PREFACE

Since 1949, the U. S. Naval Observatory has published a special series of circulars containing detailed information for upcoming solar eclipses. These predictions were provided as a public service and were of vital importance to the international astronomical community in the planning and execution of successful eclipse expeditions. Unfortunately, the USNO Circulars were discontinued in 1991.

This has left a real and tangible void for detailed and accurate predictions for future solar eclipses. The information is not only of great interest and value to the scientific community in general, but to NASA in particular. For instance, Hubble Space Telescope passed through the Moon's shadow during the recent total solar eclipse of 11 July 1991. Without adequate advanced warning of this event, the eclipse would have had serious consequences on HST's energy budget in the rapidly diminishing sunlight. Furthermore, solar eclipses are known to have important effects on Earth's ionosphere and therefore play a significant role in the interaction and understanding of the Earth-Sun environment. Finally, NASA has a history of participating in various solar eclipse experiments through both ground based and aerial (i.e. - Kuiper Airborne Observatory, sounding rockets) investigations.

With the issuance of this NASA Reference Publication, the authors plan to continue the tradition of providing special bulletins containing extensive, detailed and accurate predictions and meteorological data for future solar eclipses of interest. The eclipse bulletins are provided as a public service to both the professional and lay communities, including educators and the media. In order to provide a reasonable lead time for planning purposes, subsequent NASA RP's for future eclipses will be published 18 to 24 months before each event. Single copies of these RP's will be available at no cost, provided a written request is received after publication. A special request form for the eclipse RP's may be found on the last page of this publication, and may be returned to Jay Anderson. Comments, suggestions, criticisms and corrections are solicited in order to improve the content and layout in subsequent editions of this publication series, and may be sent to Fred Espenak.

Permission if freely granted to reproduce any portion of this Reference Publication, including data, figures, maps, tables and text (except for material noted as having been published elsewhere, or by persons other than the authors). All uses and/or publication of this material should be accompanied by an appropriate acknowledgment of the source (e.g. - "Reprinted from Annular Solar Eclipse of 10 May 1994, Espenak and Anderson, 1993"). This work is in no way associated with or supported by the U. S. Naval Observatory or its Circulars series of publications.

	Fred Espenak					Jay Anderson
	NASA/Goddard Space Flight Center		Prairie Weather Centre
	Planetary Systems Branch, Code 693		900-266 Graham Avenue
	Greenbelt, MD 20771				Winnipeg, MB,
	USA						CANADA  R3C 3V4


   Next NASA Eclipse RP :	Total Solar Eclipse of 3 November 1994

		Available:	Autumn 1993

For my mother, Asie, and my sister, Nancy.

They left this world far too soon.

FE

To Judy, who gave up the computer, the den,

and many evenings of companionship for this project.

JA

Next section NASA RP 1301: Table of Contents Annular Solar Eclipse of 10 May 1994

Table of Contents

NASA RP 1301: Eclipse Predictions: Introduction

ECLIPSE PREDICTIONS

INTRODUCTION

On 10 May 1994, an annular eclipse of the Sun will be widely visible from the Western Hemisphere. The Moon's anti-umbral shadow delineates a path through North America including northern Mexico, the American southwest and midwest, the southern Great Lakes region, New England and maritime Canada. The path crosses the North Atlantic where it sweeps over the Azores and ends at sunset in Morocco. From within the much broader path of the Moon's penumbral shadow, a partial eclipse will be seen from North American, eastern Siberia, western Europe and north Africa (Figures 1 and 2).

Next section NASA RP 1301: Eclipse Predictions: Path and Visibility

PATH AND VISIBILITY

The path of the Moon's anti-umbral shadow begins in the Pacific Ocean about 700 kilometers southeast of the Hawaiian Islands. As the shadow first contacts Earth along the sunrise terminator (15:21 UT), the path is 311 kilometers wide and the annular eclipse lasts 4 minutes 34 seconds. Quickly sweeping east-northeast across the Pacific, the shadow's first landfall occurs at 15:54 UT along the western coast of Baja California (Figures 3 and 4). The path width has diminished to 267 kilometers as the curvature of Earth's surface brings subsequent points in the path closer to the vertex of the umbra. Nevertheless, the duration of annularity has increased to 5 minutes 28 seconds. This occurs because the surface or ground component of the velocity vector in the direction of the shadow's motion has increased fast enough to over compensate for the effects that the narrower path width has on the duration of annularity. From Baja, the Sun will appear 40 deg. above the horizon and the eclipse magnitude will reach 0.939 at maximum eclipse. This corresponds to an obscuration of 0.882 of the total surface area of the Sun's disk. As the anti-umbra rushes across the Golfo de California it moves with a ground speed of 0.9 km/s to the northeast.

