Updated: 2003 July 8
This is now in three parts. The first goes through the steps used to plot the path for a grazing occultation that occurred on 2002 September 29. The second part is a partially edited and illustrated section of the old IOTA occultation manual, including the chapters that explain use of the IOTA predictions and ACLPPP lunar limb profiles to plot graze paths and set up expeditions. At the end (third part) you can obtain the prediction files for grazes in the northeastern U.S.A. (within 300 miles of Greenbelt, Maryland) for 2003. ______________________________________________________________ Recently, upon request from a local observer, I plotted the path for a grazing occultation that occurred in northern Utah on September 29th. The event was clouded out there, but timings of that graze, some with video cameras, were obtained of the graze farther west in northern California. The Utah maps are instuctive for the overall process of setting up a graze, including applying the correction for height above sea level, which is necessary at least for heights greater than 200 meters (600 ft.). In order to get the scanned figures to display and print at the right size, they are all in files created with a relatively recent version of MS Word; if you have an older version that can not open the files, let me know. I plotted the path on the 1:250,000-scale U. S. Geological Survey (USGS) map Brigham City that includes the area where the path crosses I-15 north of Salt Lake City. The path crossed Great Salt Lake; the next opportunity to reach the path to the west was in Nevada several miles west of the Utah line, near Silver Zone Pass, where the path crossed I-80. I don't have the USGS map of that area, so I used Delorme's Street Atlas USA version 8 - I highly recommend it since it's much more up-to-date than the USGS maps, and names all of the streets (that are named). I plotted the path on a 1:125,000-scale map generated by Street Atlas USA; that's easier to use than with the 1:250,000-scale USGS maps. I also made detailed Street Atlas maps of the rural area where the path crossed Riverside and Fielding just east of I-15. Street Atlas doesn't have elevation information, so for that, in this case for Nevada where I didn't have a USGS map, I obtained a plot of the USGS map of the area from www.topozone.com. Also here is a file with the plotting scales that I used, one for the 1:250,000-scale USGS maps and one for the 1:125,000-scale Street Atlas maps; I first plotted the sea level limit line on them. The units of the scale are minutes of arc of latitude, as given in the IOTA Grazereg predictions given here for this graze. The Moon's azimuth is given in the predictions, but you also need the azimuth of the limit line, as explained in the 2nd section below from the IOTA manual (the terminology of that manual is used here; you might now read it first before continuing reading this). You can obtain the azimuth of the limit just by plotting the limit line on a map, and measuring it with a protractor; azimuth is measured clockwise starting at 0 at due north, 90 at due east, 180 at due south, and 270 at due west. I used instead a numerical method, where Azlim, the azimuth of the limit, is given by Azlim = arc tan {[15.0 x cos(phi)]/[phi+7.5 - phi-7.5]} where phi is the latitude at a specific longitude, phi+7.5 is the latitude 7.5' east of the specified longitude, and phi-7.5 is the latitude 7.5' west of the specified longitude. I used -112 deg. 45' for the specified longitude; then phi is 41 deg. 35.26' = 41.58767 deg., cos(phi) = 0.74794 and [15.0 x cos(phi)] = 11.219. The difference [phi+7.5 - phi-7.5] needs to be expressed in minutes of arc; in this case, it's easiest to use ' (minutes of arc) measured from lat. 41 deg. exactly, so then phi+7.5 is 38.17 and phi-7.5 is 32.33, and their difference is +5.84. Then, tan {Azlim} is 1.9211 and Azlim = 62.5 deg. I calcalated D, the angle between the limit line and the Moon's azimuth, to be 43.0 deg., and then from the formula given in the manual below, the elevation shift factor is TANZ x sine(D) = 0.484. So if the elevation (h) is about 4400 ft., as it is near I-15, the path shifts southeast by 2130 ft. or 0.40 mile. Near I-80, the elevation is about 5990 ft. and the path shift then is 0.55 mile. These "elevation-corrected" limits are plotted on the USGS map and 1:125,000-scale Street Atlas map parallel with the sea level limit and labelled with the height above sea level in ft. Then, looking at the predicted profile (ACLPPP), which I also scanned with my annotations here, connecting the 3's and *'s to form the lunar profile, and drawing horizontal lines, I determined that the area that should be covered by an expedition would be from 0.2 mile north of the shifted limit, to 1.2 miles south of it (distances measured perpendicular to the path). I just call these extremes "N" and "S", shown on all the maps, and they can be used to determine the scale of any of the maps, since the distance between those two lines is 1.4 miles. I find it convenient to use engineering scales for plotting these distances, since at 1:250,000 scale the unit division of the 40 scale is one mile, and at 1:125,000 scale the unit division of the 20 scale is one mile. For one observer, I tried to find the place where the horizontal line might intersect the actual profile the most times, and thought that would be at the 0.55 mile south distance, where, considering the approximate 0.3-mile accuracy of the Watts datapoints, would last almost a minute before central graze. It might be even better at the top of the profile, but you would be risking a miss there; maybe right at the (shifted) limit line would be good for a 2nd observer. Any others could be spaced north and south of the best line by 0.2 to 0.3 miles or so. The basic path was plotted on the maps mentioned above. I then transferred these plots to more detailed plots with street names, etc., only transferring the N, S, and 0.55 mile south lines, by comparing where they intersected streets and other features that are shown on both maps. Below is a list of the names of the files (with links) to these more detailed maps; I used SA8 for "Steet Atlas USA version 8". Maps similar to the SA8 can be obtained on the Web from sites like www.mapsonus.com but I have not been able to get lat./long. grids to plot on them. 02929RFM.DOC - Area east of I-15 from SA8, medium view 02929RFD.DOC - Area east of I-15 from SA8, detailed, streets named 02929SZD.DOC - Silver Zone Pass, NV SA8 detailed view 02929GZU.DOC - Topozone map of the Silver Zone Pass graze area (no lines are shown on it; it was used only to obtain the height above sealevel in the area and to see the topography). ______________________________________________________________ Below are sections on using IOTA's grazing occultation predictions extracted from the draft version of the IOTA OBSERVER'S MANUAL as of 1994 July 31, by Joan Bixby Dunham, David W. Dunham, and Wayne H. Warren Jr., with very limited updates made 2002 Aug. 26 and 2002 Oct. 1. NOTE: IN THIS PRELIMINARY VERSION OF THE MANUAL, ALL FIGURES RE- FERRED TO IN THE TEXT WILL BE FOUND COLLECTED AT THE BACK OF THE DOCUMENT. That's true of the printed version, but not for this limited on-line version, where links are provided to a few of the figures only. THE FINAL VERSION WILL INCLUDE APPROPRIATE MATERIAL FROM THE U. S. NAVAL OBSERVATORY'S TOTAL OCCULTATION PREDICTION PAPERS, SINCE IOTA HAS INHERITED THAT SERVICE. THERE WILL BE SOME MINOR CHANGES TO CHAPTER 6, BASED ON THE NEW GRAZING OCCULTATION PREDICTIONS (PRODUCED BY A NEW COMPUTER PROGRAM) THAT WAS DISTRIBUTED STARTING IN EARLY 1994. A FEW SECTIONS WILL BE EXPANDED AND CHAPTER 13 WILL BE WRITTEN. TABLE OF CONTENTS (Full; only chapters 6 and 7 are included here) _________________ 1.0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1 2.0 WHAT IS AN OCCULTATION AND WHY WE OBSERVE THEM . . . . . 2 2.1 What is an Occultation? . . . . . . . . . . . . . . . . 2 2.2 What is a Graze? . . . . . . . . . . . . . . . . . . . . 3 2.3 Why Observe Occultations? . . . . . . . . . . . . . . . 3 3.0 BEGINNING OBSERVING . . . . . . . . . . . . . . . . . . 7 3.1 What to Expect . . . . . . . . . . . . . . . . . . . . . 7 3.2 Event Nomenclature . . . . . . . . . . . . . . . . . . . 8 3.2.1 The Lunar Profile . . . . . . . . . . . . . . . . . 8 3.3 Observing Equipment . . . . . . . . . . . . . . . . . . 9 3.3.1 The Telescope . . . . . . . . . . . . . . . . . . . 10 3.3.2 The Radio . . . . . . . . . . . . . . . . . . . . . 12 3.3.3 The Tape Recorder . . . . . . . . . . . . . . . . . 13 3.3.4 The Stopwatch . . . . . . . . . . . . . . . . . . . 13 3.3.5 Other Equipment . . . . . . . . . . . . . . . . . . 14 3.3.6 Equipment List . . . . . . . . . . . . . . . . . . . 14 3.4 Making Scientifically Useful Occultation Timings . . . . 16 3.5 Reporting Observations . . . . . . . . . . . . . . . . . 17 4.0 ACCURATE TOPOCENTRIC POSITION DETERMINATION . . . . . . 18 4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Accuracy Requirements . . . . . . . . . . . . . . . . . 19 4.3 Measuring Coordinates . . . . . . . . . . . . . . . . . 19 4.3.1 Coordinates from GPS Measurements . . . . . . . . . 21 4.4 Example of Coordinate Determination . . . . . . . . . . 22 4.4.1 Position Determination . . . . . . . . . . . . . . . 22 4.4.2 Errors . . . . . . . . . . . . . . . . . . . . . . . 23 4.4.3 Numerical Example . . . . . . . . . . . . . . . . . 24 5.0 TOTAL OCCULTATIONS . . . . . . . . . . . . . . . . . . . 25 5.1 Observing Techniques . . . . . . . . . . . . . . . . . . 25 5.2 Techniques for Observing Reappearances . . . . . . . . . 26 5.3 Predictions . . . . . . . . . . . . . . . . . . . . . . 28 6.0 GRAZING OCCULTATION PREDICTIONS . . . . . . . . . . . . 29 6.1 Grazing Occultation Limit Predictions . . . . . . . . . 29 6.1.1 Heading Data . . . . . . . . . . . . . . . . . . . . 