J. Brit. Astron. Assoc., 110, 1, 2000, p.49-51

Letters

Cross-cultural astronomy

As an amateur astronomer, and member of the BAA, I am particularly interested in a cross-cultural exchange of astronomical knowledge and skills. Western research has boosted our knowledge about the stars and planets considerably during the last 75 years, and that certainly is an enormous achievement. But I would rather call attention to the astronomical knowledge and skills of non-western people e.g. the American Indians, Polynesians and African tribes. I am especially interested in East Africa, mainly because of one of my short stays among the Turkana people.

In the beginning of 1998 I was involved in a teaching task in the Diocese of Lodwar. As an associate member of the Brothers of Our Lady of the Sacred Heart, I was asked to participate in setting up a computer course at one of the few secondary schools in the town of Lodwar. The Turkana are a nomadic tribe living in the plains of north-western Kenya. During my leisure I enjoyed the sparkling starry nights. The semi-desert homeland of the Turkana offers fine dark skies. Everywhere on our globe people are overwhelmed by the dome of stars surrounding them during a clear night, and this is true for the Turkana also. I wondered what interpretations they might give to the various bright shining objects rising and setting during the course of one night? Would they give names to certain groupings of stars? What meaning would they give to the white band of light crossing the sky, that we know as the Milky Way? Do they perhaps use any of the stars for navigational purposes? (They never seem to get lost in this vast semi-desert region.) The appearance of the full Moon was specially welcomed as an additional source of light; bringing an evening of dancing and singing.

My experiences in Kenya have increased my passion for Africa, its cultures and people. An essential part of education is carried out in traditional Africa through oral transmission, so I want to look among tales for possible astronomy-related stories. Let me give an example of a well-known Maasai story called ‘The Orphan Boy’. At dawn the planet Venus occasionally appears in the east as a bright morning star. At nightfall it is sometimes visible as a prominent evening star in the west. The Maasai call this star Kileken, the orphan boy. This traditional story from Africa explains the reason why Kileken appears in the sky both in the morning and early evening. It is a story specially for young children. Collecting such stories could be a challenge, and an enriching experience for both the tribe and others. It might encourage them to save those stories for future generations to come, which is something I consider worthwhile. What about other tribes’ stories related to the appearance of heavenly bodies in the sky?

I would like to get in touch with members of the BAA, preferably East African by birth, and initiate a process of sharing astronomical knowledge with them. Other interested people are of course welcome to join in. I dream of setting up a simple observing site at a rural African location, enabling the local people’s knowledge of stars to meet western-oriented interpretations and concepts, using their cultural heritage as the vantage point, and thus creating an environment to initiate a process of learning from each other, respecting each others’ heritage, and offering the interested youngsters a possibility to deepen and widen their understanding of our surrounding cosmos.

This letter is intended to find out whether other similar initiatives exist. It is also an effort to allow a wider audience to take notice of my interest as depicted here. Deep down in my heart I hope to get in touch with fellow human beings who also like to foster such, or a similar form of cross-cultural astronomy.

Transient lunar phenomena

A recent article in the New Scientist magazine (1999 October 23) caught my attention with the title ‘Moon mystery emerges from the X-files’. While this headline has a distinct flavour of science fiction to it, the content of the report is really more ‘down to earth’ than the title suggests.

Transient lunar phenomena (TLP) have been reported by astronomers for many hundreds of years, but it is only relatively recently that spacecraft orbiting the Moon have been available to confirm whether particular events reported by users of earth-based telescopes may be more definitely linked to changes occurring on the actual lunar surface. TLP descriptions have included the temporary obscuration of certain lunar features, albedo variations, colouration, and also the occasional bright flash.

The United States Department of Defense spacecraft Clementine returned over two million images of the Moon during its two-month mapping mission in March and April of 1994. During the mission planning stage a group of amateur astronomers in the US (Association of Lunar and Planetary Observers – ALPO) presented a proposal to NASA to observe the Moon where possible following the orbit of Clementine in order to have a close-up view of any transient events that might occur. The proposal was accepted and ALPO were provided with the orbital ephemerides from which were computed times when specific sites would be in view of the spacecraft cameras. Several other groups of amateur astronomers took part in this project including BAA Lunar Section members.

