Pressure and planets: taking science on holiday

Gentle warning: although shorter than my average post, it contains a higher than usual geek-like content. You have been warned.

About a month ago, as an early celebration of our 40th wedding anniversary, my wife and I went on a trip to Switzerland – by train. Whilst getting around Switzerland by train, cable car and funicular was a complete joy, it has to be admitted that the haul there and back again was a long one. Even for a supporter of train travel it was long. However, even these journeys had their mitigating factors. The slowly changing scenery moving past our window was one, much as it was when we crossed the Canadian Rockies by train some years back, ending up in Vancouver. On the way out we broke our journey in Strasbourg where, apart from a view of the buildings associated with our soon-to-be-former membership of the EU, I was able to indulge in a little glass-spotting …

One of the more spectacular stained glass windows to be found in Strasbourg Cathedral. (The original image was elliptical since I had to photograph the high-level round window from the aisle of the church: I have ‘adjusted’ the image to undo the effects of perspective.)

Conversations with our fellow travellers are a bonus as well, but a physicist’s mind also has a tendency to wander into less populated mental territory. Almost without realising it I found myself converting the displayed speed of one of ours train from the km/hr shown on its display into metres/second (over 85 metres each second!) and thence into miles per hour. That’s around 200 mph, should you wish to know. (In passing, you’ll probably be grateful that I have resisted the temptation to digress into a paragraph or two on measurement units. It will surely come, but perhaps in a future post …) Now, unless we approach the speed of sound, which is about 340 m/s near sea level, the drag due to air friction increases as the square of the speed. As an example, the drag will have increased four-fold as the train accelerated from 100 mph to 200 mph; these numbers underline the importance of streamlined designs and all the engineering behind them. Of course, the frictional drag also depends on the density of the medium through which an object is moving. For instance, the reason a submarine is subject to relatively huge frictional forces is simply because it’s moving through a medium, sea water, which is more than 800 times denser that the air at the surface. Similarly, providing it can still get enough oxygen for its engines to function, a jet is better off flying in the thinner air present at high altitude. In a (very) round-about way, this observation provides the introduction to one of the central topics of this post …

The highlight of our vacation, if you’ll forgive the weak pun, was a journey to Europe’s highest railway station, Jungfrauhoch at an altitude of 3454 m (11,371 ft). It’s a stunning location, as many are in Switzerland, and we were fortunate to get only a little snow, low wind speeds, breaks in the cloud and temperatures not too far below 0°C. Just above Jungfrauhoch – accessible via a lift/elevator I’m glad to say – is the Sphinx Observatory (here) at 3571 m. Although not used in the classic ‘star-gazing’ sense, there are several international ecological/environmental research projects based there (here). These include spectroscopic solar observation as a means of probing the Earth’s atmosphere: in others words, looking carefully at what wavelengths light is ‘filtered out’ of the Sun’s rays as a means of identifying with precision the constituents of this high-altitude air. However, as a chronic asthmatic, and having the left-overs from a recent cold the worst symptoms of which had miraculously abated the day prior to our journey, one of my pre-occupations on the day was breathing. In true geeky style, this served to prompt a simple experiment to illustrate the effects of air pressure.

The Sphinx Observatory; the inset of yours truly not only helps to prove that I was there, but also serves to mask a few unsightly cables.

The experimental setup was simple: take an empty plastic water bottle and screw it tight shut at high altitude, then simply compare it with an otherwise identical bottle back at ‘base camp’ (aka our hotel room, which happened to be at a more modest 586 m altitude). The image below says it all. 