29 6.1.2 Column Data . . . . . . . . . . . . . . . . . . . . 32 6.1.3 Ending Data . . . . . . . . . . . . . . . . . . . . 34 6.1.4 Elevation Correction . . . . . . . . . . . . . . . . 35 6.2 Profile Predictions . . . . . . . . . . . . . . . . . . 35 6.2.1 Profile Explanation . . . . . . . . . . . . . . . . 36 6.2.2 Limit Prediction and Profile Use . . . . . . . . . . 40 6.2.2.1 Topographic Maps . . . . . . . . . . . . . . . . 40 6.2.2.2 Graze Path Plotting . . . . . . . . . . . . . . 40 6.2.2.3 Profile Use . . . . . . . . . . . . . . . . . . 42 7.0 ORGANIZING GRAZING OCCULTATION EXPEDITIONS . . . . . . . 47 7.1 Preparation . . . . . . . . . . . . . . . . . . . . . . 47 7.2 Site Selection . . . . . . . . . . . . . . . . . . . . . 47 7.2.1 Observer Notification and Preparation . . . . . . . 49 7.3 Expedition Reporting . . . . . . . . . . . . . . . . . . 49 7.4 Approximate Reduction and Shift Determination . . . . . 50 7.4.1 Correction of Profile to Actual Observing Location 50 7.4.2 Correcting the Sea Level Limit Prediction for Ele- vation . . . . . . . . . . . . . . . . . . . . . . . . . . 53 7.4.3 Calculating the Time of Central Graze . . . . . . . 54 7.4.4 Plotting the Observations on the Predicted Profile 55 7.4.5 Calculating the Shift Value . . . . . . . . . . . . 55 8.0 ACCURATE TIMING . . . . . . . . . . . . . . . . . . . . 57 8.1 Methods of Timing . . . . . . . . . . . . . . . . . . . 57 8.1.1 Stopwatch method . . . . . . . . . . . . . . . . . . 57 8.1.2 Tape Recorder Method . . . . . . . . . . . . . . . . 60 8.1.3 Eye and Ear Method . . . . . . . . . . . . . . . . . 61 8.1.4 Alternate Methods for Limited Equipment . . . . . . 62 8.1.4.1 AM Radio as a Time Standard . . . . . . . . . . 62 8.1.4.2 Recording Assistant . . . . . . . . . . . . . . 62 8.1.4.3 CB Radio in Panic Mode . . . . . . . . . . . . . 63 8.1.5 Photoelectric Method . . . . . . . . . . . . . . . . 63 8.1.6 Video . . . . . . . . . . . . . . . . . . . . . . . 64 8.2 Determining Personal Equation and Timing Accuracy . . . 65 8.3 International Time Standards and Time Signals . . . . . 67 8.3.1 Time Scale Definitions . . . . . . . . . . . . . . . 68 8.3.2 Coordinated Universal Time . . . . . . . . . . . . . 70 8.3.3 Time Signals . . . . . . . . . . . . . . . . . . . . 71 8.3.4 Radio Propagation Delay . . . . . . . . . . . . . . 72 8.3.5 Time Delay of Sound . . . . . . . . . . . . . . . . 73 8.3.6 Signal Reception Quality . . . . . . . . . . . . . . 73 8.3.7 Timings Without Shortwave Time Signals . . . . . . . 74 9.0 ASTEROIDAL OCCULTATIONS . . . . . . . . . . . . . . . . 75 9.1 Predicting Asteroidal Occultations . . . . . . . . . . . 75 9.2 Asteroid Occultation Prediction Updates . . . . . . . . 76 9.3 Observing Occultations by Asteroids . . . . . . . . . . 76 10.0 OTHER OCCULTATION EVENTS . . . . . . . . . . . . . . . 78 10.1 Predictions of Special Events . . . . . . . . . . . . . 78 10.2 Observing Special Events . . . . . . . . . . . . . . . 79 10.3 Occultations by Comets . . . . . . . . . . . . . . . . 79 11.0 SOLAR ECLIPSE OBSERVATIONS . . . . . . . . . . . . . . 80 11.1 Solar Eclipse Phenomena near the Edge of the Path of To- tality . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 11.2 Eye and Equipment Safety . . . . . . . . . . . . . . . 81 11.3 Observing Techniques . . . . . . . . . . . . . . . . . 82 11.3.1 Projection . . . . . . . . . . . . . . . . . . . . 82 11.3.1.1 Visual Observation of the Projected Image . . . 83 11.3.1.2 Photography of the Projected Image . . . . . . 83 11.3.1.3 Video Recording of the Projected Image . . . . 84 11.4 Direct Photography . . . . . . . . . . . . . . . . . . 84 11.4.1 Photographing with a Movie Camera . . . . . . . . . 86 11.4.2 Photographing with a Video Camera . . . . . . . . . 87 11.5 Timing . . . . . . . . . . . . . . . . . . . . . . . . 87 11.6 Site Selection . . . . . . . . . . . . . . . . . . . . 87 11.7 Reporting Observations . . . . . . . . . . . . . . . . 88 11.8 Observing Hints and Suggestions . . . . . . . . . . . . 88 12.0 PREDICTING OCCULTATIONS . . . . . . . . . . . . . . . . 90 12.1 Lunar Total Occultations . . . . . . . . . . . . . . . 90 12.2 Lunar Grazing Occultations . . . . . . . . . . . . . . 90 12.3 Lunar Librations . . . . . . . . . . . . . . . . . . . 91 12.4 Eclipses . . . . . . . . . . . . . . . . . . . . . . . 91 12.5 Asteroidal Occultations . . . . . . . . . . . . . . . . 91 12.6 Planetary Occultations . . . . . . . . . . . . . . . . 92 13.0 ADVANCED OBSERVING TECHNIQUES . . . . . . . . . . . . . 93 APPENDIX A. OCCULTATION SERVICES AND SOURCES OF FURTHER INFOR- MATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.1 IOTA . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.2 International Lunar Occultation Centre . . . . . . . . . 94 A.3 Observer's Handbook . . . . . . . . . . . . . . . . . . 95 A.4 Sky and Telescope, Astronomy Magazines . . . . . . . . . 95 APPENDIX B. REFERENCES . . . . . . . . . . . . . . . . . . . 96 APPENDIX C. PLOTTING SCALES . . . . . . . . . . . . . . . . . 98 APPENDIX D. EQUIPMENT CHECK LIST . . . . . . . . . . . . . . 99 APPENDIX E. DARK LIMB AND TERMINATOR DATA . . . . . . . . . 101 E.1 Terminator Dark Limb Separations . . . . . . . . . . . 101 E.2 Elongation Data . . . . . . . . . . . . . . . . . . . 104 APPENDIX F. REPORT FORMS . . . . . . . . . . . . . . . . . 106 F.1 ILOC material, where to get forms, blank forms . . . . 106 F.2 Asteroid Events . . . . . . . . . . . . . . . . . . . 106 F.3 Need to add explanation of IOTA terms at the bottom . 106 APPENDIX G. SAMPLE GRAZE PROFILE . . . . . . . . . . . . . 107 APPENDIX H. FIGURES . . . . . . . . . . . . . . . . . . . . 108 H.1 Figure Captions . . . . . . . . . . . . . . . . . . . 108 6.0 GRAZING OCCULTATION PREDICTIONS ____________________________________ Grazing occultation predictions and predicted lunar profiles are distributed to IOTA members by volunteers, known as computors, who prepare the predictions from data that, through 1993, were provided by the United States Naval Observatory. From 1994 on, IOTA plans to generate different basic graze data for the computors, who will still calculate and distribute detailed pre- dictions to IOTA members. These predictions give the expected paths for northern or southern limit grazes within a travel range the observer has selected. The grazes are rated based on the ex- pected ease or difficulty of observation, and information is pro- vided about the star. Each observer is provided with a summary page listing all predicted events in the time period for which individual limit predictions are included. A summary page is il- lustrated in Figure 6-1 and a recent example is at the top of the prediction file given here. The profile predictions, prepared from Watts charts of the marginal zone of the Moon, give the observer an indication of the distance to each side of the limit line where multiple events will be seen. 6.1 GRAZING OCCULTATION LIMIT PREDICTIONS __________________________________________ The grazing occultation limit prediction data are provided as ta- bles of longitude, latitude, and time for the predicted path, with the Moon's altitude and azimuth and the Sun's altitude also indicated. Each graze prediction has a heading section, which gives information on the star and the graze rating. The lo- cations of other observers selected to receive a particular graze prediction are given at the end of the tabular data. An example of a graze limit prediction is given in Figure 6-2 and a recent example is here. Starting in 1994, IOTA started using a different computer program for graze predictions. The format, illustrated with the example at the link above (The new program is called Grazereg, by Eberhard Riedel in Munich, Germany), is a little different from the description below of the old (pre-1994) predictions, but most of the same information is given. 6.1.1 HEADING DATA ___________________ LINE 1 These include the name; super standard station letter(s); city; country, state, or province; and maximum travel radii of the observer. For the purpose of graze predic- tions, much of the world has been divided into super- standard station regions, each 1000 miles (1609 km) in diameter. Different computors (volunteers who run the computer programs to do the actual predictions) calculate and distribute predictions for the different regions. Observers whose maximum travel radii cover more than one super-standard region receive more than one set of pre- dictions, one from each region their maximum travel ra- dius covers. LINE 2 The distance in miles of the closest point in the pre- dicted limit to the posiiton specified by the observer as his location, the Universal Time (UT) of central graze at that point, and the graze rating are given here. When the program computes these quantities, it terminates the path at low Moon altitude or when the Sun is above the horizon. It may be that the actual path will be closer to the observer than the number specified as the closest point, but low altitude or daylight may make observation impossible at the true closest point. Twilight and low Moon altitude are not considered in computing the rating (except for spectacular events), but interference by sunlit lunar features and daylight are considered. LINE 3 The third line is normally blank, but sometimes a special message appears here, giving information such as the computor's address, spectroscopic binary data, or a lunar eclipse message. LINE 4 This line gives the star's name (if any), Durchmusterung (BD or CD) number, USNO reference number (X, ZC, K, C, etc.), Smithsonian Astrophysical Observatory Catalog (SAO) number, and visual magnitude, followed by the UT date. The USNO reference number and the SAO number are the numbers that should be entered on observation re- ports. SAO numbers less than 17 are not true SAO num- bers, but are error codes for stars in the Third Astronomische