you can build up your own internal map of the sky without your iPhone or Android ruining your night vision. During the late Summer and Autumn months a natural starting point is the Summer Triangle.
Also the the story behind the Summer Triangle is sort of interesting! The Summer Triangle (blue-dashed triangle on the star chart below) is formed between three of the brightest stars in the sky: Vega, Deneb and Altair.
In the 1920s the Internationational Astronomical Union decided to formalise the various star patterns that astronomers used to specify star locations. With the advent of astrophotography and the flood of variable star discoveries (which were named according to the constellation) it became important to know where one constellation ended and another began. They drew up a list of 88 constellations which are still use today, today. On the star chart above the constellations are patterns connected by the green lines (e.g. Aquila, Sagitta and so on).
There are other interesting star patterns in the sky - The Plough and Summer Triangle being the most famous - which are not part of the official list. We call these patterns asterisms. The Plough stars are part of the constellation Ursa Major. The Summer Triangle stars are part of three different constellations: Cygnus, Lyra and Aquila.
The Summer Triangle was popularised by Sir Patrick Moore on The Sky at Night and in his numerous astronomy books from the 1950s onwards. References to the Summer Triangle (or Great Triangle) can be traced back to the start of the 20th century.
Back to the Summer Triangle. Vega and Deneb mark the northernmost corners of the triangle. Altair is the star at the southern corner. The Milky Way runs through the Triangle and appears to split into two streams (separated by the Cygnus rift).
Vega is brightest star and Altair is slightly dimmer. Deneb appears to be the faintest of the three but that's just an illusion! Vega and Altair are quite nearby - 17 and 25 light-years away respectively. Deneb is an absolutely brilliant beacon shining across 1,800 light-years of space. If Deneb were at the distance of Altair it would shine as brightly as the crescent moon does! After identifying the Summer Triangle it becomes easier to find the surrounding constellations. For example, with Vega comes the tiny constellation of Lyra. Within the borders of Lyra is the Ring Nebula. Deneb is the leading star of Cygnus. When the shape of Cygnus can be recognised there are many star clusters to be found and one of the most beautiful double stars in the night sky. There are other smaller constellations with distinctive shapes nearby (Delphinus - a dolphin. And Sagitta - an arrow) in which a great number of incredible deepsky objects are waiting to be seen through your binoculars and telescopes.
The Summer Triangle will be around for awhile longer; despite the name it is visible for much of the autumn and into winter. But the relatively pleasant evenings of late summer are definitely the best to go out and find it for the first time.
Dr Adrian Jannetta
Guitar strummin' explorer of the universe. Mild mannered maths teacher by day and astronomer by night.