The bottle on the left provides the 586 m reference point, as it were, whilst the bottle on the right – sealed shut at Jungfrauhoch’s 3454 m, and therefore almost 3 km higher – has been partially crushed. The reason is straightforward. At the altitude of our hotel the air pressure was about 94480 Pa (Pascal: equivalent to about 945 mb, or 13.7 psi) but the bottle sealed at Jungfrauhoch started its journey with an air pressure of only 66154 Pa (about 9.6 psi, so only 70% of the lower altitude value). In other words, as the pressure outside the bottle started to increase as we were descending, it simply crushed the bottle, reducing its volume to the point at which outside and inside pressures were in balance again. And where does this ‘pressure’ come from? Well, from the collision of the air molecules with the bottle’s inner and outer surfaces: more collisions per second on the outside surface of the bottle than on the inner surface will result in a net force which will push the sides inwards. Why were there more collisions each second on the bottle’s outside surface as we descended? Simply because the air’s pressure is related to its density: higher pressure means higher density, which in turn means there are more molecules available to collide with the bottle. The density of the air at Jungfrauhoch was about 0.85 kg per cubic metre, but this had risen to about 1.1 kg/cubic metre by the time we had descended to the hotel.

I should add in passing that this effect had been noted by my children during a much earlier holiday, in 1998 in fact. This vacation included a stay in Yosemite National Park, within which the altitude varies between about 1200 and 1500 m. Their observation was, in a sense, the obverse of my simplistic experiment: they noted that an unopened bag of crisps (or potato chips in the local language) had inflated like a balloon. What they were seeing, of course, was the effect of higher pressure inside the bag than outside. The bag was sealed in a factory at low altitude, and was about to be consumed at higher altitude: there were more collisions each second between the air molecules and the inside surface of the bag than were occurring at its outer surface.

Ah, the joys of taking physics on vacation. There’s more from Switzerland however.

Part way through our holiday, in the depths of the night, I spotted what I initially thought might be Saturn, which I knew was supposed to be visible at the time. It was low in the sky and near the almost-full moon. The snapshot I took at the time is shown below. Just to be sure, I contacted a local amateur astronomy club via Twitter – so useful to have access to a ‘hive-mind’ on such occasions. I am grateful to @AshfordAstro and to @roger931 for letting me know that I had, in fact, been observing Mars that night. Either way, this is the sort of thing that can, for me at least, boost the spirits through any stretch of broken sleep. It also served to remind me that one of my plans for ‘retirement’ was to invest in a small telescope and to get back into the astronomy that inspired me so much as a young person. I must find the time to do that …

This was taken on our very modest compact camera, which was steadied using the window frame in our hotel room.

Climbing Over Failure

On Saturday 18th January I gave a talk at the monthly meeting my local Beacon Astronomy Group (here, or here). I was given a gentle brief a couple of months prior – as befits my very amateur status – by the co-organisers Dirk Froebrich and Tim Long: “Tells us about your journey into astrophotography”. It’s a brief that risks self-indulgence from the speaker; I’m sure I succumbed now and again, for which I apologise the those who came to listen, as well as to those who watch Tim’s recording of the talk. The questions, after I’d stopped talking, came thick and fast. I hope this was a good sign – at least people were listening. There were several more open-ended one-to-one conversations as I was packing up; these continued all the way to the car park. I spotted smartphones capturing the odd slide as well which, again hopefully, tells me that there were snippets of information folk found interesting or useful. All good. More than once I promised to complement the talk with a blog post containing the salient bits and pieces: this is it.

In truth, much of what I’ll include here has already been covered in earlier blog posts; I have been writing about aspects of my retirement hobby since the Summer of 2020. However, it’s probably easier all round to extract, condense and augment that material into one brief post than to expect you to follow a load of links and distil everything yourself. I’ll take you through the slides, including a few screen-captures, like the opening slide above, if that helps us navigate. As is customary, I began with an overview and tried to make the point that, although stargazing and photography have interested me since my early teens in the 1960s, it wasn’t until I retired that I could attempt to marry the two. Indeed, I didn’t add a dedicated camera to my first ‘proper’ telescope for almost a year after buying it; I had an enormous amount of fun simply looking through an eyepiece at the beauty above my head. That first telescope, bought a few months after I retired, reflected the advice to beginners I remembered from an episode of the BBC’s ‘Sky at Night’ programme (- which was broadcast in B&W until I was 17 years old!): it was a 150 mm (6") Newtonian, the Skywatcher 150PL. Had I tried harder to update my knowledge or, better still, talked to a few more experienced amateurs, I might have made a different selection. But, then again, perhaps I wouldn’t …

I know others have succeeded, but when I tried to capture images of what I was looking at using my smartphone, it wasn’t very satisfying.