Gesellschaft Katalog (AGK3) that are not in the SAO catalog. The name includes a proper name, Greek letter, Flamsteed number, variable-star designation, and other catalog numbers, in that order of preference, and depending on which, if any, are available. The other catalog numbers, indicated by the letters B., H1., G. and H. (for Bode, Heis, Gould, and Hevelius, respectively) should not be confused with the more commonly used Flamsteed numbers. The number immediately following "BD" or "CD" is the "zone" number, and is the star's approxi- mate declination in degrees. LINE 5 The line starts with the percent of the Moon's disk illu- minated by the Sun, where 0 is new moon, 100 is full moon, 50 is first or last quarter, 1 to 49 is crescent moon, and 51 to 99 is gibbous moon. If the Moon's appar- ent diameter is considered to be 100 units, the termina- tor crosses the Moon's equator at a point "percent sunlit" units measured along the terminator from the bright limb. The equator here is not the Moon's actual equator, but is usually very close to it; it is really the diameter line through the Moon's center pointing in the direction of the Sun. The term WAXING following the percent sunlit shows that the percent sunlit is increas- ing (between new moon and full moon), while WANING indi- cates decreasing percent sunlit (full moon to new moon). The term ECLPNG indicates that a lunar eclipse is in progress. During a lunar eclipse, the percent sunlit is the percent of the Moon's diameter not in the umbra at the central graze time given in the second line, so that 0 would imply totality. Note that the percent sunlit changes rapidly during the partial phases of an eclipse. The position angle of cusp is geocentric and only approx- imate; it is meaningless during an eclipse. DELTAT is the difference, Ephemeris Time minus Universal Time, a quantity with which observers are likely never to be con- cerned. Finally, it is noted whether the path is a northern or southern occultation limit. LINE 6 This line gives the error of the star's declination, and the phase of the Moon. The PROBABLE ERROR is a measure of the uncertainty in the star's position. There is a 50% chance that the star will actually be between the star's catalog declination + the error and the catalog declination ¯ the error. It should be used with the pre- dicted profile for determining the distance from the limit line for positioning observers. LINE 7 The SPECTRAL CLASS indicates the star's color. Stars of class O and B are blue; A, bluish-white; F, white; G, yellowish-white; K, orange; M, N, S, and C, red. The Sun (and therefore the Moon) is G2, yellow. Bright-limb grazes are easier to see if there is good color contrast, as for B and M stars. B, A, and F stars have the highest probability of being double. The POSITION SOURCE gives the catalog from which the star's position and other in- formation were taken. The most reliable catalogs are the Fourth Fundamental Catalog (FK4), its supplement (FK4S), and Washington N30 Catalog (N30). Less reliable are Robertson's Zodiacal Catalog (ZC), the Yale Zone Cata- logue (Yale University), and the AGK3, which sometimes have accumulated proper-motion errors amounting to well over 1", in spite of the stated probable error of declination. The Albany General Catalog (GC) positions are often poor, due to the early epoch of the catalog, and errors in excess of 2" occur. With some work, im- proved positions for GC and ZC stars fainter than magni- tude 5.5 can be obtained by consulting other catalogs, usually Yale. For stars north of declination ¯4 degrees, all available accurate astrometric catalogs were used , when the XZ catalog was created, to obtain the best pos- sible positions and proper motions on the FK4 system. The source for these stars is identified as "XZ". A pre- liminary version of the Zodiacal Zone Catalog (ZZ87), based on observations made around 1980 combined with re- measured and reduced 1930's data for proper motions, has been used for most SAO stars in the XZ. These FK4-based (B1950.0) catalogs will soon be replaced by FK5-based (J2000.0) catalogs, such as the FK5 itself and its exten- sions, the Positions and Proper Motions (PPM) catalog of the Astronomisches Rechen-Institut in Heidelberg, and the Astrographic Catalog Reference Stars (ACRS) catalog pre- pared at the U. S. Naval Observatory. Eventually, more accurate data will become available from the European Space Agnecy's Hipparcos satellite. IOTA has a list of program stars, including the brighter XZ objects, in the Hipparcos Input Catalogue (HIP), from which the observing program is taken. The PREDICTION BASIS is the USNO lunar ephemeris used in determining the prediction. The ob- server will rarely need to be concerned with it. LINE 8 Extra lines in the heading usually are for double-star data, including the separation(s) and position angle(s) for secondary and possible tertiary (third) components from the primary. If the star is listed in Aitken's double-star catalog, this is indicated, since his desig- nations are often used in double-star work. If the statement "THE POSITION SOURCE MUST BE CONSULTED FOR PO- SITION USED" appears, the position of the primary has usually been used for the prediction, unless the sepa- ration is less than about 3", and the secondary is nearly as bright as the primary. In this case, a mean position ( probably the center of light of the system) has been used. Offsets for mean position are computed by the pro- gram that produces the profiles. During lunar eclipses, a message describing the umbral distance is printed. 6.1.2 COLUMN DATA __________________ Twelve columns of data are given at regualar intervals of longi- tude along the graze path. The longitude is measured westward (negative numbers indicate east longitude) from Greenwich. WEST LONGITUDE The longitude in degrees and decimals of degrees. The intervals are usually 0.125 deg.in longitude, or 7.5', so they are at the margins of 7.5' USGS topographic maps. Data at 2.5', 5.0', and 10.0' intervals are also available. Below are listed the fractions of degrees at 0.125 and their equivalents in minutes and seconds for ref- erence with the topographic maps. +--------------+-------------+ | 0.875 | 52' 30" | | 0.750 | 45 00 | | 0.625 | 37 30 | | 0.500 | 30 00 | | 0.375 | 22 30 | | 0.250 | 15 00 | | 0.125 | 07 30 | | 0.000 | 00 00 | +--------------+-------------+ Table 1. Fractional Degree Equivalents NORTH LATITUDE The degrees and minutes of geodetic latitude where the predicted sea level limit crosses the longitude meridian of WEST LONGITUDE. Minutes of arc are probably easiest to use with topographic maps; if desired, the seconds of arc can be de- termined by multiplying the decimal part of the minutes by 60. UNIVERSAL TIME The coordinated universal time (UTC) of central graze as seen from the longitude and latitude. This is the time when the star is closest to the center of the Moon as seen from that location. MOON ALTITUDE Altitude of the star being occulted. The alti- tude is zero at the horizon and 90d at the zenith and is equal to 90d minus the zenith angle. At- mospheric refraction is not considered in the calculation of the altitude. MOON AZIMUTH Azimuth of the star being occulted. The azimuth is measured eastward from due north, so that 90d is due east, 180d is due south, and 270d is due west. TANZ The tangent of the zenith angle of the star. It is also the cotangent of MOON ALTITUDE and is used with MOON AZIMUTH to compute the amount the sea level limit must be moved for heights signif- icantly above mean sea level. This correction should be performed when the observer's height is more than 200 meters (aproximately 600 feet) above sea level. This is explained in "Elevation Correction" on page 35. SUN ALTITUDE The Sun's altitude in degrees and tenths of a de- gree. It is negative when the Sun is below the horizon and positive when above. Atmospheric re- fraction is not taken into account, so 0.6 deg. should be added when the altitude is within a degree of the horizon. Astronomical twilight be- gins when the Sun reaches -18d, nautical twilight begins when the Sun's altitude is -12d, and civil twilight when the Sun reaches -6d. PA OF GRAZE The position angle of central graze in degrees and tenths, measured eastward along the Moon's limb from north. North on the Moon's disk is de- fined to be from the right ascension meridian passing from the center of the Moon to the cur- rent (apparent) North Celestial Pole (NCP). CUSP ANGLE The angle measured in degrees around the limb from the cusp to the point of central graze, where N or S indicate whether it is from the north or from the south cusp, respectively. A negative number indicates that the point of cen- tral graze is on the sunlit limb of the Moon, while a positive number indicates the dark limb. The cusp is the intersection of the terminator with the Moon's limb, 90þ around the limb from the direction to the Sun from the center of the Moon. High mountains beyond this theoretical cusp often catch sunlight. During lunar eclipses, the cusp angle is meaningless and is replaced by the UMBRAL DISTANCE, the distance of the star from the center of the umbra, expressed as a percent of the radius of the umbra. U dis- tinguishes the umbral distance from the N or S given with cusp angles. 