After traveling through Mexico, the shadow reaches the American southwest where it enters south-ern Arizona, New Mexico and western Texas (Figure 4). El Paso lies just south of the center line and will witness a 5 minutes 40 second annular eclipse beginning 16:07 UT. Continuing through the panhandle of Texas, the path enters Oklahoma where Oklahoma City lies just inside the southern limit. Kansas and Missouri are the next two states in the shadow's path. Kansas City lies just outside the northern limit while Springfield barely lies within the southern limit. Both cities witness maximum eclipse at 16:45 UT with the Sun ~62 deg. above the horizon. St. Louis, Springfield and Decatur also lie in the path of annularity, while Chicago and Indianapolis lie just outside the northern and southern limits, respectively (Figure 5).

The instant of greatest eclipse[1] occurs at 17:11:27 UT when the length of annularity reaches its maximum duration of 6 minutes 13 seconds. The Sun's altitude is then 66 deg. and the path is 230 kilometers wide. Toledo stands on the center line as the anti-umbra heads across Lake Erie. Here, observers along both Canadian and U. S. shores of Lake Erie and Lake Ontario will witness the annular phase. Toronto, the largest Canadian city in the path, lies just inside the northern limit where maximum eclipse occurs at 17:24 UT. After skirting northwestern Pennsylvania, the path crosses upper New York State where Buffalo and Rochester witness the annular phase. Most of Vermont and New Hampshire fall within the path limits which continue across the southern half of Maine. Returning to Canada, the shadow crosses southern New Brunswick and Nova Scotia. At 17:56 UT, Halifax experiences an annular phase lasting 5 minutes 53 seconds with a solar altitude of 55 deg.

As the shadow leaves North America, it sweeps across the North Atlantic where it reaches the Azores at approximately 18:45 UT (Figure 6). The Sun is now 27 deg. high, the path width has grown to 270 kilometers and the central duration has diminished to 5 minutes 10 seconds. Several minutes later, the anti-umbra reaches the Atlantic coast of Morocco and heads inland where the leading edge of the shadow leaves Earth's surface at 18:57 UT. Casablanca witnesses the rare 'ring of fire' as the 4 minute 32 second annular eclipse occurs just 3 deg. above the western horizon. Finally, the annular eclipse ends at 19:02 UT as the trailing edge of the shadow leaves Earth along the sunset terminator. In a period of 3 hours and 42 minutes, the Moon's shadow sweeps along a path almost 14,000 kilometers long, encompassing 0.72 % of Earth's surface area.

Next section NASA RP 1301: General Maps of the Eclipse Paths


GENERAL MAPS OF THE ECLIPSE PATH

ORTHOGRAPHIC PROJECTION MAP OF THE ECLIPSE PATH

Figure 1 is an orthographic projection map of Earth [adapted from Espenak, 1987] showing the path of penumbral (partial) and umbral (annular) eclipse. The daylight terminator is plotted for the instant of greatest eclipse with north towards the top. The sub-Earth point is centered over the point of greatest eclipse and is marked by a '*' or asterisk. Earth's sub-solar point at that instant is indicated by a 'A' or star shaped character.

