J. Brit. Astron. Assoc., 108, 5, 1998, p.292-294
J. Brit. Astron. Assoc., 108, 5, 1998, p.292-294
(Note: The Association is not responsible for individual opinions expressed in articles, reviews, letters or reports of any kind.)
From Mr B. G. W. Manning
There is an apparently anomalous effect with diffraction gratings whereby one can view the solar Fraunhofer lines at quite high definition by simply holding the grating at a near-grazing incidence to the Sun's rays. This point was raised by Maurice Gavin in his Presidential Address,[1] but with reference to using a CD-ROM as a grating, which he suggested might have a focusing effect due to the curved tracks. Since then, he has noticed that the effect is much better with a parallel ruled grating and contacted me for an explanation. It so happens that I first observed this effect about 40 years ago when engrossed in actually ruling optical diffraction gratings and arrived at an explanation as outlined below, which I think is correct, but have never seen confirmed in print.
As everyone knows the Fraunhofer lines seen in a spectroscope are images of the slit and without a slit a continuous spectrum is formed; in effect due to the overlapping of a multitude of slits. This can be looked at in another way. A plane wavefront from a narrow slit incident at 0° to a diffraction grating, will of course encounter all the lines or grooves simultaneously (diagram A) and the diffracted wavefronts in different orders can be constructed as shown. If the slit is widened, wavefronts from different parts of the slit will be inclined (diagram B). There will be a path difference to each successive line where there was none before, and the new wavefronts for the different orders will be in new directions. The result is a fuzzy image as with a lens or mirror with wavefront errors. In the case of light from the Sun with a range of incidence angles up to ½°, there is total confusion.
In diagram C, which is the case we are interested in, with the Sun on the left, the light from one limb of the Sun is at grazing incidence i.e. 90°. The beam from the other limb would be at 89°.5, but is much exaggerated in the diagram. Even so it can be seen that the path of the two beams is of very similar length, hence wavefronts even from the two limbs will only have small phase differences for quite large lengths of grating, and the diffracted wavelets from both limbs can form a common wavefront and produce a clear image when focused by the lens of the eye.
There is actually a steady progression from normal to grazing incidence, the path difference being [sin(I1) - sin(I2)]L where I1 and I2 are the greater and lesser angles of incidence respectively, and L is the operative length of the grating. Working directly in Ångstrom units (10-10 metre), the line spacing of a 600 line per mm grating is 16667Å. For I1=0°.5, I2=0°, we have 0.0087265 × 16667 = 145.445Å per line. With eye pupil 3mm = 1800 lines this is 261801Å; in the green at 5500Å this equals 47.6 wavelengths path difference. For I1=85°.5, I2=85°, the path difference is 3.94 wavelengths, and even though a little blurred the Sodium D lines are still clearly visible in the third order. For I1=90°, I2=89°.5, the path difference is 0.207 wavelengths. This is better than Rayleigh's limit and good resolution is still obtained using a small telescope or binocular of 10 to 15mm aperture to view the spectrum even though the path difference is then over two wavelengths. In the third order two lines between D1 and D2 are visible and the Mg triplet is very clear.
Using the standard grating equation ±nl= (sina + sinb), with a=85° the third order wavelength visible at b=0° would be 5534.5 Å. With a=85°.5 the wavelength is 5538.54. From [(sin85-sin85.5) × 16667]/206265, the angle between the two is 2.48', not too much different from the resolution of the eye. Alternatively as pointed out by Mr Eades, it is the same as viewing two lines 0.18mm (0.007 inches) apart at 250mm (10 inches) distance. These figures really represent the situation for two separate sources separated by an angle of ½°. In fact, the position is better than this as a more complete calculation is required to account for the effect of the differing intensities and path differences from the whole of the disk.
