This month’s imaging object is a single star shot – this time I’ve gone for Regulus in Leo.  A nice bright star central to an image can make a spectacular picture, and Regulus is no exception.  Taken using the Sky 90 and M25C with 4-minute subs and a couple of hours total exposure time, this is the sort of result you can expect.  However – what I didn’t expect was to see a trace of the dwarf galaxy Leo 1, which looks like a tiny wisp of a cloud right next door to Regulus!  This was pretty much unexpected and I believe it is due to the superb contrast provided by the Sky 90 – I can guarantee that I wouldn’t be able to see Leo 1 in a similar Hyperstar III image.  It would be interesting to know whether you can pick up Leo 1 using reflectors and CCD cameras with Regulus providing it’s own unique form of  ”light pollution” in this region.

Recipe for a Regulus/Leo 1 image – good dark (Moonless) night, high contrast imager (refractor), moderate length subs, but lots of them – and possibly some good luck

Until April’s IOM – clear skies!

I still find it very strange that this large, bright reflection nebula does not have a “popular” name.  To me it look like a cauldron of boiling liquid oxygen, so I shall call it “the Cauldron”.  M78 is a beautiful reflection nebula in Orion, and you can see from the accompanying image that it lies very close to Barnard’s Loop.  As you will know, Barnard’s Loop is faint, so to get this showing up in the image it is a good idea to collect some narrowband H-alpha data.  The reflection nebula although appearing to be narrowband blue is in fact broadband blue (due to scattering of a broad band of short wavelengths of light) – so M78 doe not benefit from narrowband filters.  However, you can see that the whole area is also permeated by dark dust clouds, and to get these showing up at all in your image you need lots of exposure time and long subs.  This image is a composite of H-alpha data taken with the Sky90/M25C, RGB data of M78 alone taken with the original Hyperstar and SXV-H9C, and finally the main part of the template is Hyperstar III RGB data with its 2.41 x 1.6 degree field of view.  You can see that by framing the subject (M78) off to the right of the FOV you can bring in the edge of Barnard’s Loop over to the left which makes for a more interesting image.

Usual formula for a nice picture – lots of subs – long exposure time for each sub – and add some good deep H-alpha data to capture the faint Barnard’s Loop.  At least we still have long nights to do this stuff, soon the clocks will go forward and it will be back to no imaging before 9:00 p.m.

Clear skies until our March edition of IOM.

O.K. so this is getting quite a ways off deep-sky imaging, but I just clicked on a site that I thought was going to tell me about ultra-black materials and I was instead treated to a monologue of how the United States has already reverse-engineered alien technology (alien being defined as some entity from another world in this instance) for its own use.  This instantly reminded me of a hilarious incident on the TV some 15 or 20 years ago.

I was watching a programme on the same subject, basically how alien technology was being utilised by the United States government – and part of this programme was a live link to the States and a discussion with a well known Professor who was supporting the “alien technology” thesis.  He was there telling us how the strange craft coming out of Area 51 were the direct result of reverse-engineering crashed extra-terrestrial vehicles when……… suddenly…….. we lost the TV link.  Now call me a sceptic, but I have a real problem understanding how a country that has already reverse-engineered flying saucers for its own military use can possibly have trouble maintaining a video link for a few minutes.  Or maybe the break in communications was from our side

I have asked some friends to put up the Golden Solid angle on their sites to try and find where this might occur in Nature.  Some people in trying to help with a reply have gone astray with both the mathematics involved (which aren’t that complex) and the concept.  So here I will try to explain a little more about the Golden Solid angle (and solid angles in general as this doesn’t seem to be a generally understood concept).

An ordinary (planar) angle is defined by considering a circle of radius r (make r=1 for simplicity).  Now consider a length of arc on the circumference of the circle of length L, this will subtend a planar angle at the centre of the circle defined as L/r = L radians.  Now the total circumference of a circle is 2 x Pi x r so that if again we have r=1, then the total angle about the central point of a circle is 2Pi radians.  2Pi radians is therefore equivalent to 360 degrees, Pi radians is equivalent to 180 degrees, and Pi/2 radians is a right angle.  So far so good I hope.

Now let’s move onto the slightly more involved concept of a SOLID angle.  This is no more difficult in reality to the planar angle, it’s just that we don’t use it much (if at all) in every day life.

The unit of solid angle is the STERADIAN and it is defined as follows.  Consider a sphere of radius r, and consider some area on the surface of the sphere of area A.  Then the solid angle subtended by the area A at the centre of the sphere is A/r x r steradians.  The total surface area of a sphere of radius r is 4 x Pi x r x r so by using our definition of solid angle we see that the total solid angle about a point is 4 x Pi x r x r / r x r or simply 4Pi steradians (this is precisely why 4Pi turns up in the permeability of free space – but that’s another story).

Solid angle in steradians (or in square degrees) is of importance to astronomers too as it gives an indication of the size of an object in the sky – but as solid angle isn’t generally understood this also means that the apparent size of objects in the sky is also not well-understood.  When astronomers say that the Sun and Moon subtend about half a degree – they are talking PLANAR degrees and that the Sun and Moon are about half a degree in (planar) diameter.  That’s fair enough, but to put things into perspective we should know what looking out into one hemisphere means in terms of steradians (or square degrees) as it is only by looking at the “sphere of space” above us in this way that we can get some measure of how BIG our total field of view is.  A hemisphere is 2Pi steradians and if we convert this to square degrees we can get some idea of how big the celestial sphere is for an observer with a telescope with a typical field of view of 1 square degree.