The limits of the Moon's penumbral shadow delineate the region of visibility of the partial solar eclipse. This irregular or saddle shaped region often covers more than half of the daylight hemisphere of Earth and consists of several distinct zones or limits. At the northern and/or southern boundaries lie the limits of the penumbra's path. Partial eclipses have only one of these limits, as do central eclipses when the shadow axis falls no closer than about 0.45 radii from Earth's center. Great loops at the western and eastern extremes of the penumbra's path identify the areas where the eclipse begins/ends at sunrise and sunset, respectively. If the penumbra has both a northern and southern limit, the rising and setting curves form two separate, closed loops. Otherwise, the curves are connected in a distorted figure eight. Bisecting the 'eclipse begins/ends at sunrise and sunset' loops is the curve of maximum eclipse at sunrise (western loop) and sunset (eastern loop). The points P1 and P4 mark the coordinates where the penumbral shadow first contacts (partial eclipse begins) and last contacts (partial eclipse ends) Earth's surface. If the penumbral path has both a northern and southern limit (as does the May 1994 eclipse), then points P2 and P3 are also plotted. These correspond to the coordinates where the penumbral shadow cone becomes internally tangent to Earth's disk.

A curve of maximum eclipse is the locus of all points where the eclipse is at maximum at a given time. Curves of maximum eclipse are plotted at each half hour Universal Time. They generally run from the northern to the southern penumbral limits, or from the maximum eclipse at sunrise and sunset curves to one of the limits. The curves of maximum eclipse run through the half-hourly outlines of the umbral shadow, from which the Universal Time of each curve can be identified. The curves of constant eclipse magnitude[2] delineate the locus of all points where the magnitude at maximum eclipse is constant. These curves run exclusively between the curves of maximum eclipse at sunrise and sunset. Furthermore, they're parallel to the northern/southern penumbral limits and the umbral paths of central eclipses. The northern and southern limits of the penumbra may be thought of as curves of constant magnitude of 0.0. The adjacent curves are for magnitudes of 0.2, 0.4, 0.6 and 0.8. For total eclipses, the northern and southern limits of the umbra are curves of constant magnitude of 1.0. Umbral path limits for annular eclipses are curves of maximum eclipse magnitude. The magnitude is always less than 1.0 for annular eclipses.

In the upper left corner of Figure 1 are the Universal Times of greatest eclipse and conjunction of the Moon and Sun in right ascension, followed by the minimum distance of the Moon's shadow axis from Earth's center in Earth radii GAMMA and the geocentric ratio of diameters of the Moon and the Sun RATIO. To the upper right are exterior contact times of the Moon's shadow with Earth. P1 and P4 are the first and last contacts of the penumbra; they mark the start and end of the partial eclipse. U1 and U4 are the first and last contacts of the umbra; they denote the start and end of the annular eclipse. Below the map are the geocentric coordinates of the Sun and Moon at the instant of greatest eclipse. They include of the right ascension RA, declination DEC, apparent semi-diameter SD and equatorial horizontal parallax HP. The Saros series for the eclipse is listed, followed by a pair of numbers in parentheses. The first number identifies the sequence order of the eclipse in the Saros, while the second is the total number of eclipses in the series. The Julian Date JD at greatest eclipse is given, followed by the extrapolated value of Delta_T[3] used in the calculations. Finally, the geodetic coordinates of the point of greatest eclipse are given, as well as the local circumstances there. In particular, the Sun's altitude ALT and azimuth AZ are listed along with the duration of umbral eclipse (minutes:seconds) and the width of the path (kilometers).


STEREOGRAPHIC PROJECTION MAP OF THE ECLIPSE PATH

The stereographic projection of Earth in Figure 2 depicts the path of penumbral and umbral eclipse in greater detail. The map is oriented with the point of greatest eclipse near the center and north is towards the top. International political borders are shown and circles of latitude and longitude at plotted at 20deg. increments. The saddle shaped region of penumbral or partial eclipse includes labels identifying the northern and southern limits, curves of eclipse begins or ends at sunrise, curves of eclipse begins or ends at sunset, and curves of maximum eclipse at sunrise and sunset. Curves of constant eclipse magnitude are plotted for 20%, 40%, 60% and 80%, as are the limits of the annular path. Also included are curves of greatest eclipse for every thirty minutes Universal Time.

Figure 2 may be used to quickly determine the approximate time and magnitude of greatest eclipse for any location from which the eclipse is visible.

