Introduction

 An occultation is an event involving two bodies, one of which partially or completely : hides the other. Generally, however, for an event to be described as an occultation the body that is hidden (the more distant of the two) should have a smaller apparent diameter than the occulting body.

The best-known events are those that involve the Moon, and a star or planet. For example, a series of occultations of the Pleiades by the Moon began in 1987. Strictly speaking, solar « eclipses » are occultations, as are the events that occur in « eclipsing » variables. [Technically, eclipses occur when the shadow of a body partially or completely obscures another object, as in a lunar eclipse.] When the apparent diameter of the occulting body is smaller than the body occulted, we use the term « transit ». Transits of the Galilean satellites in front of Jupiter are more frequent events than transits of Venus or Mercury in front of the Sun.

As regards occultations, we have to determine which of the many possible events are visible and are of scientific interest to amateurs. ln general, observations are more valuable if the occulted body is a star. Its apparent diameter is so small (< 0.01 arc-second) that timings of disappearance and reappearance are extremely accurate.

One of the most famous examples is in 1977 March the discovery of the rings around Uranus from observations of the occultation of a bright star. Short disappearances that were recorded before and after the occultation that was caused by the disk of Uranus itself enabled the characteristics of the system of rings to be determined. Occultations involving planets and stars are only of real interest if the planets concerned are remote ones, such as Uranus, Neptune and, in particular, Pluto, which will not be visited by space-probes for many years. It should be noted that most of these events are not observable in amateur telescopes : the brightness of the planet drowns the faint light from the star.

Finally, it is possible we may be able to predict and observe the occultation of a distant star by another that lies closer to us. Such an event would last several days and would be more akin to variable-star observing. It is possible that the event would not result in a decrease in the combined magnitude of the two stars, but in an increase, because of the gravitational lensing effect that might concentrate the light from the occulted object.

Perhaps we should close this short introduction. by recalling, for the record, the unique observation made on 1737 May 28 from Greenwich by John Bevis, who, using a refractor with an OG about 70mm in diameter, was able to observe the occultation of Mercury by Venus, when the two planets were very close to the horizon.

 Determining the time

The principle behind all occultation observations is to measure, with an accuracy of 0.5 second or better, the exact times of contact between the occulting body and the one occulted. The methods and the equipment used for this vary from observer to observer; the items most frequently employed are a clock (DCF77), a tape-recorder and a stopwatch.

The DCF77 broadcast « pips » every second and a silence at the 59th second of every minute or longer pulse for a receiver with short waves. The tape-recorder simultaneously records these time signals as well as clicks, electronic tones, or other noises indicating the times of contact, and which may be produced by any convenient means.

On occasions, observers have been able to arrange for time signals to be retransmitted on a more convenient frequency by a local radio station or radio amateur. ln many countries, such as the United Kingdom, however, such a procedure is prohibited under the terms on which licences are issued. It is, in any case, essential to ensure that no delay is introduced into the signals. Now, what becomes more and more frequent, it is the GPS, that can be as well source of grave errors as an extreme precision.

Measuring a single time

For observations when only a single contact has to be timed, two methods are commonly used. ln the first one, a stopwatch is started at the third pip after a minute marker. These 3 seconds are very useful for the very simple, and good, reason that one is often surprised by the minute marker. To avoid having too much drift in the stopwatch, it is advisable to choose a time signal only a few minutes before the event. The observer should check carefully whether the stopwatch was started at precisely the same time as the signal, and any difference should be noted. Finally, at the precise instant that the event occurs, the stopwatch is halted.

The second method consists of waiting, halted stopwatch in hand, for the event, and starting the watch as it occurs. A second timing may also be recorded if the stopwatch has a split timing feature. Finally the watch is stopped 3 seconds after a suitable minute marker following the time of observation. All that remains to do is to subtract the time indicated by the stopwatch.

A « speaking clock » service may also be used instead of a radio, but especially not with a mobil phone. In the absence of a short-wave receiver or a telephone, it is possible to use, as a last resort, the « pips » broadcasted every hour by many radio stations. The fact that these signals are infrequent, however, means that certain precautions must be taken. The stopwatch should be started at the event and the elapsed time should be noted - without stopping the watch - at several subsequent hour markers so that any errors may be averaged out. In addition, the stopwatch should have been carefully calibrated beforehand to determine its overall drift (which is likely to be fairly considerable over several hours). The results thus obtained may be corrected for reaction time, as described in the section concerning personal equation, before being recorded on the report form. (Note that observations to be submitted to the International Lunar Occultation Center (ILOC) in Japan are generally recorded as uncorrected times, personal equation being entered separately. If reaction time is subtracted, this must be noted on the report forms.)

