Nik271

Seems hard to find. It's mentioned in this memorial article about Struve in the Astronomical register from 1865 https://articles.adsabs.harvard.edu/full/1865AReg....3...89. specifically on page 94: Sadly I can't find any reference to a publication. The Bodlean library in Oxford does not have a publication by Struve from 1820, just checked their catalogue. Perhaps you can try asking someone at the library of the former university of Dorpat , now Universtiy of Tartu in Estonia. Surely they must have a lot of Struve's writings. Good luck!

I believe Struve published his first catalogue in 1820 with just 720 double stars, it's probably what he refers to in the last column.

If it's any help I recently carried Celestron 15x70 bins in my hand luggage on Wizzair from Luton. No problem at all.

All things being equal the weight increases proportionaly to the cube of the linear increase, so 20% extra in aperture gives (1.2)^3=1.728 so about 73% heavier.

I guess the meaning of consistent here is 'regular and not random'. Admittedly not clear how to define something which is 'not random' in a deterministic universe. Perhaps not random' should be taken to mean predictable by some rule that we can study, e.g a set of input data and an algorithm deciding when the event occurs. Anyway this is just my best guess.

Indeed at the time 1930s there was a lot of research into measures motivated both internally within maths and by the need of applications to physics. Dirac's function is an example of a point measure and such measures (=probability distributions) arose from the need of quantum mechanics where the usual notion of eigenvalues of matrices is no longer sufficient. Instead one gets a probability distribution on the real line which is the 'spectrum' of a linear operator. In this way maths and theoretical physics developed together. I always thought that the main mathematical ideas were created first, in the 1900 by Hilbert, Lebesque and others but I may be wrong. It's probably hard to tell now who was influenced by who.

Actually I was trying to say that there is not even one maths, what we have is a consensus maths based on a list of axioms that common sense tells us reflect the real world. But a different universe may require different maths i.e. very different axioms. For example one can describe the real numbers as a purely mathematical object with some axioms. A universe without real numbers will be something totally unimaginable to us, but still there will be some list of true statements about it some of which can be deduced from others by logical deduction. I would call this list the maths of that universe. So to return to our universe, we do have the current maths which we believe reflects the universe really well. But how well is really well? As we get closer to understanding some singularity point, say a black hole or the origin of the univese itself our maths may turn out to be insufficient. We can fix it by adding some more axioms according to what we discover further about the universe. So even the axioms of maths can evolve! I admit this has not happened yet in the real world, at least I don't know an instance where real applications have required rewrting of mathematical axioms. But it could happen. This is actually the same issue as the philosophical question, is maths created by us or imposed on us by the universe.

When we propose to disregard some mathematical statements the truth of which we agree not to investigate then we face the question which are the mathematical statements which actually have 'interpretation' or meaning in the real universe? It gets a bit philosophical from here on. Ags points out the transcendental numbers, they are of a lot of interest to mathematicians but somewhat hard to find use in the 'real world' For example it has long been known (= proved) that e and pi are both irrational and even transcendental. It's still an open question if e+ pi is irrational. I'm sure a big prize awaits those who find the answer to this question. But is this of any use in the real world? Hard to see now, but who knows I think we can agree that the arithmetic of natural numbers is important, for example positive integers govern the energy levels of electrons in shell in the Bohr model of the atom and thus are key to understanding chemisty. The pereidic table is a consequence of some simple relations concerning integers. Some irrational numbers appear often in nature for example in the golden ratio, pi and e. I think we can agree these are also important. Suppose we have some very complicated logical statement about real numbers that we can neither prove nor disprove. Does this tell us something about universe? Godel and some later work by more people tells us the following: there is some polynomial P(x,y,z,..) with integer coefficents in several variables ( I think 13 variables is enough) such that we are not able to prove or disprove if the equation P=0 has integer soluton x,y,z,... or not. So is there some physical interpretation of this polynomial and its zeroes? I have no idea.

Godel's proofs use only the natural numbers to prove both of his theorems. So any theory which includes the familiar properies of natural numbers (addition, multiplication and induction, the so-called Peano axioms) will be incomplete as well. There is the question what is allowed to be called 'a proof'. Godel's theorems and most of maths is concerned with finite proofs, that is a finite series of logical deductions starting from the axioms. If you allow infinite proofs then a lot of these obstacles disappear.

