Fig. 1. Occultation residuals.
Orwell Astronomical Society (Ipswich)
Analysis Of Lunar Occultations, 1992 - 2002
Introduction to lunar occultations.
During the period 11 November 1992 - 12 September 2002, members of OASI observed and timed lunar occultations and provided reports of their observations for collation and analysis. Table 1 gives a summary of observations reported during this period.
| Year | No. Obs. | Observer | Location | Instrument |
| 1992 | 4 | Unspecified | Orwell Park Observatory | Tomline Refractor |
| 1993 | 6 | Unspecified | Orwell Park Observatory | Tomline Refractor |
| 1 | Mike Harlow | Felixstowe | 250 mm reflector | |
| 1 | David Payne | Wickham Market | 400 mm reflector | |
| 1994 | 1 | James Appleton | East Ipswich | 110 mm reflector |
| 9 | Martin Cook | East Ipswich | 110 mm reflector | |
| 1 | Pete Richards | Orwell Park Observatory | Tomline Refractor | |
| 2 | Alan Smith | Orwell Park Observatory | Tomline Refractor | |
| 1995 | 3 | James Appleton | East Ipswich | 250 mm Meade SCT |
| 4 | James Appleton | Orwell Park Observatory | Tomline Refractor | |
| 14 | James Appleton | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 15 | Martin Cook | East Ipswich | 250 mm reflector | |
| 1 | Martin Cook | Orwell Park Observatory | Tomline Refractor | |
| 1 | Martin Cook | Orwell Park Observatory | 110 mm reflector | |
| 3 | Martin Cook | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 1 | Mike Harlow | Orwell Park Observatory | Tomline Refractor | |
| 12 | Mike Harlow | Felixstowe | 250 mm reflector | |
| 1 | David Payne | Wickham Market | 400 mm reflector | |
| 1 | Pete Richards | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 5 | Ian Swann | Ipswich | 250 mm Meade SCT | |
| 1 | Ian Swann | Orwell Park Observatory | 110 mm reflector | |
| 1 | Ian Swann | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 1996 | 11 | James Appleton | East Ipswich | 250 mm Meade SCT |
| 1 | Martin Cook | East Ipswich | 250 mm reflector | |
| 2 | Mike Harlow | Felixstowe | 250 mm reflector | |
| 1997 | 1 | James Appleton | west of Ipswich | 10x50 binoculars |
| 16 | James Appleton | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 41 | James Appleton | East Ipswich | 250 mm Meade SCT | |
| 2 | James Appleton | East Ipswich | 10x50 binoculars | |
| 5 | Martin Cook | East Ipswich | 250 mm reflector | |
| 1 | Martin Cook | Orwell Park Observatory | Tomline Refractor | |
| 2 | David Payne | Orwell Park Observatory | Tomline Refractor | |
| 1998 | 10 | James Appleton | East Ipswich | 250 mm Meade SCT |
| 5 | James Appleton | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 3 | James Appleton | East Ipswich | 10x50 binoculars | |
| 1 | Martin Cook | Orwell Park Observatory | 250 mm Dobsonian reflector | |
| 2 | Mike Harlow | Newbourne | 300 mm reflector | |
| 1999 | 7 | James Appleton | East Ipswich | 250 mm Meade SCT |
| 2 | James Appleton | East Ipswich | 10x50 binoculars | |
| 3 | Martin Cook | East Ipswich | 250 mm reflector | |
| 2000 | 3 | James Appleton | Orwell Park Observatory | Tomline Refractor |
| 10 | James Appleton | East Ipswich | 250 mm Meade SCT | |
| 1 | James Appleton | East Ipswich | 10x50 binoculars | |
| 21 | Martin Cook | East Ipswich | 250 mm reflector | |
| 2001 | 2 | James Appleton | East Ipswich | 250 mm Meade SCT |
| 2002 | 1 | James Appleton | Orwell Park Observatory | Tomline Refractor |
| Total | 241 |
Table 1. Observations of lunar occultations reported during 1992 - 2002 by members of OASI.
Table 1 lists 241 observations; however, in approximately one quarter of cases circumstances were problematic either in terms of poor weather conditions resulting in low confidence in reported timings, ambiguity in the star, or other confusion. Deleting the doubtful cases leaves 187 observations for which weather conditions were acceptable, the star was identified unambiguously and the observer had reasonable confidence in the reported timing.
All the reported observations were timed by the observer at the eyepiece either by clicking a stopwatch button and referring later to an accurate time source (e.g. the BT speaking clock), by looking away from the eyepiece to read the time from a clock or by calling out the occurrence of the event to a colleague observing a clock. In each case one or more personal reaction times are involved. The reaction time of the observer can be up to about a second for an amateur observer with little practice; a skilled observer can achieve less than 0.25 second, but this takes much practice. Personal reaction times limit the accuracy of the timings reported to me and I therefore rounded all reported event times to the nearest second prior to further analysis. I then calculated theoretical estimates of event times for the observations summarised in table 1, excluding doubtful cases. Figure 1 is a histogram of the residuals, defined, for each observation, as:
residual = measured occultation time – predicted occultation time (in seconds).