We can go back to our PLANAR definition of angle to work this one out.

Pi radians = 180 degrees, so

Pi x Pi steradians = 180 x 180 square degrees, so

4Pi steradians = whole celestial sphere = 4 x 32,400/Pi square degrees  = 41,252.96 square degrees, so

2Pi steradians = celestial hemisphere = 20,626.48 square degrees.

So our observer with a 1 square degree field of view would have a roughly 1 in 20,000 chance of randomly hitting a selected object – it gives an indication of how BIG it is up there!

As a corollary:  1 steradian = 3,282.81 square degrees or equivalently 1 square degree = 3E-4 steradians.

Returning back to the Golden Solid angle!

We now consider a sphere whose surface area has been divided into two, one of area unity and one of area phi (the golden ratio or 1.618…) and the unity surface area will subtend some solid angle, let’s call it gamma, at the centre of the sphere.  In exactly the same way we define the Golden Ratio on the line, or the Golden angle for the circle, we can come up with an equation for the Golden Solid angle for the sphere:

(4Pi – gamma)/gamma = 4Pi/(4Pi – gamma) which is a quadratic in gamma which can be solved in the usual way to give:

gamma = 1.52786Pi steradians or 15757.2 square degrees.  If you (for whatever reason) wanted to take a slice through the sphere to see what PLANAR angle this solid angle corresponded to  you would get an angle of  152.7 degrees – though I’m not sure what use this information is except that it is NOT the same as the Golden planar angle of 137.5 degrees.

For completeness:  The solid angle corresponding to the Golden angle of 137.5 degrees is 1.275Pi steradians.

So I return to my original question – anyone seen the Golden Solid angle anywhere in Nature???

First of all Happy New Year to you all!  I won’t say let’s hope for better imaging weather this coming year as so far it hasn’t been anything to write home about.  Moving on.  This month’s Imaging Object of the Month is the beautiful Jellyfish nebula in Gemini.  This is a very difficult time of the year for imagers as there is so much up there in a good imaging position right now, including all the stuff in Auriga and of course Orion and Monoceros.  IC443 is pretty faint and does well with the addition of narrowband data to the RGB, especially H-alpha and S-II.  IC443 is also BIG – you can see from the accompanying image that the rather large FOV of the Sky 90/M25C combination (2.22 x 3.33 degrees) is just about perfect for the region.

This image took a LOT of work.  This is 3 hours of RGB, 9 hours and 40-minutes of H-alpha, and 3 hours and 40-minutes of  SII giving a total exposure time of 16 hours and 20-minutes – and it could have easily done with the same again!!  So the message is, lots of time, add narrowband – and perhaps make this your winter mega-project if you can manage to keep away from Orion

Clear skies until February!

I opened up the pinhole cameras a couple of days early just in case they were set in the wrong position, and also to check if the wettest November on record had made its mark.  One pinhole camera unfortunately DID let in some water (not surprising really) – but the other pinhole camera was bone dry (and that was surprising!).  The view is towards the south, so the pinhole camera is imaging the Sun’s path across my southern horizon.  Breaks in the path are due to cloud – and you can see there are quite a few days where we didn’t see the Sun at all.

I spent quite some time trying to work out what that object is at the middle/bottom.  Shows you how slow I am – that is my fibreglass (observatory) dome!  The bright bits are the hinges/locks on the door.

Well – not a resounding success, but also not too bad for a first try.  I will attempt to do better next time.

On Sunday 20th December 2009 I will open up the two pinhole cameras on my south-facing wall, remove the exposed film, and replace with two new sheets of film.  I will then leave the cameras open from 21st December 2009 until 21st June 2010 – that is from the winter Solstice until the summer Solstice.  So this coming Sunday we will see if the pinhole camera project has been a success – or not!

There’s plenty of clouds at the moment but I’m hoping for just a few gaps in the cloud tonight.  No Moon – and it should be the peak in the Geminid meteor shower (13th – 14th December 2009).  Went out for a bit of practice last night with the 40D piggy-backed on the C11 – just as well really as every picture was out of focus!  I know how to sort that particular problem out tonight – if it decides to clear.  Rather than squinting at the little dim LCD on the back of the 40D I shall hook up the laptop in “Remote Shooting” mode and use the Remote Liveview plus the magnifier to carefully focus (also through the laptop so no fumbly paws trying to do the job) the 40D.  When satisfied with the focus flick the switch from autofocus to manual (so things don’t change) and trigger the remote timer to take the frames.  It’s as much of a pallava as doing “real” deep-sky imaging with the main scope.  Please let’s have at least a couple of clear hours and plenty of meteors tonight – pretty please

Well as the weather is not allowing me to take outer-space images, it’s back to some inner space work again.  This time an opalescent beetle leg gets photomicrographed using a 23-frame focus stack put together using the Helicon Focus software.  SEM-like depth of field, but in full colour!

The Golden Ratio (and the closely associated Fibonacci series) makes many appearances in the “living world” – here’s my question – not including Mathematics and man-made objects, does the Golden Ratio appear naturally in any inorganic systems?  There is a link between quasicrystals and the Golden Ratio, but I’m looking for a more direct link than these.  Once again, does anyone out there know of a clear example of the Golden Ratio making an appearance in a non-organic system?  If you do – please let me know ASAP