EQUIDISTANT CONIC PROJECTION MAPS OF THE ECLIPSE PATH

Figures 3, 4, 5, and 6 are equidistant conic projection maps which isolate specific regions of the eclipse path. The projection was selected to minimize distortion over the regions depicted. Once again, curves of maximum eclipse and constant eclipse magnitude are plotted along with identifying labels. A linear scale is included for estimating approximate distances (kilometers) in each figure. Within the northern and southern limits of the annular path, the outline of the umbral shadow is plotted at ten minute intervals. Figures 4, 5, and 6 are drawn at the same scale (~1:12,270,000) and include the center line as well as the positions of many of the larger cities or metropolitan areas in and near the central path. The size of each city is logarithmically proportional to its population.

Next section NASA RP 1301: Elements, Shadow Contacts and Eclipse Path Tables

ELEMENTS, SHADOW CONTACTS AND ECLIPSE PATH TABLES

The geocentric ephemeris for the Moon and Sun, various parameters and constants used in the predictions, the besselian elements (polynomial form) are given in Table 1. The eclipse predictions and elements were derived from solar and lunar data contained in the DE200 and LE200 ephemerides developed jointly by the Jet Propulsion Laboratory and the U. S. Naval Observatory for use in the Astronomical Almanac for 1984 and after. Unless otherwise stated, all predictions are based on center of mass positions for the Sun and Moon with no corrections made for center of figure, center of motion, lunar limb profile or atmospheric refraction. Furthermore, these predictions depart from IAU convention by using a smaller constant for the mean lunar radius k for all umbral contacts (see: LUNAR LIMB PROFILE). Times are expressed in either Terrestrial Dynamical Time (TDT) or in Universal Time (UT) where the best value of Delta_T available at the time of preparation is used.

Table 2 lists all external and internal contacts of penumbral and umbral shadows with Earth. They include TDT times and geodetic coordinates with and without corrections for Delta_T. The external contacts of the penumbral P1 and P4 mark the instants when the partial eclipse begins and ends, respectively. The external contacts of the umbral U1 and U4 mark the instants when the umbral eclipse begins and ends. Likewise, the extremes of the penumbral and umbral paths, and extreme limits of the center line are given. The IAU longitude convention is used throughout this publication (i.e. - eastern longitudes are positive; western longitudes are negative; negative latitudes are south of the Equator).

The path of the umbral shadow is delineated at five minute intervals of Universal Time in Table 3. The coordinates of the northern limit, the southern limit and the center line are listed to the nearest tenth of an arc-minute (~185 m at the Equator). The Sun's altitude and azimuth, the path width and umbral duration are calculated for the center line coordinates. Table 4 presents a physical ephemeris for the umbral shadow at five minute intervals of Universal Time. The center line coordinates are followed by the topocentric ratio of the apparent diameters of the Moon and Sun, the eclipse obscuration[4], and the Sun's altitude at that instant. The path azimuth differs from the Sun's azimuth and represents the direction of the umbral shadow's motion projected onto the surface of the Earth. The central path width, the umbral shadow's major and minor axes and its instantaneous velocity with respect to Earth's surface are included. Finally, the center line duration of the annular phase is given.

Local circumstances for each center line position listed in Tables 3 and 4 are presented in Table 5. The first three columns give the Universal Time of maximum eclipse, the center line duration of annularity and the altitude of the Sun at that instant. The following columns list each of the four eclipse contact times followed by their related contact position angles and the corresponding altitude of the Sun. The four contacts[5] identify significant stages in the progress of the eclipse. The position angles P and V identify the point along the Sun's disk where each contact occurs[6]. The altitude of the Sun at second and third contact is omitted since it's always within 1deg. of the altitude at maximum eclipse (column 3).

Table 6 presents topocentric values at maximum eclipse for the Moon's horizontal parallax, semi-diameter, relative angular velocity with respect to the Sun, and libration in longitude. The altitude and azimuth of the Sun are given along with the azimuth of the umbral path. The northern limit position angle identifies the point on the lunar disk defining the umbral path's northern limit. It's measured counter-clockwise from the north point of the lunar disk. In addition, corrections to the path limits due to the lunar limb profile are listed. The irregular profile of the Moon results in a zone of 'grazing eclipse' at each limit which is delineated by interior and exterior contacts of lunar features with the Sun's limb. The section LIMB CORRECTIONS TO THE PATH LIMITS: GRAZE ZONES describes this geometry in greater detail. Corrections to the center line durations due to the lunar limb profile are also included. When added to the durations in Tables 3, 4, 5, and 7, a slightly shorter central annular phase is predicted.