6.1.3 ENDING DATA __________________ Following the columns of data are statements indicating the ver- sion of the prediction program used, the prediction data source, and the name of the computor who ran the program. The last in- formation given is a result of the observer scan, indicating which other observers have been selected to receive these predic- tions, if any. In the scan, the observer's specified travel radii are given in miles after the latitude. An asterisk follow- ing the spectacular radius signifies those who expect to organize expeditions more often than join expeditions set up by others. The super standard station, in which the observer's position is located, is given after his name. The time of closest approach is in hours and decimals of an hour. Some, but not all, versions of the graze prediction programs gen- erate a one-page summary of all grazes. The observer's station coordinates are given in the heading. The summary includes cir- cumstances at the point of closest approach, including the longi- tude and latitude of the closest point given in the main list. Some summaries give the bearing of the limit (the azimuth of the motion of the shadow), the double-star code (under "DBL"), and the faintest magnitude for variable stars. 6.1.4 ELEVATION CORRECTION ___________________________ MOON AZIMUTH and TANZ can be used to make corrections for ele- vations above sea level. If the elevation above sea level is h (in feet or meters), the magnitude of the correction to be ap- plied, d, is given by the formula d = (TANZ) h where d is applied in the direction of the Moon's azimuth; see the small diagram (Fig. 6-3) in the upper right corner of the graphic shown here. If the limit is plotted and its direction or azimuth is measured, the distance, x, that the limit should be shifted, x measured perpendicular to the limit, is given by the formula: x = sin (D) d = sin (D) (TANZ) h where D is the difference of the Moon's and the limit's azimuth. This is illustrated in the map diagram in the upper left part of the graphic shown here (x is the distance from I to H shown on the diagram). When the altitude of the star is small, TANZ is large, and D is small (the azimuth of the limit is nearly equal to MOON AZIMUTH). For grazes north of latitude +31d, note that shifts are always southward (unless the elevation is below sea level). 6.2 PROFILE PREDICTIONS ________________________ Graze observers are provided with computer-generated profiles of the limb of the Moon as it is predicted to be observed at the time of the grazing occultation. The data used to compute the profiles are the Watts' Marginal Zone of the Moon in computer form, with additional corrections determined from occultation ob- servations. These profiles are not exact; they are only a pre- diction of what the observer might see. They are used by observers to determine where the best region is in the occultation path for observing. The profiles are for the point on the limit line closest to the observer. The Watts angle of central graze, position angle of the graze, and cusp angle are all shifted from the longitude and latitude printed on the pro- file to the longitude and latitude of the closest point on the limit line. The time of central graze printed under the profile is not shifted, and should not be used. The central graze time for the intended observation area should be obtained from the limit predictions. A recent example of IOTA's ACLPPP profiles is here. The format is almost identical to that described below. These profiles are now mostly quite accurate, especially if they are based on observed data (profile points coded as 3 or 4). The profiles that accompany the Grazereg limit predictions are almost as accurate but should be used only if an ACLPPP profile is not available; ACLPPP provides information about the "worst" terminator (see below), and double and triple stars, that is not in the Grazereg profiles. 6.2.1 PROFILE EXPLANATION (for ACLPPP profiles) __________________________ PROFILE HEADING DATA The following information is found in the heading: LINES 1-2 These are the scale in Watts an- gles. The values on the scale are printed in one-degree inter- vals from the Watts angle of central graze. LINE 3 This is the time from central graze in one-minute intervals. Vertical bars are generated for each minute through the plot, with the one for central graze so labeled. Negative numbers indicate minutes before central graze, and positive numbers min- utes after central graze. PROFILE PLOT Horizontal bars are drawn across the plot at regular intervals to help in scaling the distance from the predicted limit. One of the lines is the predicted limit, and is labeled as "PREDICTED LIMIT" on the right side, and "0" on the left side. The verti- cal scale on the right side is the number of miles or kilometers from the limit, while the scale on the left side is seconds of arc from the limit. A negative value is south of the limit and a positive value is north of the limit. The actual profile data are a series of letters, numbers, and asterisks that can look busy and bewildering. Some observers have found that drawing smooth curves through the points for the limb and for the predicted profile help in understanding the plot. There are at least two curves re- presented on each plot, and sometimes more. Each plot has a curve for the smooth mean limb of the Moon, and a more jagged plot for the predicted profile. In addition, the terminator may appear on the plot, if it is near the central graze. If the star is double, and both components will graze, the profile for the secondary (and terti- ary, if there is one) component will also be provided. The codes for the limbs and terminators are: D dark limb of the Moon B bright limb of the Moon T terminator W "worst" terminator, where two-mile (3-km) high lunar mountain peaks can be sunlit. Areas enclosed by W's will usu- ally be sunlit at the south limb, where high mountains are common, and will usu- ally be dark at the relatively smooth north limb The codes for the profile points are: * good limb correction, typically accurate to #0 . overlay '"' 15 1 fair limb correction, accurate to #0 '.' overlay '"' 3 2 meaningless limb correction, either ex- treme librations or in the Cassini re- gion (see "The Lunar Profile" on page 8). 3 good limb correction from previously ob- served graze data, accurate to #0 '.' overlay '"' 4 4 poor limb correction from previously ob- served graze data, accurate to #1"; 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 correction applied (*[or 0] + 5) 6 fair limb correction with an empirical correction applied (1 + 5) 7 meaningless limb correction with an em- pirical correction applied (2 + 5) P shifted limb of the primary component of a multiple star (when the star is not at the position used for the limb predic- tions, which is often the case when a center-of-light, or mean position, is used) S shifted limb of the secondary component of a multiple star R shifted limb of the tertiary component of a multiple star When drawing curves through the plotted points, the following groups should be con- nected together. A different color pen for each group makes the profile more readable. B AND T enclose bright area of the Moon D encloses dark mean limb W encloses area where sunlit peaks may exist and cause observing dif- ficulties ("worst" terminator) *,1-7 the predicted limb for mean star position P the predicted limb for a primary star not at the mean star position S the predicted limb for a secondary component R the predicted limb for a tertiary component At the bottom of the profile are seven lines of additional information about the profile and the star. LINE 1 The date, time and latitude libration of the graze is given. LINE 2 The star number in the ZC or X catalog, the version of the USNO profile prediction program that generated the data for the plot, and the longitude libration of the graze are given. The time is for the "standard" longitude given in line 5. LINE 3 This line gives the limit (northern, southern) of the graze, the vertical profile cor- rection (VPC) in seconds of arc (north is positive), and the po- sition angle of the graze at the "standard" longitude given on the 5th line. LINE 4 The Watts angle of central graze (for the point in the limit closest to the observer), graze height (of the predicted limit from the mean limb in seconds of arc, with positive values indi- cating a shift away from the center of the Moon), the cusp angle, and the name of the per- son running the profile program are given. LINE 5 The longitude for the basic pre- diction data (this either is the closest point in the predicted limit, or west of the closest point), the horizontal profile scale (HPS) in minutes of time per degree of Watts angle, the position angle for the point in the limit closest to the ob- server, and the person for whom the profile was produced are given. LINE 6 The latitude for the basic pre- diction, the vertical profile scale (VPS) in seconds of arc per mile or per kilometer, the distance of the observer to the limit line, and the observer's home location are given. LINE 7 The empirical corrections ap- plied are identified. LINES 8-9 Additional information is given if the star is multiple. The type (double, triple), the dis- tance of the primary from the mean position, the magnitude, separation, position angle, and the vertical and horizontal shift in the profile for each component are listed. Vertical shifts are given in miles (or kilometers) and seconds of arc, horizontal shifts in time. In- formation is given for compo- nents that do not show on the plot. 6.2.2 LIMIT PREDICTION AND PROFILE USE _______________________________________ Observers can use the grazing occultation predictions, described later in this section, and the predicted profiles to calculate the approximate sequence of events that will be visible from any point in the vicinity of the northern or southern limit of an occultation. Therefore, observers can position themselves in the best locations near the limit to see the most spectacular se- quence of events to obtain the most useful data. 6.2.2.1 TOPOGRAPHIC MAPS First, the observer should examine a map of his/her state or re- gion using the computer predictions to determine an approximate location where the graze might be observed. One or two alterna- tive locations might be selected in case bad weather or other circumstances prevent observation at the first location. Aer- onautical charts obtainable at any airport, topographic index maps, atlas maps, and even the rare road maps with latitude and longitude lines can be used for the selection of approximate lo- cations. The 1:250,000-scale topographic maps available for most areas show virtually all roads, cover a large area, and can be used for most graze planning work. But, if possible, the ob- server should obtain the most detailed topographic maps that cover the selected area, so that observation sites can be chosen near features shown on the maps. Index maps are necessary for ordering the topographic maps. They may also give a listing of local map dealers from which the maps can be purchased, and li- braries that may have them. Topographic maps are discussed in more detail in Section 4. 