Personal equation

The effect of reaction times

One's personal equation or reaction time is a very important factor that must be taken into account in deriving accurate timings. Between the time one detects an event and the instant at which one reacts there are a few tenths of a second. The more experienced the observer, the easier it is to estimate this amount. Everyone has his own personal equation, largely as a result of his own physiology and powers of concentration. Other factors may influence it, however, and observers will find these easier to recognize with experience. (They include fatigue, discomfort, mental stale, seeing conditions, telescope aperture, concentration, etc.)

There is a very easy way of determining one's reaction time. With a piece of paper, hide the figures representing seconds on your stopwatch. When you see the minute figure change, press the stop button. You can then read off the time that you required to react in hundredths of a second. This reaction time may vary from about two-tenths of a second to 1 second according to the various factors that we have mentioned.

Deriving times from the magnetic-tape recording

Before beginning to analyze the recording of one's observations, it is useful to determine the exact duration of several minutes as recorded on the tape. This is necessary because the analysis is made at a different temperature from that prevailing when the recording was made, and this nearly always slightly affects the speed of the tape.

The steps to be carried out are as follows : first, count the number of seconds between the preceding minute marker and the audible signal for the event; this will give you the time to the nearest second. Second, obtain the time to a tenth of a second by starting the stopwatch at an earlier second marker and stopping it at the exact instant of the audible signal. If you feel that the measurement is affected by reaction time, this should be taken into account or, better still, the measurement should be repeated. Ideally, the measurement should be repeated several times, and the mean taken. If the personal equation for the event is subtracted from the result, we obtain the time of true first contact. Do the same for any other times of contact that were recorded.

Accuracy of the measurements

A point that must be borne in mind is the accuracy of the final timing of the event given the errors introduced by the reaction time and by the method of analysis. This accuracy is weighted as follows : 0.I-O.2s - excellent ; 0.3-O.4s - good ; 0.5-O.7s- fair ; 0.8-1 s - poor. Beyond 1 second the measurement is of doubtful validity. This accuracy is entered on the report forms, and should not be confused with personal equation.

It is also necessary to calculate the geographical position of one's observing site (using a map to a scale of at least 1:25 000). This information should be given to an accuracy of at least 1 second of arc (about 30 m in latitude and 20 m in longitude), together with the height in meters above sea level.

Occultations of stars by minor planets

ln 1952, Gordon Taylor, an astronomer at the Royal Greenwich Observatory, and Director of the BAA's Computing Section, undertook the prediction of occultations by  minor planets. Initially, the ephemerides of only four minor planets - 1 Ceres, 2 Pallas, 3 Juno and 4 Vesta - were sufficiently accurately known for their positions to be compared with the Yale catalogue. The result of this study was rather meagre : there were very few truly observable events in a year. Although it seems that this type of occultation had been observed accidentally earlier, it was 1958 February 19 before such a predicted event was accurately recorded. That night Per Ake Bjorklund and Svend Aage Müller, near Malmo in Sweden, observed the occultation of the star BD +6° 808 by 3 Juno. Three years later, a second success came with the occultation of BD -5° 5863 by 2 Pallas, observed from Naini TaI in lndia with a photoelectric photometer. It was not until the beginning of 1975 that several stations were able to observe the same event simultaneously (433 Eros and K Geminorum), the subsequent analysis of results providing interesting information. As yet the best- observed occultation by far was the one organized in the U.S.A. on 1983 May 28: 130 stations recorded the occultation of 1 Vulpeculae by 2 Pallas. ln Europe, the event of 1983 January 3 wh en AGK 3 +25° 0989 was occulted by 106 Dione, was observed by 10 stations in the Netherlands, Denmark, and the Federal German Republic. To date, only about 20 of these events have been sufficiently well observed to add to our knowledge of these still-enigmatic objects.

Current and future predictions

Towards the end of the 1970s, improvements in methods of calculation and in our general knowledge of the ephemeris of minor planets made it possible to increase the number of predictions, by including both more minor planets and more stars. G. Taylor in the U.K., L. H. Wasserman and D. W. Dunham in the U.S.A., and E. Goffin in Belgium were primarily responsible for this. The average apparent diameter of a minor planet 150 km across is 0.1 arc-second, so we can understand the considerable uncertainty involved in the new « sport » of chasing occultations of stars by minor planets.

It is possible to reduce this uncertainty a few days before the event by taking, with astrometric telescopes, plates that simultaneously record both the star and the min or planet. The positions may then be measured and compared with the predictions. However, this practice does not allow the uncertainty to be reduced below about 0.3 arc-second.

