Memo On: Reductions of Grazing Occultations revised 25 Feb, 1997

by Robert Sandy

Published on Robert Sandy's Web Site (, as well as periodic issues of I.O.T.A.'s Occultation Newsletters, and also snail-mailed to observers, are Pictorial Reductions of past grazing occultations observed by observing expeditions. P.R.'s are quite simply drawings that give a visual comparison of what was predicted to occur versus what was observed as reported by the observer/s.

EXPLANATION OF REDUCTION: In order to visually analyze observed phenomena associated with grazing occultations, the predicted profile of the moon's limb (i.e., edge) in the graze region, must first be plotted; this is accomplished through the use of limb correction charts by Dr. C.B. Watts ("The Marginal Zone of the Moon", Astronomical Papers of the American Ephemeris, Vol. 17, U.S. Government Printing Office, Washington, D.C., 1963). The Watts' limb corrections have been, for several years now, been placed into computer "memory".

The predicted lunar profile plotted is reliant on the predicted lunar topocentric librations at time of the Subject graze, and these are calculated by Dr. Mitsuru Soma at the National Astronomical Observatory in Japan, using a computer program he wrote. Sometimes, though, the predicted profile shown on the P.R. may be taken (i.e., derived) from excellent observations taken from one, or several past-observed grazes that occurred in the Watts angle Region of Subject graze, especially when (1) MANY accurate timings were made, and (2) the lunar librations (especially Latitude=B) during past graze/s AND the Subject graze are similar. If this is the case, a statement will be made in a "cover" letter enclosed with my P.R. will state such, or this "case" may be noted on the P.R. itself. The statement will indicate (1) what past graze datum's were used, (2) how many accurate timings were made, and (3) the Longitude (i.e., L) and Latitude (i.e., B) librations of the Moon during the PAST graze/s.

Next, the predicted path of the star in relation to the Moon is plotted for EACH observer (again, calculated by Mitsuru Soma, and based on the reported geographical coordinates and elevation of EACH observer) with the reported points of star contact with the lunar features indicated by "tick" marks. For each observer, the star moves along a CURVED path from left-to-right, observer designations being indicated at the left-hand side. Periods when the star was reported visible are indicated by a solid line, while during periods of reported invisibility, the line is "greyed". A dashed line plotted (at times) indicates that observations were discontinued, or that no timings were made because of timing equipment failure, etc. Note: If the viewer of Subject P.R. notices some "jiggling" of the observer star tracks, the jiggling is caused from observer-reported star "quivering" (pun)!!!

EXPLANATION OF ABBREVIATIONS AND SYMBOLS SHOWN ON P.R.: V.P.C.= Vertical Profile Correction applied to the predicted profile to bring it into closer agreement with observations (usually VPC is set at 0."00 anyway). H.P.C.=Horizontal Profile Correction in the position of lunar limb features (again, usually set at 0.00-degrees of Watts angle). P.E.I.S.D.= Probable Error in Star's Declination (expressed in seconds of arc). This value is taken from the PREDICTION GRAZEREG-VER. 4.0 by IOTA/ES limit prediction heading. Note: Any value shown for PEISD should only be considered correct to within a 50-50 PROBABILITY of being within a RADIUS of the stated PEISD value.

COMPUTER VERSION: (i.e., 85-C, 85-D, 85-E by Mitsuru Soma, or 1978-A, 1980-H, etc., by the U.S.N.O. several years ago)---the designation of the set of empiracal corrections made to the lunar ephemeris that were used in producing the Subject P.R.

SYMBOLS: B = (blink; a D followed by an R in less than one-second); F (flash; an R followed by a D in less than one-second of time); note: B's and F's may not be plotted on my P.R., for reason of not "cluttering" the P.R., especially if MANY obsever "tracks" are plotted. ? = Uncertain timing or events that are reported by observer/s, OR observer/s timing/s are questioned because of an obvious discrepancy of timing/s when compared with timings made at other observing stations/sites). A.T. = Altered Time (an observer made an obvious error in a reported timing, usually based on observers ABOVE and BELOW him/her, who got seemingly accurate timings). It should be noted, though, that (1) a reported timing is altered ONLY when there is considerable indication that a particular timing may be in error by several seconds (in most cases, this amounts to either a thirty-second or sixty-second mistake in the reported timing), and (2) that even though the timing has been altered, it should not be considered as being as accurate as other reported timings.

The numerical codes for the profile limb points are:

0 (or *): Good limb correction, usually accurate to within +/-0.2" (or Error Bar Length of 0.4").

1 Fair limb correction with some extrapolation from Watts' observed data, accurate to +/-0.4" (or Error Bar Length of 0.8").

2 Meaningless limb correction due to extrapolation far beyond Watts' observed data, either extreme librations or in the Cassini region (see "The Lunar Profile" on page 8). It is best to use observed graze data instead for these points, but if none are available, in most cases 0.0" can be used as the limb correction. In the southern Cassini region (Watts angle angles between 174 deg. and 188 deg., and latitude libration less than -2 deg.), use -0.7" (or Error Bar Length of 1.0") for the limb correction; this low region beyond the Moon's south pole is part of the Aitken Basin established by Clementine observations in 1994, but known from graze observations since late 1964. In most cases, the result should then be within +/-0.5" of the actual limb (Error Bar probably shown on R. Sandy's P.R.'s as 1.0" long).

3 Good limb correction from previously observed graze data, accurate to better than +/-0.1" (or Error Bar 0.2" long) at the SAME latitude libration and using the SAME prediction basis as the reduction basis, for the observed graze. However, due mainly to limited coverage of observed grazes (that is, the latitude librations being different) and star position errors, the errors are usually +/-0.2" (Error Bar Length = 0.4") if the prediction/reduction bases are the same, and +/-0.4" (Error Bar Length = 0.8") if they are different.

4 Limb correction from previously observed graze data, but poorer than 3 because the data have been extrapolated by 0.4 deg. to 0.8 deg. of Watts angle from the observed data, so the accuracy is ABOUT twice that of code 3 described above. Most of the Cassini regions have been crudely "mapped" with previously observed grazes, so 3's and 4's usually dominate the profile when a graze occurs in these regions.

5 Good limb correction with an empirical vertical correction applied (* [or 0] + 5) based on previous graze observations; like *, the accuracy is expected to be +/-0.2" (Error Bar Length then shown = 0.4"). Watts' data are still used, but with an overall vertical shift. In general, it is better to use specific observed graze data (codes 3 and 4), and we are working to replace the 5, 6, and 7 codes with 3 and 4 codes when that is practical.

6 Fair limb correction with an empirical correction applied (1 + 5); see discussion for code 5. Since a vertical correction based on observed grazes has been applied, the accuracy should be +/-0.3" (Error Bar Length = 0.6"), a little better than uncorrected code 1.

7 "Meaningless" limb correction with an empirical correction applied (2 + 5). In this case, based partly on observed data, the correction should not be as "meaningless" as code 2. An accuracy of +/-0.5" (Error Bar Length = 1.0") is expected.

Correspondence about Pictorial Reductions of grazes should be sent to: Robert L. Sandy; 4901 S. Valley View Rd.; Blue Springs, MO. 64015; U.S.A. E-mail address Home Phone: 816-795-8116

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