6.2.2.2 GRAZE PATH PLOTTING After obtaining the best map(s) for the location(s) selected, the observer plots the (sea level) limit line directly from the pre- dictions. To do this, the longitudes at the east and west edges of the topographic map are found in the limit predictions, and plotted at the points (A and B in Figure 6-4 in the upper left of the graphic shown here) where the limit crosses the edge meridians on the map (using the NORTH LATITUDE, or 2nd and 3rd, columns of the predictions). The line, AB, be- tween these two points is the sea level limit line. Both points will often not be on the map and it may be necessary to tape a piece of paper to the map to extend one of the longitude meridians. Scales to facilitate plotting are given in "Appendix C. Plotting Scales" on page 98 (not included here, but they can be provided on request as PostScript files that can be read and printed with Ghostview); scales for 1:250,000 and 1:125,000 maps are in a Word document here. If necessary, and always for elevations above 200 meters or 500 feet, the limit line should be shifted to take into account the elevation above sea level. The limit lines will always be shifted south for high elevations in latitudes north of 31 deg. N (unless the elevation is below sea level). MOON AZIMUTH and TANZ in the graze limit predictions are used to compute the corrections, as described in "Elevation Correction" on page 35, using Eqn. 6-1. The sea level and corrected limits are shown in Figures 6-3 and 6-4 in the upper part of the graphic shown here. As explained in "Elevation Correction", if the elevation above sea level is h (in feet or meters), the magnitude of the correction to be ap- plied, d, is given by the formula d = (TANZ) h where d is applied in the direction of the Moon's azimuth. The shift x is negative if the shift is toward the south for heights above sea level. An example of a corrected limit line is shown in Figure 6-4. The instructions for producing such a correction are as follows: 1. Using a protactor, plot the Moon's azimuth (eighth column of the predictions) at point A; it is angle G or angle VAH, al- ways measured clockwise from north. 2. From the topographic chart, determine the approximate average elevation where observations will be made; this is h (shown in Figure 6-3). Multiply h by TANZ (ninth column in the predictions) to get d, the distance the point A should be shifted in the direction of the star's azimuth. The distance AH is d in Figure 6-4; therefore, since G is the Moon's azimuth, H is a point in the elevation-corrected limit. F or angle VAI is the azimuth (or bearing) of the limit and can be measured with a protractor; therefore D or angle IAH is the difference of G and F. 3. The perpendicular shift of the limit, x or HI, to take elevation into account is then (AH) sin(D), or (d) sin(D), or (h)(TANZ)sin(D). 4. Now, draw the line JK parallel to the limit line AB through H; JK is the northern limit corrected for elevation above sea level. In the example, if sin (D) TANZ is given in the predictions, the process is simplified, since the Moon's azimuth does not need to be plotted. Just obtain x by multiplying h by sin(D) TANZ, and plot the point H a distance x perpendicular to the sea level limit line, on the north side of the limit if sin (D) TANZ is positive and on the south side if it is negative. 6.2.2.3 PROFILE USE The profiles are used to select the region of the graze path where observers should be concentrated. Once the graze path has been plotted, the observers can be placed north and/or south of the predicted limit where the tracks across the profile would in- dicate that multiple events will be seen. For any location within a few miles of the predicted limit the star will appear to move in a horizontal line across the profile chart, as shown in the example in Figure 6-5 in the lower part of the graphic shown here. The region of the profile chart where two or more mountains will occult the star is indicated by two dashed horizontal lines on the profile, and is labeled "L". This is the suggested range. It should be extended north and south by the amount W (in seconds of arc, or left hand scale on the pro- file), which is the probable error of the star's declination; it is given in the heading of the limit predictions. This makes the suggested range NM in Figure 6-5. The range in miles or kilome- ters is determined by using the vertical scale on the right side of the profile. With this scale, the suggested range NM, the predicted limit line corrected for elevation, and the perpendic- ular distances, XM and XN (Figure 6-4), from the limit line to the edges of the range can be determined. These are used to cunstruct the lines through points N and M that are parallel to the corrected limit JK. These lines are LP and QR, respectively. The observing sites should be selected between these two lines. In the example in Figure 6-4, there are three sites along a road within the range. Expeditions involving two or more stations should usually try to spread vertically across the path by about 1.0" of lunar graze height. This is always more than a mile in dis- tance perpendicular to the graze path. But if the predicted range of multiple events is very narrow, then a narrower range can be covered, especially when the profile is based on previous graze observations (3's points). Once the sites have been selected, the next step is to determine the time of the earliest event as seen from the sites. The Uni- versal Time of central graze is determined by interpolating the times given in the predictions between the longitudes of A and B in Figure 6-4. Near the top of Figure 6-5, the time with respect to central graze is given in minutes, with negative values being times earlier than central graze time. The earliest event in the selected range on the profile chart is where the dashed line marking the lower edge of the suggested range intersects the lunar profile, usually before central graze. In Figure 6-5, it is at S, which is a disappearance about 1m 20s before central graze. So, observers would expect to see their first event about the time of central graze minus 1m 20s. Ob- servers should be ready to time events about a minute or two be- fore the expected time of the first event. Unexpected shifts (prediction errors) can cause events to be early. Using the profile chart, it is hypothetically possible to predict the sequence of events as seen from the three sites. The three horizontal lines labeled 1, 2, and 3 in Figure 6-5 are plotted at the perpendicular distances of sites 1, 2, and 3 from the cor- rected limit line in Figure 6-4. Where these horizontal lines intersect the profile is when, relative to the time of central graze, the events will occur. In the case of a known double star where there is a possibility of observing the secondary, two lunar profiles will be provided on the profile chart, one for each component. Observers can use the profiles to position themselves to observe grazing phenomena of either or both components. In general, the expedition leader should station most observers in the zone where multiple events can be seen for the component whose profile is deepest into the lunar shadow. Then, most observers should see some complete dis- appearances of the star, which are usually easier to observe than the partial drop in light when one of the two stars disappears. However, if the difference in component magnitude is 1.5m, it is best to position observers for the profile of the brighter component (indicated by P, for primary component). Often, the two stars will be so close that observers will not be able to tell that the star is double until the graze begins. Due to the grazing geometry, the step-wise events sometimes seen dur- ing total occultations of double stars are much prolonged. Visu- ally observed grazes in flat lunar terrain are capable of a resolution of 0.01", nearly equivalent to the resolutions obtained in photoelec- tric work with total occultations. Several close double stars have been discovered during grazing occultations. However, grad- ual or fading events seen during grazes are more often due to grazing enhancement of Fresnel diffraction at the Moon's limb rather than to stellar duplicity, which is more noticeable by events occurring in distinct steps. PROFILE CORRECTION FOR LONGITUDE: Each profile is prepared for a specific position angle of central graze, as given on the pro- file; it is automatically adjusted from the position angle at the "standard" longitude to a point in the limit closest to the ob- server's station. If observations will be made from a different location (for example, if weather forces an observer to travel far to the east or west of the closest point), the profile will require correction, which amounts to shifting the geometry of the observer and lunar surface lines. Motion in longitude has two effects on grazing occultation position angles: a shift along the limb, which is the dominant effect, and motion along the sur- face, a much smaller effect near the lunar poles, but dependent on the lunar motion