At this point in the timeline I give huge credit to Dirk Froebrich for the opportunity to experience astronomical imaging at a professional level. Dirk, a colleague of mine before I retired, needed someone to look after the Beacon Observatory during the periods he was away over one particular summer. This was a time when his Citizen Science project ‘HOYS’ was in its infancy – there are many more volunteers and partners now. (This is a wonderful project and I heartily recommend it.) I was trained in the basics of running the observatory remotely from my PC at home and sat through quite a few clear nights following the observation script I had been given. I confess to being little more than a ‘trained monkey’ at that point, and I know I made more mistakes than I ought, but I did collect usable data which found its way into a full-blown research paper. I was hooked.

My first dedicated astro-camera was a simple ‘entry-level’ colour model, the Altair Astro 290c, and with it I managed to image all the planets other than Mercury (which I can only ever see through binoculars from an upstairs window due to surrounding trees, houses and so on). I could also image bright/easy-to-find individual stars and a few binary star systems. When trying to image the Moon or Sun (using homemade solar filters – take care!) the limitations of my little astrocam were immediately apparent: it enabled great images, but of only a small portion of these larger targets.

The field of view, FoV, from my reflector telescope and astrocam combination is indicated by the yellow rectangles shown in this smartphone-captured image of the Plough (part of the constellation Ursa Major). This was adequate for binary stars and planets but less so for the Moon and Sun and far too restricted for larger targets such as nebulæ and nearby galaxies: the Andromeda galaxy, for example, covers five times as much of the sky as the Moon (- although it’s so faint that we don’t see it sitting beyond the foreground stars of our own galaxy, the Milky Way). 'FL' in the light blue insert above refers to Focal Length by the way.

Even relatively simple astrocams (or DSLR cameras) need specialist kit and software if one is to gather imaging data successfully. The tripod and mount on which the telescope sits must be able to compensate for the Earth’s rotation: to keep pace with the stars as there appear to move across the sky and thereby to keep the chosen target in your system’s field of view. A key first step is to be able to polar align the mount, which means aligning it to the celestial pole – near to Polaris. I mostly use a Skywatcher HEQ5 mount. Beyond that, software is needed to run the camera and thereafter to process the exposures collected.

For pre-planning and target identification I use Stellarium and Carte du Ciel on my PC, along with useful tools such as those found here, here and here. Useful phone apps include SkyMap, Lunar Map HD and Stellarium along with your favourite weather apps (I use the UK Met Office app alongside ‘Weather & Radar’). For capturing data from my astrocam I use Sharpcap and in order to process that data through to a final image I’ll typically use packages like Autostakkert, Registax, Photoshop / Affinity Photo2 and PIPP. A quick online search will lead you all of these. There are a great many ‘tutorials’ on YouTube, enough of which are sufficiently useful to get you started; better still, join your local amateur astronomy club and tap into the expertise of more experienced people. I’m a member of two that meet in my part of the country, and although I can no longer attend meetings in person I can nevertheless ask questions – and sometimes answer them – via social media, typically Facebook.

There’s one important aspect of all this I’ve yet to mention: the need to mitigate the effects of atmospheric turbulence. The higher the magnification, the more your target will appear to ‘wobble’ as it’s distorted by changes in the atmosphere; it’s the same issue that leads us to talk about the twinkling of stars. The way forward is to use a statistical approach: a method referred to as ‘lucky imaging’. We collect many individual exposures (hundreds, often thousands, using Sharpcap in my case) pick only the best, perhaps the best 10-20%, and then stack them (integrate them in essence; this is where Autostakkert comes in) to generate a decent image. This may be sharpened, colour-balanced or even colour-enhanced, labelled and so on using packages such as Registax and AffinityPhoto.

