Today was graduation day for those students that started my course last September. Most were happy but not all of them passed. It's been a hectic few weeks dealing with the admin side of their course ending too: exams, resits, marking and preparing stuff for the external examiners. All the while teaching the other cohort of students. In the next couple of weeks I've got a deadline approaching to finish changes to my course textbook (two of them!) After that....the days of calm. From next week I'll be down to just 49 students (those that started in January) and 7 hours of teaching per week until they leave in the summer.
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Finally found a bit of time to get a star chart for the June night sky done. Based on my location in Northumberland  download the high quality PDF here because it contains a lot more information about the star chart and some of the stars, planets and other sights visible in the sky this month.
I'm a big fan of LaTeX and PSTricks and I use them often to create diagrams and graphs for my various maths and astronomy lecture notes. But to create this lunar phase diagram it was much more convenient to use another package called TikZ!
It's a pretty standard diagram; sunlight is shown streaming from the right. The Earth is at the centre with the moon shown in a (blue) circular orbit and presented at various positions around the orbit. The phase of the moon (the shape of the illuminated portion we see from Earth) is shown outside the orbit. I added some arrows and arcs to show the traditional waxing (growing larger) and waning (growing smaller) sections of the orbit and finally, the number of days since new moon.
Technical details of the code below the fold.
I don't think the MESSENGER mission to Mercury ever captured the imagination of the general public in the same way Cassini is still doing at Saturn. MESSENGER ended its 11 year mission yesterday. With no more fuel aboard the spacecraft the peturbing force of solar gravity finally brought MESSENGER down with a bang on the surface. Prior to 2011 Mercury was a largely unknown planet with just onethird of its surface imaged in the 1970s. MESSENGER has transformed our view of Mercury since its first flyby in 2011 and sent back views of the planet like these:
Mercury has clearly been battered and scarred from impacts sustained since the earliest days of the solar system.
Meanwhile, on the other side of the solar system the New Horizons spacecraft is hurtling towards a July rendezvous with an explanet called Pluto. New Horizons is now close enough to Pluto  a world even smaller than Mercury  for its cameras to pick out surface details:
NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute
The orbiting moon is called Charon and it's quite big compared to Pluto. Pluto appears to wobble because the centre of mass (the barycentre) of Pluto and Charon is some way outside Pluto. The closeup view shows a lot of variation in brightness across the disk. Clearly Pluto is going to be an interesting place to see when New Horizons eventually arrives!
Had long walk today up on Simonside Hills near Rothbury. Fantastic view across a lot of Northumberland. Made a panorama to try and convey what the view is like from the top:
Hope to go back in the future to visit the solstice stone.
Numbers are so familiar to us that it might seem unimaginable that there was a time when the very concept didn’t exist. Indeed the invention of numbers is lost in antiquity. Historians of mathematics speculate that the origin of numbers was probably connected with real problems of life at the time, like describing whether there was one animal, or more than one animal as food source (or a threat). A certain level of abstraction was required to use numbers. Three rabbits, three stars and three rocks only share the property of threeness. Manipulation of number – with no connection to physical objects – was a great intellectual leap. Beyond countingNegative numbers arrived on the scene much later. Trading and commerce meant that profit and loss should be accounted for properly. Negative numbers were used to represent an absence or a loss. Despite this the negative numbers were not immediately accepted by mathematicians. Early practitioners of algebra would often discard negative values when they appeared as solutions. After all it’s easy to picture three people in a room. Or two. Or one. Or even none. But what does minus one person in a room look like? One of my students recently suggested it would be like a ghost! There may be grounds for rejecting negative numbers as the solution to a particular problem but in other situations their use may be perfectly acceptable. Negative numbers eventually found their place in our number system because they can be solutions of equations – just as valid as their positive namesakes. Likewise the history of zero is just as fraught with controversy and confusion. Zero initially served as a placeholder in the representation of number. For example, it is the zeros which tell you about the size of the numbers 15 and 105 and 1005. But zero as a number in its own right took a long time to gain acceptance. Just like negative values, the solutions to some equations can be zero. The negative and positive numbers (integers and all the values between them) along with zero can be represented on a numberline stretching infinitely in both directions. For most people that’s the end of the story – we usually don’t need other types of number to survive in life. Or do we? Another day, another diagram. This one is for a forthcoming talk about quasars and active galactic nuclei. Synchrotron radiation plays a big part in powering jets emerging from the centres of active galaxies and quasars. I needed a simple picture and used PSTricks to rustle one up. Details of how this was coded are below. I needed a diagram for an article on noctilucent clouds. They range from pretty (and copyrighted) to pretty ugly online so I had a go at making my own. As usual this was done with LaTeX (via LyX) and PSTRICKS. Here's the finished picture: The diagram is simple: part of a circle, some tangent lines, cloud symbols and labels. Then shade between the various curves and lines. Finally, a multido loop to draw the Sun. Details below the fold.
If the Earth suddenly stopped moving around the Sun  how long would it take to fall into the Sun?
First of all, this is a situation that will never, ever happen! It would take a phenomenal amount of energy to stop planet Earth in its tracks. A passing malevolent alien attack fleet imparting that much energy to the Earth would likely destroy it! (Another problem for another day :p ) Nevertheless it's an interesting maths problem to think about (maybe only to me) on a lazy afternoon.
Method
We can use conservation of energy to solve this. The Earth has kinetic energy (from its motion) and gravitational potential energy because of its position in the gravitational field of the Sun. Ignoring the effects of other planets, the sum of those energies is constant and we can use that fact to figure out the fall time. Click below if you want to avoid the maths and just to skip to the answer!

Dr Adrian JannettaGuitar strummin' explorer of the universe. Mild mannered maths teacher by day and astronomer by night. Archives
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