The method is of limited practical use because the photometric efficiency is very low. It is handy however for demonstrating a solar spectrum without having to carry a spectroscope. A cheap replica transmission grating could be used. As a matter of interest the same effect can be seen with a prism, although not nearly so well, but is not advised. I have tried it with a dense flint 60° prism and could detect the merged D lines and and a couple in the green and blue, also I think one of the calcium lines, this probably because the spectrum was so bright. In fact a word of WARNING for anyone who tries it: due to the small dispersion of a prism the light could be nearly as bright as looking directly at the Sun, and even at grazing incidence and a low sun, I had an unpleasant after image for quite a time. Finally, Maurice Gavin has drawn my attention to a reference in The Observers Guide to Astronomy vol. 2,[2] chapter 18, 'Spectroscopy' by Oliver Saint-Pé. A formula for resolution is given with suggestions for photographic recording. I have not yet had time to follow this up.
Brian Manning
Moonrakers, Stakenbridge, Churchill, Kidderminster, Worcs. DY10 3LS
[1] Gavin M. V., 'Amateur Spectroscopy', J. Brit. Astron. Assoc., 108(3), 137 (1998)
[2] Martinez P. (ed.), The Observer's Guide to Astronomy, Vol. 2, Cambridge University Press, 1994
From Mr Michael Hendrie
I agree with John Vetterlein (Letters to the Editor, JBAA 1998 June) that aircraft condensation trails have been a problem for astronomers in many parts of the world for many years. While more noticeable during the day they are often present at night too. Near Colchester we are in the Clacton-on-Sea air traffic control sector which, I understand, is the busiest in the British Isles, covering as it does London Heathrow, Gatwick, Luton and Stansted flights to and from the Continent and further east, as well as other routes overflying the area. At night there are usually at least half a dozen bright aircraft lights visible at any one time, many the equal of Jupiter or even Venus. Ever increasing numbers of civil aircraft now cause serious interference with daytime observations, for example of the Sun.
Flights into Stansted, the nearest airport, are no problem by day even though they fly directly over the observatory as the aircraft are below the level at which contrails normally form, but high enough to make the sound unobtrusive. Most other routes pass to the south of us where they can be joined by aircraft coming up from the south. These are at a height where, given the right conditions, condensation trails form readily and may persist for hours, gradually spreading and merging to form an amorphous mass of high cloud. A beautiful bright blue morning sky can be turned into a game of noughts and crosses in under an hour. The picture (which Turner might have called 'A winter sunrise with contrails') is one of many I have taken in the past few years and is by no means an extreme example, though in fairness there is probably some thin natural cloud present also.
Light pollution has largely destroyed our visual and photographic view of the night sky and aircraft condensation trails are now destroying the daytime sky. One might have thought that light pollution would have been the greater problem, but electronic detection and processing methods have helped to mitigate the worst effects. I wonder what are the chances of a development to nullify the obscuring and sometimes turbulent effects of aircraft condensation trails on astronomical observation? These may yet turn out to be the more serious problem. It seems strange to me that while we are being urged to leave the car at home and turn down the central heating in order to save the world, the growth in cheap air travel and all that comes with it is accepted as inevitable and above serious challenge or discussion.
M. J. Hendrie
'Overbury', 33 Lexden Road, West Bergholt, Colchester, Essex CO6 3BX
From Mr Pieter Morpurgo
As producer of the BBC TV The Sky at Night programme, I am due to retire at the end of this month. The programme itself with - of course - Patrick Moore is due to run for maybe even another forty-one years.
May I through the pages of your journal thank all of those in the astronomical community with whom I have worked over the past most pleasurable eighteen years on The Sky at Night. There are far too many people to write to individually, as we have had help, advice and suggestions from observatories both amateur and professional, universities, and scientific establishments throughout not just Britain but across the world. We have been welcomed everywhere with the greatest friendship and warmth, and encouragement to continue our efforts to bring the fascinating world of astronomy to the public. But we could not continue to achieve that without the help of the astronomical community. I am sure that you will help my successor, Ian Russell, in the same way.
Thank you all so much. Working with you all has been a very great pleasure. In fact, as many of you will have heard me say, 'It's been better than working for a living'.
Pieter Morpurgo
Producer, The Sky at Night, 1981-1998
BBC, White City, 201 Wood Lane, London W12 7TS
From Mr Gerald North
In his excellent paper on spectroscopy for the amateur,[1] Maurice Gavin gives the first edition of my book Advanced Amateur Astronomy as a reference. Readers will be frustrated if they attempt to seek this edition as it is now out of print. However, there is a new edition, published by Cambridge University Press in 1997. It has been reviewed in a recent Journal. In this new edition I have expanded the chapter on spectroscopy (Chapter 15 in the new edition) to include details of the spectrograph that I built onto my own telescope. It was easy and cheap to make and I show how readers can design and build such a unit for themselves based on the underlying principles discussed in the chapter.