Figure 1 shows a form that is roughly normally distributed, as would be expected. The median residual is one second, accounted for by the reaction times of the observers. Attempts to establish a relationship between the difficulty of the observation (represented by the magnitude of the star and the phase of the Moon) and the residual proved negative.
Fig. 1. Occultation residuals.
If one regards the lunar limb profile as known (or its effect approximately averaged out over multiple observations) then the residuals in occultation timings are associated entirely with the observer’s personal reaction time.
Table 2 compares the residuals for all observers who reported more than one occultation during the 11 years 1992 – 2002. It lists, for each observer, the number of observations reported and the mean and standard deviation of residuals. The latter quantity is a measure of the consistency of the observer’s timings. Top observer according to this table is clearly Martin Cook, who achieved a large number of
observations together with a relatively small average personal reaction time (mean residual 0.5 seconds) and a good consistency (low standard
deviation of residuals).
| Appleton | Cook | Harlow | Payne | Smith | Swann | |
| No of observations | 92 | 54 | 16 | 4 | 2 | 7 |
| Mean residual (s) | 0.8 | 0.5 | -0.8 | 1.0 | 1.0 | 0.3 |
| Std Dev of residuals (s) | 2.9 | 1.5 | 8.2 | 0.7 | 0.0 | 1.2 |
Table 2. Comparison of occultation observers’ residuals.
Universal Time (UT), the basis of measures of civil time, is based upon the rotation of the Earth. However, the Earth’s rotation is generally slowing down and moreover is subject to unpredictable irregularities (some associated with movements of masses within the liquid core of the planet). Astronomers need a uniform time scale to predict astronomical phenomena. From 1960 to 1983, Ephemeris Time (ET), based on the motion of the planets, provided a uniform time scale. In 1984, Dynamic Time (DT), based on atomic clocks, effectively superseded ET; however, DT may be thought of as a continuation of ET.
The quantity ΔT, pronounced delta T, provides the link between the variable timescale of civil life and the constant timescale of astronomical phenomena. Mathematically, ΔT = ET – UT. The exact value of ΔT cannot be predicted in advance and can only be deduced retrospectively from observations.
The BAA and other astronomical organisations produce estimates of ΔT retrospectively based on the movements of the planets. It is possible to analyse the results of occultation timings to estimate ΔT and its change over the years. The method is complex (see chapter 10.6 of [1]) but in essence each timing of an occultation can be used to produce an estimate and, by plotting individual estimates against the date of the observation and calculating a best fitting straight line, it is possible to smooth out the variability of the individual data points and estimate the underlying trend over time. Figure 2 illustrates the estimates obtained by this means (excluding three outliers) together with the best fitting straight line.
Fig 2. Estimates of ΔT.
Table 3 illustrates the corresponding estimates of ΔT together with the values adopted by the BAA (based on a straight line fit to
values in the BAA handbook over the period 1993 – 2002): clearly, agreement is excellent!
| Source | Estimate of ΔT (s) |
| OASI | 59.3 seconds at the start of 1993, increasing by 0.88 seconds per annum thereafter. |
| BAA | 59.0 seconds at the start of 1993, increasing by 0.88 seconds per annum thereafter. |
Table 3. Estimate of ΔT compared with BAA adopted values.
The coming decade promises many good opportunities for observing lunar occultations. The Moon’s orbit is defined by a range of periodicities, both short and long term. The short term periodicities mean that the Moon’s path through the sky tends to follow a pattern whereby it almost repeats itself every month. However, the longer term periodicities gradually shift the orbit so that no particular pattern of approximate repetition can last more than a few years. This results in so called "occultation seasons", lasting for some years, during which particular stars are repeatedly occulted, or repeatedly not occulted.
The effect of occultation seasons is most obvious for the brightest stars subject to occultations, particularly the four first magnitude stars Aldebaran, Spica, Antares and Regulus. Of the first magnitude stars, only Regulus is subject to occultations visible from East Anglia during the decade 2003-2012, with two occultations in October 2007. The next occultation of a first magnitude star after Regulus does not occur until September 2015 when an extensive series of occultations of Aldebaran begins.
Another visually appealing spectacle is that of the Moon occulting the Pleiades star cluster (M45). The next occurrences of this phenomena are in September and December 2006.
[1]
O. Montenbruck and T. Pfleger, "Astronomy On The Personal Computer", 2nd edition, Springer-Verlag, 1994.
James Appleton