and librations at graze time. There are two methods for translating a profile to a different longitude. One, which will not be covered here, involves drawing a new reduction profile using data from the USNO OCC program. The other method requires drawing a new line of central graze (CG) and a new predicted limit line on the existing profile for the distant expedition. The Watts angle (WA) of the new line of central graze (WAn) is calculated by the equation given below; WA has the same scale and direction as the position angle, PA, but is virtually always off- set with respect to it. Let us define the following quantities: PAO the position angle of CG for the original profile (given as ]POS ANGLE XXX.XXX PROFILE FOR ¼¼¼Ø in the footer data). PAN the position angle of CG for the distant expedition (as de- termined from the limit prediction). WAO the Watts angle of CG for the original profile. Then we have the relation: 'WA' sub n = 'WA' sub o + ('PA' sub n - 'PA' sub o) where WAn is corrected by 360 deg. if negative or -360 deg. Now draw a new line of CG for the distant expedition vertically at an WA of WAn. The new limit's intersection point with the new CG line is determined by maintaining the limit line to mean limb distance (the HEIGHT given in the footer data) for both expe- ditions. Because of the vertical exaggeration (VE) of profile plots, the new predicted limit line will slant with respect to the original, especially if the two expeditions had a significant r difference. The slope, s, of the new limit is determined as follows; let 16.2766 the number of arcseconds that 1d of the Moon's limb subtends at its mean distance. It is the product of 932.58, the mean apparent angular radius of the Moon in seconds of arc, as subtended from the Earth, and 0.01745329, the conversion factor from degrees to radians. R the ratio of vertical distance on the profile (miles or kilometers) to horizontal distance for one degree (1þ) of WA (a measured quantity). VPS the vertical profile scale given in the footer data. Then the vertical exaggeration is: 'VE' = < 16.2766 R > over 'VPS' and eqn. 6.4 's' = tan (PA sub o - PA sub n) times 'VE' The time scale, or horizontal profile scale (HPS), will change if the two locations are a large distance apart. If they are within several hundred miles of each other, the change should be small. If no HPS is available for the distant expedition, a first-order correction can be made. The equation below approximates the amount that the Earth's rotation vector subtracts from the lunar orbital vector, based on the lunar altitude and the observer's latitude; the calculation is not valid over extreme distances. Define: AN the lunar altitude of the distant expedition, as deter- mined from the limit prediction; extrapolate if neces- sary. AO the lunar altitude of the original expedition. D the average of the geographical latitudes of the two ex- peditions. HPSO the HPS of the original expedition. HPSN The HPS of the new expedition. Then the new horizontal profile scale is: 'HPS' sub n = 'HPS' sub o + 0.92 (sin a sub o - sin a sub n) cos Note that HPSn is applied in the original horizontal direction, not the slanted direction of the new limit. 7.0 ORGANIZING GRAZING OCCULTATION EXPEDITIONS _______________________________________________ Grazing occultations are most successfully observed when a group of people meets at a prearranged site and sets up a chain of ob- servers across the graze path. Someone must obtain the graze predictions, select the best site, notify other observers, and assign observing locations before the graze. Afterward, someone must determine the location of each of the observing sites, re- port the locations, and collect and report the observations. The graze organizer obviously bears the burden of the work. This section is intended to detail the steps involved in organizing a successful graze. A single observer, acting on his own, can ob- serve a chord across the graze, and these data are useful, espe- cially if they can be combined with other cords obtained by observers to the east or west during the same graze. However, the resolution obtained by having a line of well-spaced observ- ers, even if only a few, across the predicted graze path, is much better, and worth the time it takes to set up such an event. Ob- server safety should be the top priority of all expedition lead- ers. The articles discussing expedition safety (Occultation Vol., 5, No. 11, 1993 March, pp. 284-286) should be read by all graze expedition leaders. 7.1 PREPARATION ________________ The time and effort needed for organizing a graze will vary de- pending on the number and experience of the people expected to observe. As a general rule, the more people who want to observe, the more elaborate the preparations must be. The graze organizer will need to select the sites, notify the observers, often help the observers find equipment and transportation, and teach the new observers what to do. 7.2 SITE SELECTION ___________________ The graze organizer first needs to obtain predictions of the grazing occultations for his local area. These are available to members of IOTA. Also, predictions for the brightest events are published in Sky and Telescope, the Handbook of the Royal Astro- nomical Society of Canada, etc., for the areas those publications cover. A graze organizer, however, will usually want the predic- tions distributed by IOTA. These are the predictions discussed in "Grazing Occultation Predictions" on page 29. The graze predictions can be used to determine approximately where the grazes might be observed. Any map of the state or gen- eral region that gives latitude and longitude can be used for predicting where the grazes can be observed. Aeronautical charts obtainable at airports, topographic index maps, atlas maps, maps from National Geographic, and even the rare road maps with lati- tude and longitude lines are often suitable. The 1:250,000 maps from the USGS and most other national mapping agencies can also be used. The predicted graze limit line at sea level can be plotted on the maps directly from the predictions. If the edges of the map cor- respond to longitudes in the predictions, the organizer can plot the points where the limit crosses those edges by using the lati- tudes that accompany the edge longitudes. The plotting of limit lines and correcting them for elevation when necessary, are dis- cussed in "Profile Predictions" on page 35. The region of expected events can be determined from the pre- dicted profile, as discussed in "Grazing Occultation Predictions" on page 29. This region is the area near the predicted limit where observers should be stationed. It will be more than a mile (1.6 km), and sometimes several miles (¼5 km) in length. The ob- serving sites should be selected to fall within this suggested range. It should be stressed that the suggested range and the profile are predictions of what is going to happen, and that in- accuracies in the predicted stellar and lunar positions, as well as the lunar profile, will mean that the exact location having the most events cannot be precisely predicted. All locations within the suggested observing range will have approximately the same chance of seeing multiple events, with the edges having slightly less chance. Features to consider when selecting the sites from among the can- didates are the ability to see the Moon at the time of graze from the site, the accessibility of the site to the observers, light- ing, parking, traffic if the site is a road, what permission is needed if the site is private property, and whether public au- thorities will need to be notified if the site is public prop- erty. (It is advisable to notify local authorities, such as the sheriff's office, or the office of the local police force, espe- cially for expeditions with three or more sites.) Also, the ob- servers will need reference points to locate their stations when their positions are determined. Observers will want to be able to move their equipment to find the best observing locations for grazes at low Moon altitude. It may not be possible to determine the effects of local obstacles, such as houses, trees, and hills until actually arriving at the graze location to observe. If the observing sites chosen are along a road, observers with cars will need places to park completely out of the traffic. The shoulder may be sufficient, but the smaller country lanes may not have them. Also, if the road is heavily traveled by trucks, the observers will need to be well away from the traffic to avoid problems from equipment vibration and traffic noise. Railway tracks and railway rights of way are not public property; they are the property of the railroad. They should not be used by graze expeditions without permission. As a practical matter, even if the observers will not be in the right of way but only nearby, it might be wise to contact the rail line to determine if there are any trains scheduled near the time of the graze. The vibrations from a train passing nearby can shake a telescope so that observations are impossible. Public parks may be closed after sunset. If accessible, they are often very good sites, because they do not have many lights or much traffic. The organizer may want to inspect the sites before the graze, ei- ther to check their suitability, or to mark the locations se- lected for the sites. If the observing location selected is devoid of landmarks, the observers are not going to find their stations unless they are marked. This can be done with marked or numbered stakes pounded into the ground, cards tied (not nailed, that is not always legal) to utility poles. Water-soluble spray paint or chalk can be used to write station numbers at the side of a road. 7.2.1 OBSERVER NOTIFICATION AND PREPARATION ____________________________________________ Notification of the observers can be as simple as a telephone call, or through a local astronomy club newsletter, or through graze notices sent to anyone who has expressed an interest. The notification should tell the observers when and where the graze will be, a meeting time and place, a telephone number to call for notice of weather cancellation, and what equipment they will need for observing. The graze organizer will want to know who is in- terested in observing a particular graze, to help in planning the observations. 