To aid and assist in the plotting of the umbral path on large scale maps, the path coordinates are also tabulated at 1deg. intervals in longitude in Table 7. The latitude of the northern limit, southern limit and center line for each longitude is tabulated along with the Universal Time of maximum eclipse at each position. Finally, local circumstances on the center line at maximum eclipse are listed and include the Sun's altitude and azimuth, the umbral path width and the central duration of annularity.

Next section NASA RP 1301: Local Circumstances Tables

LOCAL CIRCUMSTANCES TABLES

Local circumstances from over 900 cities, metropolitan areas and places in North America, Europe and Africa are presented in Tables 9 through 14. Each table is broken down into two parts. The first part, labeled a, appears on even numbered pages and gives circumstances at maximum eclipse[1] for each location. The coordinates are listed along with the location's elevation (meters) above sea-level, if known. If the elevation is unknown (i.e. - not in the data base), then the local circumstances for that location are calculated at sea-level. In any case, the elevation does not play a significant role in the predictions unless the location is near the umbral path limits and the Sun's altitude is relatively small (>20deg.). The Universal Time of maximum eclipse (either partial or annular) is listed to an accuracy of 0.1 seconds. If the eclipse is annular, then the umbral duration and the path width are given. Next, the altitude and azimuth of the Sun at maximum eclipse are listed along with the position angles P and V of the Moon's disk with respect to the Sun. Finally, the magnitude and obscuration are listed at the instant of maximum eclipse. Note that for umbral eclipses (annular and total), the eclipse magnitude is identical to the topocentric ratio of the Moon's and Sun's apparent diameters. Furthermore, the eclipse magnitude is always less than 1 for annular eclipses and equal to or greater than 1 for total eclipses.

The second part of each table, labeled b, is found on odd numbered pages. It gives local circumstances for each location listed on the facing page at each contact during the eclipse. The Universal Time of each contact is given along with the altitude of the Sun, followed by position angles P and V. These angles identify the point along the Sun's disk where each contact occurs and are measured counter-clockwise from the north and zenith points, respectively. Locations outside the umbral path miss the umbral eclipse and only witness first and fourth contacts. The effects of refraction have included in these calculations although no correction has been applied for center of figure or the lunar limb profile.

Locations were chosen based on position near the central path, general geographic distribution and population. The primary source for geographic coordinates is The New International Atlas (Rand McNally, 1991). Elevations for major cites were taken from Climates of the World (U. S. Dept. of Commerce, 1972). In this rapidly changing political world, it is often difficult to ascertain the correct name or spelling for a given location. Therefore, the information presented here is for location purposes only and is not meant to be authoritative. Furthermore, it does not imply recognition of status of any location by the United States Government. Corrections to names, spellings, coordinates and elevations is solicited in order to update the geographic data base for future eclipse predictions.

Next section NASA RP 1301: Detailed Maps

DETAILED MAPS OF THE UMBRAL PATH

The path of annularity has been plotted by hand on a set of eight detailed maps appearing in the last section of this publication. The maps are Global Navigation and Planning Charts or GNC's from the Defense Mapping Agency which use a Lambert conformal conic projection. More specifically, GNC-2 covers the North American section of the path while GNC-11 covers Africa. GNC's have a scale of 1:5,000,000 (1 inch ~ 69 nautical miles), which is adequate for showing major cities, highways, airports, rivers, bodies of water and basic topography required for eclipse expedition planning including site selection, transportation logistics and weather contingency strategies.

Northern and southern limits as well as the center line of the path are draw using predictions from Table 6. See PLOTTING THE PATH ON MAPS for sources and more information. The GNC paths also depict the curve of maximum eclipse at five minute increments in Universal Time [ Table 3].