So far, so good. We still have the issue of a narrow field of view, FoV, and the matter of locating those fainter objects like galaxies and nebulæ that we can’t actually see.

I solved my immediate FoV problem by buying a telescope having a shorter focal length (Altair Astro 80EDR to complement the Newtonian) and an astrocam with a significantly larger detector chip (Altair Astro 533c). With an optical add-on called a reducing lens, this enabled me to increase my FoV to a whopping 1.46 x 1.46°. Whilst a huge improvement, this still represents about as much of the heavens as you can cover with your thumbnail held out at arm’s length: there’s a lot to see up there!

So-called GoTo mounts help circumvent the issue of navigating to faint objects, although I confess to having only modest success using the default control pad that comes with them – especially when limited to my original narrow FoV. I now rely on using Carte du Ciel, which controls my Skywatcher HEQ5 telescope mount from my laptop via ASCOM-EQMOD software … and a game-changing process called plate-solving. The beauty of plate-solving is that the various software packages offering it can use an image of whatever patch of sky you’re pointing at and employ the pattern of the stars present to identify exactly where you are. Integrate that utility within a program like Sharpcap (or APT, or …) and it becomes straightforward to designate a target within Carte du Ciel, which will slew the telescope to somewhere in its close vicinity, then use the plate-solving utility in Sharpcap to refine your targeting.

Having navigated to our target object, with a properly polar-aligned telescope+astrocam combination offering a suitable field of view, we can begin taking the longer exposures necessary for fainter objects. Depending on the mount’s alignment and the quality of its tracking motion one might expect to achieve exposure times of the order of ten seconds or so. It’s still necessary to collect many frames and then to stack them, although the software for this is somewhat different to that typically used in the context of ‘lucky imaging’. I use Deep Sky Stacker, DSS, for this. The image above, unfortunately in monochrome rather than colour due to an error on my part, is derived from 132 4s exposures. In addition, calibration files now become desirable in order to avoid problems with electronic camera noise, bits of dust in the optics etc. – these may become noticeable for longer exposures. Atmospheric turbulence is still present of course, but with exposures very much longer than those typically used for solar system ‘lucky’ imaging, we have by default averaged these distortions. (Thus, light from stars will appear to be spread across several pixels.)

The next important step is to increase exposure times from seconds to minutes. Even with excellent polar alignment and a good tracking mount this isn’t practicable without the use of guiding. In essence, one fits a small secondary telescope, the guidescope, to the main one such that it’s pointing in the same direction. A more modest camera is fitted to the guidescope (ideally monochrome, but that’s not essential) and this is connected to the laptop and to the tracking mount. Using a piece of software called PHD2, which apparently stands for ‘push here dummy’ v.2, our guidescope and camera may be set up to lock onto the positions of a number of the stars in its field of view – meaning that the tracking mount’s position can be corrected in real-time. In theory, and mostly in practice, this means that we’re now safe to use exposures running to hundreds of seconds.

In the screenshot above you’ll notice the circled stars that are being used; there’s a ‘target’ on the right illustrating the scatter in position around the designated centre – it’s calibrated is seconds of arc (one arcsecond is a sixtieth of an arcminute, which itself is a sixtieth of a degree). The interesting bit is the plot at the bottom: this shows the error in Right Ascension (RA, East-West) and Declination (Dec, horizon-pole; see here) – and the corrective pulses sent to the RA and Dec motors in the tracking mount to bring it back to the axis. 

The end result, after lots of image processing which I’m not going to write about here, is an image like this …

My penultimate slide sums it all up:

Whatever else you do, please continue to treat yourself by looking upwards on those beautiful clear nights whenever they come along.