A description of an event

Before the event, when the minor planet is approaching the star, the motion is generally apparent over a period of a few minutes, which enables the observer to check that the correct star has been located. A little before the event, the minor-planet/star pair becomes difficult to resolve. As the two objects apparently merge, the total brightness increases. An occultation is indicated by a sudden drop in brightness (only the minor planet being visible), and then, after a few seconds, the overall brightness suddenly returns to maximum. The decline in brightness is all the greater, the fainter the min or planet. It is considered possible to observe a drop of 0.5 magnitude under normal conditions (star neither too faint nor too bright, low atmospheric turbulence), but attention, the sparkle gives many of false positive.

Unfortunately, the observer is most likely to see the two bodies approach one another, fuse, and then separate again, with no actual occultation. Such an appulse is still of interest, however. If an occultation occurs, the event may sometimes take a somewhat unusual form. With a slow minor planet (velocity less than about 10 arc-seconds per hour) and a large-diameter star (over 0.001 arc-second), or both, the expected decline in brightness may be less abrupt and may even last a few seconds in extreme cases. The object being observed appears to shrink, like a toy balloon. If the star is a very close double, the occultation may appear to take place in two steps.

Scientific interest

It is obvious that the observer's task is to measure, as accurately as possible, the absolute times of disappearance and reappearance of the star. The accuracy should be close to 0.1 second, and should not exceed 0.5 second.

Two or three good observations may provide a lot of information. For example :

. the diameter and the shape of the minor p1anet, from the duration (the projected chords) of the various occu1tations ;

. the accuracy of the ephemeris of the minor planet (even with only an appulse);

Under certain conditions, and even en though a photoelectric observation is obviously better, it is possible to deduce the apparent diameter of stars to within 0.001 arc-second, which is equal to the accuracy given by good speckle-interferometric measurements. ln the same way, we may add :

. detection of close double stars;

. the presence of any possible satellites to the minor planet. Although the existence of such companion bodies is still in some doubt, several observations however confirmed their presence ; Hermione seems triple, and Kalliope also.

Observational equipment

Stars for which predictions are available are generally brighter than 12th magnitude. So that observation will be reasonably easy, it is a good idea to use a telescope that will reach magnitude 12-14, if one wants to follow all the events predicted. Obviously a simple pair of binoculars may suffice for events down to about magnitude 8. It is not necessary for the minor planet to be, visible, but certainly the star must be, because it is its light that will be hidden. If your mounting has a drive, monitoring, which generally lasts twenty-odd minutes, will be much easier. It is also very useful to have a properly aligned finder with sufficient aperture to reach magnitude 7 easily. Finally, a low-power eyepiece will help you to find the star, and will also allow you, to monitor the brightness of stars close to the target star.

Observational techniques

 A good observation is very valuable, but it is vital for it to be confirmed by another independent station some tens to hundreds of metres away. It is therefore quite a good idea for observers to set up double stations. Isolated individuals should not be discouraged, their observations will retain their value, especially if the event has been particularly well-covered. It is also possible to use photographic equipment, which can play the part of a second observer.

The first difficulty is to identify correctly the star in question. To ensure this, the European network, for example, prepares detailed observing charts. If the, observers are not used to this sort of exercise, it is advisable for them to identify the star several days or, at the, very least, a couple of hours before the event. Correct identification of the star may be confirmed by detecting (if possible) the movement of the minor planer. Once the star bas been found, the most suitable eyepiece for easy observation should be selected, while still retaining a sufficiently large field for the brightness of neighbouring stars to be monitored. If a disappearance occurs, an elementary precaution is to check to ensure that a cloud bas not obscured the stars !

During the period of continuous watch, which may last 15-20 minutes not nowadays , but for TNOs (predictions are not serious for this kind of objects), centered on the predicted time of the event, it is essential for the observer to be as comfortable as possible, so maximum concentration may be maintained. It is advisable not to stare at the star, because the tension that this produces is likely to cause the image to wander onto the eye's blind spot, so that one runs the risk of thinking that short disappearances have occurred. It is preferable to scan the field slowly and continuously. This technique is not necessary with binocular observation.

The disappearance, when it occurs, always takes the observer by surprise. Pay attention to your reaction time : a second is soon gone ! It would be useful to make experiments on one's reaction time under various conditions, and to try to restrict the value to less than 1 second. If an occultation is recorded, it is still useful to continue observing for a while, because a second event may occur - one never knows.

As the reader will have realised, absolute honesty and a rigorously scientific attitude are essential.

Organizations handling observations

 Whether the observation was positive (an occultation) or negative (an appulse), observers should carefully reduce their observations and accurately determine their geographical positions, fill in the appropriate forms and forward them quickly.

A negative observation may be very important and may fix the limit of the zone of occultation, but attention, it's unnecessary to send a report if the weather conditions have prevented the observation of the phenomenon.