7.3 EXPEDITION REPORTING _________________________ The expedition leader needs to collect the observed times, or the unreduced observation tapes, for all observers. Also, the accu- rate geodetic coordinates for all successful stations must be de- termined (see "Accurate Topocentric Position Determination" on page 18), and the expedition leader usually must take charge of that task as well. See "Appendix F. Report Forms" on page 106 for information on how to prepare the final expedition report. 7.4 APPROXIMATE REDUCTION AND SHIFT DETERMINATION __________________________________________________ The expedition leader should make an approximate reduction of the observations by plotting the observed timings made by each ob- server on the predicted profile. This allows an estimate to be made of the shift of the graze shadow from its nominal, or pre- dicted, position. The graze shift is the distance and direction the predicted shadow of the Moon would need to be moved on the ground to match the actual shadow observed during the graze; its scale is in seconds of arc subtended at the Moon's mean distance and is the vertical scale on the right side of IOTA's ACLPPP pre- dicted profiles. The shift may be thought of as the residual of the observations for the entire expedition; it is used to warn future expedition organizers of stars with poorly determined po- sitions and to identify poor quality Watts limb correction data (which are used to generate profile plots). This section de- scribes the procedures used to plot graze observations on the predicted profile in order to determine this shift. Plotting the expedition's data is the best way to verify that all stations of a graze agree with one another. Plots can also reveal large, un- predicted mountains or valleys on the lunar limb that should be added to the data set used in predicting profiles. All processes should be applied to every successful station of the expedition, even though the process is described as singular here. If a value is needed from the limit prediction (the sheet that gives the latitudes and longitudes of points in the limit), it should be determined for the specific longitude of the actual expedition. This discussion assumes that an IOTA Automatic Com- ____ puter Lunar Profile Printing Program (ACLPPP) profile is being used; by convention north is at the top and time increases toward the right for these plots. Plotting the observations on the predicted profile is very much like the process of determining predicted event times described in "Grazing Occultation Predictions" on page 29. 7.4.1 CORRECTION OF PROFILE TO ACTUAL OBSERVING LOCATION _________________________________________________________ The predicted profile is generated for a point in the limit near the closest approach to the coordinates the observer specified when requesting IOTA predictions; this is usually one's home. If no point was specified, then an approximate location would have been established by IOTA based on the mailing address (latitude, longitude, and elevation), along with very small (3-mile) default travel radii for marginal, favorable, and spectacular grazes; one should contact the IOTA secretary giving specific values if the defaults are not acceptable. If the graze was not observable at the point of closest approach due to a low lunar altitude or to strong twilight or daylight there, then the profile will be gen- erated for the first point in the limit at which the graze can actually be observed. A correction will usually be needed if the actual location of the expedition was either up or down track from the point for which the profile was generated. The position angle of graze for the actual location of the expedition, PA(a), is determined from the limit prediction (see Figure 7-1). The position angle for which the profile was generated, PA(p), is given in the footer of the profile as "POS ANGLE XXX.XXX PROFILE FOR (your name)" (see Figure 7-2). If PA(a) and PA(p) are within approximately 0.2 deg., the correction is small and may be neglected. For a difference >0.2 deg., a new line of central graze and a new sloping predicted limit line should be drawn on the profile for the actual location.(7) It is necessary to use the Watts angle scale to position the new line of central graze, since position angle is not graphed on the profile; the two have the same scale and direction, but are usu- ally shifted with respect to one another. Let WA(p) be the cen- tral graze Watts angle for which the profile was plotted (given in the footer data); then the Watts angle of the new line of cen- tral graze, WA(a), is given by the equation (similar to Eqn. 6.2): WA(a) = WA(p) + lb PA(a) - PA(p) rb If WA(a) does not fall within the range of 0 to 360d, it should be normalized by either adding or subtracting 360. A new line of central graze for the actual location is then drawn vertically at a Watts angle of WA(a). The new limit's intersection point with the new central graze line is at the same distance above the mean limb as the original limit was above the mean limb. Due to the vertical exaggeration (VE) of profile plots, the new predicted limit line will slope with respect to the original profile's limit. Slope is defined as the change in the vertical (y) coordinate divided by the change in the horizontal (x) coordinate. The vertical exaggeration and slope are then de- termined as described in "Profile Correction for Longitude" on page 44. When using this method to combine the results of two or more ex- peditions on one profile, the profile of one of the expeditions should be considered the "original" profile (the one calculated for the "point closest to home" in the previous discussion) and the other expedition's profile should be considered the "actual", or "new" location. More than two expeditions may be combined by 7 This procedure can also be used to combine the results of separate graze expeditions on one predicted profile. having multiple "actual" locations. If the HEIGHT values listed in the footer data of the profiles differ significantly, the dif- ference should be applied when plotting the actual limit's verti- cal position. (These HEIGHT values represent a set of global empirical vertical corrections applied to the lunar mean limb at the time the profile is generated). The same is true for the HPS; since its value is available for both locations when combin- ing results, any difference between expeditions should also be taken into account when plotting the observations. A fictitious example using an actual graze prediction follows (no expedition was actually attempted). Figure 7-2 is a profile gen- erated for a position angle PA(p) of 345.38 (POS ANGLE 345.380 PROFILE FOR DON STOCKBAUER). If an expe- dition had actually obtained data at longitude 99.75 deg. West, the actual position angle of graze, PA(a), would be 344.7d (from the limit prediction, Figure 7-1). The Watts angle for which the profile was generated, WA(p), is 5.29; the Watts angle at which to draw the new line of central graze for the actual lo- cation, WA(a), is 5.29 + 344.7 - 345.38 = 4.61 deg. Since the predicted limit was scaled off the top of the northern boundary of the plot, it is drawn in as a dotted line. The original limit is 0.77 miles north of the mean limb (repres- ented by the series of D's), so the actual limit must maintain this distance above the mean limb at its new position. The ratio of one mile to one degree of Watts angle is measured as (1.04/0.74) inch, which equals 1.40. The VPS is given as 0.85" per mile in the profile's footer data. The vertical exagger- ation is (see Eqn. 6.3): VE = ( 16.2766 * 1.40 ) over 0.85 = 26.81, and the new limit's slope (from Eqn. 6.4) is: s = tan % ( 344.7 - 345.38 ) * 26.81 = -0.318. The new limit for the actual location slopes 0.318 unit down (south) for every unit of distance to the right (toward increas- ing time). "Graze height" is defined as an observer's perpendic- ular distance on the ground to the elevation-corrected limit, with north positive by convention (not to be confused with the HEIGHT shown in the profile's footer mentioned earlier). In Fig- ure 7-3, the graze height for an observer at point N would be NF; since N is south of the corrected limit, it is a negative quan- tity. In Figure 7-2, parallel lines representing graze heights of ¯1 to ¯4 miles are also drawn. These graze heights are offset vertically on the profile from the new sloping limit, not at a right angle to it. The graze height scales along the right-hand border of the plot (in miles or kilometers) and the left-hand border (in seconds of arc) should be relabeled with the new val- ues; the new values are circled in the example. 