I very much wish to echo the call Maurice Gavin makes for more amateur involvement in spectroscopy - great things may ensue as a result.
Gerald North
9, Camperdown Street, Sidley, Bexhill-on-sea, East Sussex, TN39 5BE
[1] Gavin M., J. Brit. Astron. Assoc., 108(3), 137 (1998)
From M. Jean Meeus
Inspired by the letter of Mr Peter Macdonald in the 1998 June Journal (108(3), p. 136), I calculated for some places the number of solar eclipses visible between 1901 and 2200. My results are as follows:
London 126 107 Moscow 116 98 New York 100 89 Tokyo 106 93 Johannesburg 121 95 Sydney 121 101 Montevideo 111 95 North Pole 128 128 South Pole 120 120
For each place, the first number is that of all solar eclipses of which at least a part takes place above the horizon. The second number is that of the eclipses for which the maximum occurs above the horizon. Of course, almost all the eclipses are partial at the given place. In some cases, the eclipse is practically unobservable. This was the case for the eclipse of 1944 January 25, where at London first contact occurred only seven minutes before sunset. Nevertheless, for completeness such odd cases are included in the totals. In other cases, while the eclipse is wholly visible, its magnitude is very small. This was the case at the eclipse of 1983 December 4, when at London only 3 percent of the diameter of the solar disk was covered by the Moon.
For the North and South Poles, the two numbers are equal, which is not surprising. At these places, the Sun remains the whole day either below or above the horizon, except on two dates during the year. The rather larger number of eclipses visible at London is remarkable. Compare London and New York! Even if we consider the much longer period from A.D. 1001 to 3000, we find that London is still slightly favoured: 826 eclipses at London, 762 at New York.
From the above, it results that at a given place the number of visible solar eclipses is about 38 per century, of which 32 have their maximum phase above the horizon. Their distribution over time is irregular, however. For instance, while two solar eclipses were visible at London in 1982, there was a ten-year gap without any eclipse from 1984 to 1994.
Jean Meeus
Heuvestraat 31, B-3071 Erps-Kwerps, Belgium
From Mr Martin Ratcliffe
In the course of some research I was doing for an article about Pluto, I needed the date for the moment Pluto returns to being the ninth planet in order of distance from the Sun. Since 1979, Pluto has been closer to the Sun than Neptune, a situation caused by its highly eccentric orbit. Pluto is due to return to its position as the ninth planet sometime during 1999.
The JPL Space Calendar[1] on the Web page of the Jet Propulsion Laboratory (JPL) indicated the event would take place on 1999 February 10. However, a further reference I often use is Guy Ottewell's Astronomical Calendar.[2] In his 1998 edition, he indicates that the event occurs on 1999 January 14. To make matters even murkier, Michael Seed's college text, Horizons: Exploring the Universe[3] gives yet another date, 1999 March 14.
This spurred me to do my own research, so armed with access to JPL's Ephemeris Generator, I compiled a daily ephemeris for Neptune and Pluto. This ephemeris generates the heliocentric distance for each planet. What I discovered was that all three dates were in fact wrong. The date that Pluto becomes farther from the Sun than Neptune is 1999 February 11. Not satisfied with that result, I went one step further and generated an ephemeris for every 10 minutes around that date, and plotted the results. The graph shows clearly that Pluto becomes the ninth planet again at 14:20 Universal Time (± 5 minutes) on 1999 February 11.
I hope this information will be useful and avoid future confusion.
Martin Ratcliffe
Director of Theaters and Media Services, The Exploration Place, 711 W Douglas Ave, Suite 101, Wichita, KS 67213, USA [martinr@southwind.net]
[1] http://newproducts.jpl.nasa.gov/calendar
[2] Ottewell G., Astronomical Calendar 1998, Universal Workshop
[3] Seeds, Michael A., Horizons: Exploring the Universe, Wadsworth Publishing Co., 1998
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