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 one-third 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 ex-planet 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 close-up 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 three-ness. Manipulation of number – with no connection to physical objects – was a great intellectual leap.
Negative 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?
A copy of the PDF used in my NASTRO talk at The Trap this evening can be downloaded here.
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 multi-do 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.
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!
It was solar eclipse day yesterday I managed to observe it despite the pretty grim weather forecasts in the days prior. This is me getting set up with telescopes on the roof of a building at Newcastle University. Absolutely perfect spot to see it and no real danger of accidentally tumbling over the side of the building!
It was mostly cloudy during the eclipse though. There was clear blue to the west and a little to the north but clouds mostly remained in front of the Sun during the morning. They broke completely minutes after the eclipse ended. Oh yes!
I was joined on the roof by staff and students at INTO. We did see some of the eclipse. The cloud gaps were small but slow moving. Here's my first eclipse pic taken about 20 minutes after it began:
A small sunspot is visible on the solar disk and the clouds, damn them, add something to the photograph. Lucky me. The Sun never really shone brightly enough for the PST (hydrogen alpha) telescope to be of much use.
The clouds covered the Sun up until mid-eclipse. But in the west and overhead the sky stayed clear. The temperature dropped a little - maybe a couple of degrees. By the time of maximum eclipse arrived the ambient light level had dropped to a level more like dusk. Exterior lights on neighbouring buildings began to switch on. The Sun reappeared through gaps in the cloud. I took some more pictures.
More than 90% of the solar disk was obscured at mid-eclipse. The Sun was visible through the clouds and the eclipse viewers and solar filters were useless under those conditions. It was comfortable to look at the Sun as it faded in and out of view during the half an hour after mid eclipse. This was the unfiltered camera view as the moon was uncovering the Sun:
The clouds returned and obscured the final stages of the eclipse. Nevermind. Felt lucky to see any of it if I'm honest. I packed up at around 10.40am as the eclipse was officially ending in Newcastle. I carried my gear along a corridor, into a lift and then down some stairs. As I left the building I was faced with full sunshine and not many clouds. Ten minutes later I was back on my normal timetable and teaching geometric series to my students in a nearby classroom.
That was yesterday.
Fast forward roughly 34 hours and the moon is in the evening sky. A narrow crescent just 3% illuminated by the Sun. This is how it looked an hour after sunset from near my home.
The next eclipse I'm hoping to see is a total lunar eclipse in the early hours of September 28th later this year.
It's been a crazy busy month at work and at home. Lots of classes and exam papers to mark. Astronomy-wise, I've had quite a few public outreach events around Northumberland to contend with as well as a number of late night observing sessions centred around Comet Lovejoy. On top of that it looked like Mir and me might have to move house imminently but now, fortunately, that danger seems to have past!
Since January I've been studying a course on Coursera called "Galaxies and Cosmology". It's been a bumpy ride and there have been times where I've submitted the weekly assessments just moments before the deadline (typical student!) I'd like to have taken the course when I was a bit less busy with work. But, it is just for fun and I've been pleasantly surprised at how deeply immersed I've become in cosmology again. Given how much I learned a about maths when I had to start teaching it, I'm going to put together a short course on Cosmology for presentation at NASTRO later in the year. It'll go into the subject in a bit more detail than I've done in the past and allow me to spend more time talking about the methodologies of cosmologists and the evidence for the Big Bang theory.
It's going to be awhile until this busy period at work passes so there might be more posts about maths (teaching) than astronomy over the next few weeks.
Dr Adrian Jannetta
Guitar strummin' explorer of the universe. Mild mannered maths teacher by day and astronomer by night.