Next section NASA RP 1301: Eclipse Predictions: Estimating the Times of Second and Third Contacts

ESTIMATING TIMES OF SECOND AND THIRD CONTACTS

The times of second and third contact for any location not listed in this publication can be estimated using the detailed maps found in the final section. Alternatively, the contact times can be estimated from maps on which the umbral path has been plotted. Table 7. lists the path coordinates conveniently arranged in 1deg. increments of longitude to assist plotting by hand. The path coordinates in Table 3. define a line of maximum eclipse at five minute increments in time. These lines of maximum eclipse each represent the projection diameter of the umbral shadow at the given time. Thus, any point on one of these lines will witness maximum eclipse (i.e.: mid-annularity) at the same instant. The coordinates in Table 3 should be added to the map in order to construct lines of maximum eclipse.

The estimation of contact times for any one point begins with an interpolation for the time of maximum eclipse at that location. The time of maximum eclipse is proportional to a point's distance between two adjacent lines of maximum eclipse, measured along a line parallel to the center line. This relationship is valid along most of the path with the exception of the extreme ends where the shadow experiences its largest acceleration. The center line duration of annularity D and the path width W are similarly interpolated from the values of the adjacent lines of maximum eclipse as listed in Table 3. Since the location of interest probably does not lie on the center line, it's useful to have an expression for calculating the duration of annularity d as a function of its perpendicular distance a from the center line:

d = D (1 - (2a/W)**2)**(1/2) seconds [1]

where: D = duration of annularity on the center line (seconds)

W = width of the path (kilometers)

a = perpendicular distance from the center line (kilometers)

If tm is the interpolated time of maximum eclipse for the location, then the approximate times of second and third contacts (t2 and t3, respectively) are:

Second Contact: t2 = tm - d/2 [2]

Third Contact: t3 = tm + d/2 [3]

The position angles of second and third contact (either P or V) for any location off the center line are also useful in some applications. First, linearly interpolate the center line position angles of second and third contacts from the values of the adjacent lines of maximum eclipse as listed in Table 5. If X2 and X3 are the interpolated center line position angles of second and third contacts, then the position angles x2 and x3 of those contacts for an observer located a kilometers from the center line are:

Second Contact: x2 = X2 - ArcSin (2 a/W) [4]

Third Contact: x3 = X3 + ArcSin (2 a/W) [5]

where: Xn = the interpolated position angle (either P or V) of contact n on center line

xn = the interpolated position angle (either P or V) of contact n at location

D = duration of annularity on the center line (seconds)

W = width of the path (kilometers)

a = perpendicular distance from the center line (kilometers)

(use negative values for locations south of the center line)

Next section NASA RP 1301: Mean Lunar Radius

MEAN LUNAR RADIUS

A fundamental parameter used in the prediction of solar eclipses is the Moon's mean radius k, expressed in units of Earth's equatorial radius. The actual radius of the Moon varies as a function of position angle and libration due to the irregularity of the lunar limb profile. From 1968 through 1980, the Nautical Almanac Office used two separate values for k in their eclipse predictions. The larger value (k=0.2724880) representing a mean over lunar topographic features was used for all penumbral (i.e. - exterior) contacts and for annular eclipses. A smaller value (k=0.272281) representing a mean minimum radius was reserved exclusively for umbral (i.e. - interior) contact calculations of total eclipses [Explanatory Supplement, 1974]. Unfortunately, the use of two different values of k for umbral eclipses introduces a discontinuity in the case of hybrid or annular- total eclipses.

In August 1982, the IAU General Assembly adopted a value of k=0.2725076 for the mean lunar radius. This value is currently used by the Nautical Almanac Office for all solar eclipse predictions [Fiala and Lukac, 1983] and is believed to be the best mean radius, averaging mountain peaks and low valleys along the Moon's rugged limb. In general, the adoption of one single value for k is commendable because it eliminates the discontinuity in the case of annular-total eclipses and ends confusion arising from the use of two different values. However, the use of even the best 'mean' value for the Moon's radius introduces a problem in predicting the character and duration of umbral eclipses, particularly total eclipses. A total eclipse can be defined as an eclipse in which the Sun's disk is completely occulted by the Moon. This cannot occur so long as any photospheric rays are visible through deep valleys along the Moon's limb [Meeus, Grosjean and Vanderleen, 1966]. But the use of the IAU's mean k guarantees that some annular or annular-total eclipses will be misidentified as total. A case in point is the eclipse of 3 October 1986. The Astronomical Almanac identified this event as a total eclipse of 3 seconds duration when in it was in fact a beaded annular eclipse. Clearly, a smaller value of k is needed since it is more representative of the deepest lunar valley floors, hence the minimum solid disk radius and ensures that an eclipse is truly total.