7.4.2 CORRECTING THE SEA LEVEL LIMIT PREDICTION FOR ELEVATION ______________________________________________________________ The limit prediction is calculated for sea level and needs a cor- rection applied for other elevations. No correction is needed if all stations were less than 300 feet above sea level. If all ob- servers were situated at approximately the same elevation (to within 150 feet), then an average correction based on their aver- age elevation may be used. The elevation correction (EC) is de- rived as follows: a vector is constructed originating at the elevation of the observer's location directed either toward or away from the star, so positioned that it terminates on the sea level limit (constructing the vector in this manner will give north as a positive correction, and south as negative). The product of the elevation and the tangent of the star's zenith an- gle (TANZ) gives the magnitude of this vector projected onto the horizontal plane. The sine of the difference between the limit's bearing and the lunar azimuth (SIND) times the magnitude of the vector in the horizontal plane gives the elevation correction perpendicular to the sea level limit. The elevation correction is given by Eqn. 6.1. If the limit prediction gives the product SIND * TANZ, then the factor SIND need not be computed. (TANZ is always provided in the limit prediction either by itself or as a factor of the prod- uct SIND * TANZ.) To calculate SIND, the Moon's azimuth for the location of the ac- tual expedition is determined from the limit prediction. If the prediction does not give the bearing of the limit, then it must be measured using the plot of the limit on the topographic map. It has values between 0þ and 180þ and is measured eastward from north (e.g., north = 0, east = 90, and south = 180þ). Then SIND = SIN (limit's bearing - Moon's azimuth), paying attention to signs. The corrected limit should be drawn perpendicular to the sea level limit at a distance equal to the magnitude of the elevation correction; its direction is north of the sea level limit if the correction was positive, or south if negative. "north" and "south" here only mean on which side of the sea level limit the corrected limit should be drawn; the correction is always applied at a right angle to the sea level limit, not due north or south (unless, of course, the sea level limit has a bearing of 90þ). As a check, the corrected limit should always be in the direction of the Moon's azimuth from the sea level limit for positive ele- vations, and opposite it for negative elevations (this can be checked by plotting the azimuth of the Moon beside the predicted limit on the map). The elevation correction's magnitude can range from zero to several times the observer's elevation. For locations at positive elevations north of latitude 31þ North, the corrected limit will always lie south of the sea level limit. The graze height is then measured for each station. Figure 7-3 represents a section of the topographic map used for the fictitious graze in the previous example. AB is the sea level limit, angle VAB is the limit's bearing, angle WBH is the Moon's azimuth, HB is the elevation correction's projection onto the horizontal plane, and HE (the elevation correction) is the correction's projection perpendicular to the sea level limit. The elevation of the observer is 2300 feet; TANZ from the limit prediction (Figure 7-1) is 3.67, the sea level limit's bearing is measured from the map as 105.8þ, and the lunar azimuth from the limit prediction is 282.5 deg. The elevation correction HE is: sin % ( 105.8 - 282.5 )%%degrees * 3.67 * 2300%%feet = -486%%feet The corrected limit is drawn as line CD, 486 feet perpendicular to the sea level limit; since the correction is negative, it is drawn on the south side of AB. 7.4.3 CALCULATING THE TIME OF CENTRAL GRAZE ____________________________________________ The Coordinated Universal Time (UTC) when the line of sight to the star passed closest to the apparent center of the Moon's disk is then calculated for each observer; this is called the time of central graze, or just central graze. If one uses the method de- scribed in "Calculating the Shift Value" on page 55 to determine the shift (that of fitting the profile to the observations by al- lowing both horizontal and vertical movement), then the following simplified method will suffice to determine central graze. In Figure 7-3, central graze for a site at N would be determined by interpolating for the time at point R (N's perpendicular projection onto the sea level limit) using the times given in the predictions for points A and B. If a precise absolute time of central graze is needed, then station N's location would need to be projected onto the sea level limit using the Moon's azimuth instead of a perpendicular projection; that point would then be used for the interpolation or extrapolation. This is due to the fact that curves forming equal times of central graze propagate in the direction of the Moon's azimuth, which is not usually at a right angle to the limit. However, the simplified method has traditionally been used because if the lunar altitude is low (as in this example), the limit's bearing and the lunar azimuth be- come nearly equal. The projection distance can then become quite large; the data fitting method described in "Calculating the Shift Value" on page 55 avoids this problem. If all central graze times for all stations of the expedition fall within a one second time interval, then an average time may be used to repre- sent them all. In Figure 7-3, point R is 0.139 of the distance from point A to B. The time at point A is 5:23:45.6 UTC (determined by interpo- lating for longitude 99 deg. 47' between 99 deg. 52.5' and 99 deg. 45'; point A is not at a standard topographic map boundary); the time at B is 5:23:46.6. Interpolating for the time at point R gives 5:23:45.7. 7.4.4 PLOTTING THE OBSERVATIONS ON THE PREDICTED PROFILE _________________________________________________________ A line is then plotted that corresponds to the station's graze height using the mile or kilometer scale on the right-hand side of the profile, or the slanting graze height coordinate system for an adjusted profile. This line represents the track of the line of sight from the observer to the star made across the pre- dicted profile. The differences between the observed time of each event and the central graze time are computed in minutes and fractions of a minute. The station's timings are plotted along this line using these time differences; the scale used is the one of minutes from central graze given at the top of the profile. Negative time differences are before central graze (to the left); positive times are to the right. In Figure 7-2, the observer was stationed at a graze height of -1.43 miles, or -1.22" (i.e., 1.43 miles, or 1.22" south of the elevation corrected limit). The observer had a disappearance (D) at 5:22:17.7 UTC and a reappearance (R) at 5:24:55.7, which gives time differences of -1.467 minute and +1.167 minute, respec- tively. The time differences are marked on the observer's graze height line by measuring horizontally to the adjusted line of central graze, which is at Watts angle WA(a). A break in the line is used to show the period when the star was behind the Moon. 7.4.5 CALCULATING THE SHIFT VALUE __________________________________ In Figure 7-2, the scale on the left hand side of the profile (the unlabeled numbers) is in arc seconds and is the one used to measure the shift. Note that because this profile was adjusted, the arcsecond scale was also adjusted and is now represented by the circled numbers. The period when the star was observed to be behind the Moon is higher (more northerly) than the predicted profile would indicate, so a north shift was seen (i.e., the pre- dicted profile would have to be shifted north to match the obser- vations). To measure the shift accurately, the predicted profile information is transferred to a translucent medium such as trac- ing paper or a clear transparency. The tracing is moved horizon- tally and vertically with no diagonal skewing with respect to the original until the predicted profile on the tracing fits the ac- tual observations best. This takes liberties with the time of central graze by making it a free parameter, but a better fit is almost always obtained using this procedure because of various inaccuracies present in the profile generation process. However, if the observations are shifted by a large extent with respect to the calculated time of central graze (by about 20s or more), then either a mistake was made or the prediction was grossly in error; this should be noted when making an observation report. The shift (in tenths of an arcsecond) can then be measured directly from the amount the overlay had to be moved. Its direction is north if the overlay was moved upward, or south if moved down- ward. Both the magnitude of the shift and its direction should be reported. For this example, an accurate measurement of the shift gives 0.5" north. The shift can also be calculated numerically. If this is done, an average should be taken based on individual values measured from 0.2 deg. bins of Watts angle, not on individual values measured for each event timing. From time to time it is suggested in Occultation Newsletter that an empirical correction be applied to a certain class of profiles to better position graze stations based on trends in the graze shifts noticed by recent expeditions. These suggested shifts are for positioning observers only and should be ignored when comput- ing and reporting the shifts for individual expeditions. IOTA's grazing occultation coordinator can supply report forms and instructions on their usage upon request, and can assist ob- servers with any aspect of the topics covered in this section. ______________________________________________________________ Click here to obtain the prediction files for grazes in the northeastern U.S.A. (within 300 miles of Greenbelt, Maryland) for 2003. Unzipping the file will produce 5 prediction files: areg03.153 Grazing occultation limit predictions from Grazereg argn03.153 ACLPPP profiles for the grazes in areg03.153 srsm03.153 The summary list at the top of areg03.153 alcm03.153 Asteroidal/planetary appulse local circumstance predictions for Greenbelt, Maryland aoccn153.003 Predictions of total lunar occultations for Greenbelt, Maryland produced with Occult Click here for plotting scales (in minutes of arc of latitude and decimal fractions) for the DeLorme Maryland/Delaware and Virginia Atlas and Gazetteers.