Once we dig deep down into the foundations of maths there are lots of surpsises: There is no proof that the maths we all use: arithmetic is consistent. This was discovered by Godel in 1930s and is known as Godel's second incompleteness theorem. 'Consistent' here means non-contradictory: there is no statement P such that both the validity and the falseness of P is provable from the standard set of math axioms. The first Godel theorem is actually even more depressing: mathematics as we know it is incomplete, that is there always will be a statement X such that neither 'X is true' can be proved nor 'X is false' can be proved. So what can do when we encounter such a statement? We can make a choice and add either 'X is true' or 'X is false' to our axioms of maths and go on. Buth then there will be another statement call it Y such that we can neither prove no disprove the validity of Y and we will face the same dilemma and so on. This created a big storm within maths at that time because until then many people believed that everything in maths is in principle provable from a fixed set of axioms. Hilbert in particular famously said 'We shall know.' He was wrong. In this sense maths will never be completely satisfatory model of the universe. Godel and Einstein became good friends in Princeton, I think I can see why.

Its all a part of the ineffable plan 🙂

Thanks for the suggestion, Ed! I saw Barnard's star several years ago with a Skymax 127, but forgot it's nearby. I'll give it a try next clear night with the 70mm refractor. It's fun to revisit same targets with different telescopes, for a different perspective.

I don't know how I've missed this one. It's a gem, two very unequal yellow-orange stars 6'' apart. I recently bought a 70mm F6 Svbony refractor which I mainly use for solar observation and I keep ready on a tripod in case there is a break in the clouds. It's a perfectly good performer in the night as well, on days when the forecast is iffy and I haven't put up a 'proper' scope. It has very little CA and gives sharp views on the Moon up to about x100. Last evening was supposed to be cloudy but at 9:40pm the sky was clear! I focused on the setting Moon and started looking at the usual suspects which I can find in twilight. Izar and the double double are near the limit of this small scope with a 4mm Nirvana (x105) , but the seeing was good and I could resolve them with careful observation. Once it got a bit darker I began to spot brighter stars in the south sky: Rasalgethi, Rasalhague, Calabrai, and I remembered a double star I read about recently: 70 Ophiuci. It's a close neighbour of ours, a pair of K-type stars just 16 light years away. I started from Calabrai with a 20mm EP giving a 3 degree field of view, no need of a finderscope. 70 Ophiuci is 5 degrees east from Calabrai among a bunch of other 4-th magnitude stars. At magnification x21 it looked like a single orange star. When I put in the 8mm BST for x53 it resolved into a pair of very unequal orange stars, the dimmer 6-th magnitude one being east from the primary. For this nearby system you can apparently observe orbital motion in a few years, the orbital period is 88 years. William Herschel who discovered it took note of the movement and argued correctly that it is the two stars orbiting each other, thus verifying Newton's law beyond our solar system. There were many conjectural companions and even planets claimed for this system over the years (Herschel himself suspected another companion) but nothing definite has been found so far. Currently the pair are as far apart as they get, at 6.7''. They will start to close in and by 2076 they will be a serious challenge at 2'' apart. Not likely I will be there to worry about it 😉

I'm a bit surprised that your 130mm Dob is not showing decent views of the planets. Jupiter can be tough due to the low contrast of its belts but Saturn is an easy target, at x100 -x150 magnification and 130mm aperture you should be able to see a lot of detail. If 5 inch Dob is not working for you, try the 5 inch Mak Cass as suggested already. My 127 Skymax shows tons of detail on the planets and in good seeing I can push it to x250 magnification with no problem. It's small, compact so does not need a beefy mount, you can even put it on a manual alt az, though the GTi is the recommended package.

I believe it is the thick corrector plate of the Mak which blocks a lot of the UV. Reflectors are better suited, as glass naturally blocks much of the near UV.