The partnership proved successful and of thirteen possible transient events recorded by lunar observers,¹ Clementine imaging covered at least four. One reported TLP occurred on 1994 April 23: a possible obscuration lasting 40 minutes from 03.50 to 04.30 UT over the Cobra Head on the Aristarchus plateau. Although no images appear to have been taken by Clementine of the suspect area on 23 April, a team at JPL Pasadena subsequently analysing the data are reported² to have found that there was an approximately 15% increase in colour ratio (0.4 to 1.0 microns) in images of the Cobra Head taken on 27 April compared with 3 March, indicating that some sort of change may have occurred during this period.

The Cobra Head is a collapsed lava tube at the southern tip of Schroter’s Valley and, together with the crater Aristarchus, has been the source of a number of TLPs reported in the past. One such possible event occurred on 1987 September 5 when a dull reddish plume of misty appearance was observed from the crater Herodotus, fanning out across the head of Schroter’s Valley including the Cobra Head. It was seen by several members of the BAA Lunar Section including the writer, and lasted over two and a half hours.

Apart from the region in and around Aristarchus, there are many other lunar craters and mountains where such transient events have been reported. For example the small impact crater Torricelli B on the Sinus Asperitatis was the focus of attention by BAA lunar observers on 1983 January 29, and a paper on the crater has been accepted for publication in this Journal.

Use of the arccosine function

I refer to J. E. Jones’ paper ‘Lunar limb corrections for total solar eclipses’ in the October Journal (JBAA 109(5), p. 260). In his formula (2), Mr Jones uses the arccosine function to calculate the angular separation between the centres of the solar and lunar disks. Although the formula is mathematically correct, the arccosine function is ill-defined for small angles, as is always the case for the said separation during a total solar eclipse.

Consider, for instance, the eclipse of 1999 August 11 at Penzance, Cornwall. At the time of maximum eclipse there, the ratio of the diameters Moon/Sun was 1.0264 and the Sun’s semidiameter was 947 arcseconds. Consequently, at second and third contacts the separation between the centres of the two bodies was only 25 arcsec, an angle whose cosine is 0.999,999,992,655.

For small angles, it is better (and easier) to find the separation by taking the square root of

(Da.cosd)² + (Dd)²

where Da and Dd are the differences in right ascension and declination, respectively, both in arcseconds, and d is the declination of either body.

Jean Meeus
Heuvestraat 31, B-3071 Erps-Kwerps, Belgium. [jmeeus@compuserve.com]

A new observing project to detect eclipsing dwarf novae

This is to let Journal readers know about a new Pro-Am project run by the Variable Star Section to detect eclipses in dwarf novae not previously known to exhibit eclipses. Both visual and CCD amateur observations are needed. Keele Observatory, where Dr Tim Naylor is Director, have offered to confirm positive results; their view is that the results are publishable whether positive or negative.

A simple check shows that out of 400+ known dwarf novae (DNe), no more than a dozen or so are known to undergo eclipses due to the secondary star blocking out light from the accretion disk (and sometimes the primary star) during orbital motion. Theoretically about 34% of DNe should show eclipses, implying that eclipsing systems are under-represented by a factor of 10 amongst known DNe. Recent discussions with professional astronomers strongly support the view that this shortfall is due largely to under-observation rather than to any selection effect. This in turn suggests that a systematic survey of DNe aimed at detecting eclipses should reveal a considerable number of hitherto unknown eclipsing systems, many (perhaps half) of which should be deeply eclipsing. Eclipsing systems are highly valued by professionals because eclipse light curves can help to understand the mechanisms underlying the dwarf nova outburst cycle. Thus for example the eclipsing systems U Gem and Z Cha have been particularly important in establishing the present understanding of DNe.

The CCD technology now being used by amateurs is ideal for the necessary time-resolved photometric observations. Although many of the candidate target stars are probably too faint in quiescence, observations during outburst will in most cases show eclipses if they occur in the system at all. Furthermore it is not necessary to use filters in order to detect eclipses. The most important role for visual observers in this project is to detect outbursts and report as quickly as possible, as is currently done in the Recurrent Objects Programme. However in some cases eclipses may be detectable visually, just as superhumps in SU UMa stars have on occasions been visually detected.

Whatever the observing technique, eclipse detection needs observing runs at least as long as the orbital period of the dwarf nova, which is generally in the range 80 minutes to 2 hours for SU UMa-type stars and upwards of 3 hours for U Gem and Z Cam stars. For practical reasons the upper limit should be 10 hours. The more demanding long-period systems should provide ideal targets for users of automatic telescopes. Prof F. A. Ringwald (Florida Institute of Technology) has suggested that once three orbits of a star have been covered, it should be clear whether eclipses are present or not, and the star can be removed from the programme. A rolling programme is therefore envisaged in which the target list is updated regularly.