Of primary interest to most observers are the times when central eclipse begins and ends (second and third contacts, respectively) and the duration of the central phase. When the IAU's mean value for k is used to calculate these times, they must be corrected to accommodate low valleys (total) or high mountains (annular) along the Moon's limb. The calculation of these corrections is not trivial but must be performed, especially if one plans to observe near the path limits [Herald, 1983]. For observers near the center line of a total eclipse, the limb corrections can be closely approximated by using a smaller value of k which accounts for the valleys along the profile.

This work uses the IAU's accepted value of k (k=0.2725076) for all penumbral (exterior) contacts. In order to avoid eclipse type misidentification and to predict central durations which are closer to the actual durations observed at total eclipses, we depart from convention by adopting the smaller value for k (k=0.272281) for all umbral (interior) contacts. This is consistent with predictions published in Fifty Year Canon of Solar Eclipses: 1986 - 2035 [Espenak, 1987]. Consequently, the smaller k produces shorter umbral durations and narrower paths for total eclipses when compared with calculations using the IAU value for k. Similarly, the smaller k predicts longer umbral durations and wider paths for annular eclipses.

Next section NASA RP 1301: Lunar Limb Profile

LUNAR LIMB PROFILE

Eclipse contact times, the magnitude and the duration of annularity all ultimately depend on the angular diameters and relative velocities of the Sun and the Moon. Unfortunately, these calculations are limited in accuracy by the departure of the Moon's limb from a perfectly circular figure. The Moon's surface exhibits a rather dramatic topography which manifests itself as an irregular limb when seen in profile. Most eclipse calculations assume some mean lunar radius which averages high mountain peaks and low valleys along the Moon's rugged limb. Such an approximation is acceptable for many applications, but if higher accuracy is needed, the Moon's actual limb profile must be considered. Fortunately, an extensive body of knowledge exists on this subject in the form of Watt's limb charts [Watts, 1963]. These data are the product of a photographic survey of the marginal zone of the Moon and give limb profile heights with respect to an adopted smooth reference surface (or datum). Analyses of lunar occultations of stars by Van Flandern [1970] and Morrison [1979] have shown that the average cross-section of Watts' datum is slightly elliptical rather than circular. Furthermore, the implicit center of the datum (i.e. - the center of figure) is displaced from the Moon's center of mass. In a follow-up analysis of 66000 occultations, Morrison and Appleby [1981] have found that the radius of the datum appears to vary with libration. These variations produce systematic errors in Watts' original limb profile heights which attain 0.4 arc-seconds at some position angles. Thus, corrections to Watts' limb profile data are necessary to ensure that the reference datum is a sphere with its center at the center of mass.

The Watts charts have been digitized by Her Majesty's Nautical Almanac Office in Herstmonceux, England, and transformed to grid-profile format at the U. S. Naval Observatory. In this computer readable form, the Watts limb charts lend themselves to the generation of limb profiles for any lunar libration. Ellipticity and libration corrections may be applied to refer the profile to the Moon's center of mass. Such a profile can then be used to correct eclipse predictions which have been generated using a mean lunar limb.

Along the eclipse path, the Moon's topocentric libration (physical + optical libration) in longitude ranges from l=-0.7deg. to l=-2.5deg.. Thus, a limb profile with the appropriate libration is required in any detailed analysis of contact times, central duration's, etc.. Nevertheless, a profile with an intermediate libration is valuable for general planning for any point along the path. The center of mass corrected lunar limb profile presented in Figure 7 is for the center line at the instant of greatest eclipse (17:11:27 UT). At that time, the Moon's topocentric librations are l=-1.65deg., b=- 0.12deg. and c=-17.18deg., and the apparent topocentric semi-diameters of the Sun and Moon are 950.3 and 896.2 arc-seconds respectively. The Moon's angular velocity is 0.289 arc-seconds per second with respect to the Sun.