I decided to grab some images of the current big sunspot 3363. Skymax 127, Baader solar filter, Canon 250D full disc single frame, AR 3363 detail stacked in AS!2

It was pure luck for me, I had almost stopped trying. The Thames is 1km away to the south and I've noticed there is some local air movement when the weather is still. Usually it brings mist in winter but also in the summer cool air moves in and disturbs the seeing. I'm so glad I gave it a go yesterday.

This one is very beautiful, as if from orbit, well done, Kon! Yesterday evening was very lucky indeed, there were moments of great seeing. I had a look at Venus at about 8pm and it was still quite steady. Visually I didn't see clouds but the horns did seem brighter than the rest of the crescent. Later at 10pm I got another lucky seeing spell with Antares. The strange thing was the seeing deteriorated rapidly after that in the space of just 10 minutes. Carpe diem as they say...

Last evening I managed to split Antares for the first time! I didn't have high expectations, since I had tried numerous times over the past 5 years without success. Last evening it was a clear warm and still, at 10pm there are not that many targets available, so I thought - let's try it again. Antares rises only 11 degrees above the horizon for me and I have just a 45 minutes window of observation from our house while it moves between two big trees on the other side of the road. As I said I didn't have high hopes so I just brought the simple AZ5 mount on a surveyor tripod and set up the tube 20 minutes early to cool. Ar 10pm I had trouble spotting Antares with naked eyes, but the finder showed it just clearing the first tree. I focused with a 20mm EP giving x75 and it was noticeable that the orange star was very steady. Encouraged I decided 'to go all in' and went back inside and fetched my 6mm EP which gives x250 in the Skymax, about its maximal magnification. At other times Antares was just a dancing orange blob but this evening I was treated to a reasonably well defined diffraction pattern, with occasional shimmer around the first diffraction ring. And just outside it was a tiny green spark showng intermittently! Wow, I could not belive my eyes! I stayed at the scope for 10 minutes and the secondary kept appearing and disappearing but always in the same position west of the orange primary. It was 10:20pm, still quite light. I went inside the house to bring my partner but when we tried again just 10 munutes later the seeing had deteriorated and Antares was back to a blob. Having seen it, I believe that this double is not that hard from a more southern lattitude. The separation is similar to Delta Cyg with a bit more of magnitude difference, I think its perfectly doable in good seeing with any quality scope of 100mm aperture. From the UK the single most important factor is the seeing at this low elevation. 11 degrees is just brutal. So keep trying, you never know when the seeing will cooperate! Clear skies, Nik

Since you already have the Esprit, why don't you try some white light imaging first? Solar imaging is very different from DSO, aperture of course determines maximal theoretical resolution but the seeing is actualy the biggest factor, generally seeing is worse during the day than in the night because of thermals from the ground. A Baader whitelight filter on the front of your scope will cost very little to get started. Once you know how the seeing conditions are in your location you can decide whether a full disc Ha scope or a Quark with ERF for your Esprit for close up images suit you better.

Some good targets for a Mak in twilight: Venus (for the next few weeks), the Moon, a few famous double stars (can be seen when Sun is 6 degrees below horizon or more): Mizar, Albireo, Izar, the double double in Lyra, Rasalgethi. If you get up early you can also catch Saturn about an hour before sunrise. Saturn and Jupiter will get even better at the end of the summer.

Thanks, @Stu1smartcookie, I hope you reclaim your western sky back from the dust! Just to clarify this is not my picture but a simulation from https://svs.gsfc.nasa.gov/5048, very handy for planning moon observations.

The 3 days old Moon looks great tonight, just high enough to be still above the treeline for me at 10pm. The elusive Vallis Snellius is showing rather well as a sequence of indentations in a straight line going between the craters Snellius and Stevinus.

I use a manual EQ mount so the sidereal west is always the direction of drift and with a diagonal view north is 90 degrees clockwise from west. I should have clarified that I just refer to the sidereal directions, not the Sun's own east/west, which due to the tilt of both Sun and Earth axes of rotation differs a lot from the sidereal during the year.

Just came back from a quick solar session between clouds. There are several large proms, I counted three big ones in the south and one flimsy detached one on the western limb that looks like its trying to fly away. Did not move much in 20 minutes, so it may hang on for some time.