The sample of DNe studied in this project will be flux-limited, i.e. only stars brighter than magnitude 15 are to be observed. In most cases this will apply to outburst magnitudes, since relatively few (e.g. EY Cyg) are bright enough to observe in quiescence at a sufficient data rate and with adequate signal-to-noise ratio to obtain reliable results. A useful rule-of-thumb for the necessary data rate might be about 100 data points per orbit. Thus for SU UMa stars probably 1 estimate or CCD frame per minute is needed, while for U Gem and Z Cam stars a rate of 1 every 2 or 3 minutes is probably adequate to detect eclipses.

Interested observers should contact me to register their interest and to obtain further details. The BAAVSS web pages [http://www.telf-ast.demon.co.uk/] will carry background information on the project and a regularly updated list of programme stars.

W. J. Worraker
65 Wantage Road, Didcot, Oxon. OX11 0AE.
[bill.worraker@hyprotech.com]. Tel. 01235 812181 (up to 10.30 pm).

Satellites and moons

I am interested to know how and when it became acceptable among astronomers to refer to the natural satellites of the planets of the solar system as ‘moons’.

I have perused respectable tomes such as Proctor’s Saturn and its System (1882), Young’s Text Book of Astronomy (1889), Spencer Jones’s General Astronomy (1922), J. C. Duncan’s Astronomy a Textbook (1945) without finding a single reference to satellites, other than the Moon, as ‘moons’.

Contemporaries of the aforementioned early treatises are to be found extolling the ‘moon’ as synonymous with ‘satellite’. Thus, Sir Robert Ball (in his numerous works, now hopelessly outnumbered by our own Patrick Moore) is not ashamed to be allied with Agnes Giberne (educator of the young with her delightful Among the Stars (1889), the cover illustration of which has two stars in front of the sickled Moon), and Agnes Clarke in her magnificent A Popular History of Astronomy (1887). No less a populariser of astronomy than Sir James Jeans, The Stars in their Courses (1931), speaks of ‘satellites or moons’. Even Webb has some ‘little moons’ in his famous Celestial Objects for Common Telescopes (1893 – fifth edn.). To feel really safe, however, one has to go to Sir John Herschel with his A Treatise on Astronomy (1851). Sir John appears perfectly happy with ‘satellite’ to the extent, along with most of us I imagine, of spelling ‘moon’ (our Moon) in the lower case throughout.

When I was at school (some donkeys years ago) I was reprimanded by our physics master for referring to satellites (there was no such thing as an artificial satellite then) as ‘moons’. He said, ‘If you want to use that baby talk, then do it out of my hearing’.

John Vetterlein
Springfield, Rousay, Orkney KW17 2PR

When in Rome – Part IIIV

The Roman way of expressing numbers is somewhat more involved than implied in Peter Macdonald’s letter in the December JBAA (109(6), 354 (1999)). The facts he states assume the use solely of the subtraction method, that is 4 written as IV, 9 as IX, etc. This has become the more formal and modern way of writing Roman numerals, but the Romans themselves were less strict in their numbering, also using the IIII and VIIII forms as is sometimes seen on clock faces. This system would make 1999 the longest year to date at 16 characters, namely MDCCCCLXXXXVIIII. The large amount of flexibility used is seen in the fact that 19 could easily have been written XIX, IXX or XVIIII. Even 18 has been seen as IIXX. Their numbering system is more akin to our use of times, such as 3.55 or 5 minutes to 4.

Even now one can find examples of variation. In Leominster, Herefordshire there is a building with the date MXM on it instead of the ‘normal’ MCMXC. Both would have been just as clear to the Romans as their numbers form a concept and not a sequence of values as in our 1, 2, 3 etc. Along these lines 1999 could have been MLM – look at the newsprint that would have been saved!

The use of M only came in later as early Roman numbering uses CI in place of M for 1000. For larger numbers the early form used CCI for 10000, CCCI for 100000, etc. Later the larger numbers were created by adding a bar over the letter indicating the number is 1000 times larger. Hence V is 5000, C is 100000 etc., implying, assuming the bar does not count as a character, that the year 4000 can be represented by two characters, namely IV and the year 5000 by one character, V. What happens after M is not clear, but the Romans probably did not need numbers as large as a billion in their lives.

There are many other, mostly earlier, variations for the larger numbers involving more symbolic forms. These even included the symbol we now use for infinity, ¥ , to represent 1000.

So when it comes to Roman numbers it is VI of one and IIIIX of the other!

Alan Welch
7 Frost Road, Ledbury, HR8 2UW