The radial scale of the profile in Figure 7 (see scale to upper left) is greatly exaggerated so that the true limb's departure from the mean lunar limb is readily apparent. The mean limb with respect to the center of figure of Watts' original data is shown along with the mean limb with respect to the center of mass. Note that all the predictions presented in this paper are calculated with respect to the latter limb unless otherwise noted. Position angles of various lunar features can be read using the protractor in the center of the diagram. The position angles of second and third contact are clearly marked along with the north pole of the Moon's axis of rotation and the observer's zenith at mid-annularity. The dashed line arrows identify the points on the limb which define the northern and southern limits of the path. To the upper left of the profile are the Moon's mean lunar radius k (expressed in Earth equatorial radii), topocentric semi- diameter SD and horizontal parallax HP. As discussed in the section MEAN LUNAR RADIUS, the Moon's mean radius k (k=0.2722810) is smaller than the adopted IAU value (k=0.2725076). To the upper right of the profile are the Sun's semi-diameter SUN SD, the angular velocity of the Moon with respect to the Sun VELOC. and the position angle of the path's northern/southern limit axis LIMITS. In the lower right are the Universal Times of the four contacts and maximum eclipse. The geographic coordinates and local circumstances at maximum eclipse are given along the bottom of the figure.

In investigations where accurate contact times are needed, the lunar limb profile can be used to correct the nominal or mean limb predictions. For any given position angle, there will be a high mountain (annular eclipses) or a low valley (total eclipses) in the vicinity which ultimately determines the true instant of contact. The difference, in time, between the Sun's position when tangent to the contact point on the mean limb and tangent to the highest mountain (annular) or lowest valley (total) at actual contact is the desired correction to the predicted contact time. On the exaggerated radial scale of Figure 7, the Sun's limb can be represented as an epicyclic curve which is tangential to the mean lunar limb at the point of contact and departs from the limb by h as follows:

h = S (m-1) (1- cos[C]) [6]

where: S = the Sun's semi- diameter

m = the eclipse magnitude

C = the angle from the point of contact

Herald [1983] has taken advantage of this geometry to develop a graphical procedure for estimating correction times over a range of position angles. Briefly, a displacement curve of the Sun's limb is constructed on a transparent overlay by way of equation [6]. For a given position angle, the solar limb overlay is moved radially from the mean lunar limb contact point until it is tangent to the lowest lunar profile feature in the vicinity. The solar limb's distance d (arc-seconds) from the mean lunar limb is then converted to a time correction Delta_ by:

Delta_ = d v cos[X - C] [7]

where: d = the distance of Solar limb from mean lunar limb (arc-sec)

v = the angular velocity of the Moon with respect to the Sun (arc-sec/sec)

X = the center line position angle of the contact

C = the angle from the point of contact

This operation may be used for predicting the formation and location of Baily's beads. When calculations are performed over large range of position angles, a contact time correction curve can then be constructed.

Since the limb profile data are available in digital form, an analytic solution to the problem is possible which is straight forward and quite robust. Curves of corrections to the times of second and third contact for most position angles have been computer generated and are plotted in Figure 7. In interpreting these curves, the circumference of the central protractor functions as the nominal or mean contact time (using the Moon's mean limb) as a function of position angle. The departure of the correction curve from the mean contact time can then be read directly from Figure 7 for any position angle by using the radial scale in the upper right corner (units in seconds of time). Time corrections external to the protractor (most second contact corrections) are added to the mean contact time; time corrections internal to the protractor (all third contact corrections) are subtracted from the mean contact time.

Across most of North America, the Moon's topocentric libration in longitude at maximum eclipse is within half a degree of its value at greatest eclipse. Therefore, the limb profile and contact correction time curves in Figure 7 may be used in all but the most critical investigations.

Next section

LIMB CORRECTIONS TO THE PATH LIMITS: GRAZE ZONES

The northern and southern umbral limits provided in this publication were derived using the Moon's center of mass and a mean lunar radius. They have not been corrected for the Moon's center of figure or the effects of the lunar limb profile. In applications where precise limits are required, Watt's limb data must be used to correct the nominal or mean path. Unfortunately, a single correction at each limit is not possible since the Moon's libration in longitude and the contact points of the limits along the Moon's limb each vary as a function of time and position along the umbral path. This makes it necessary to calculate a unique correction to the limits at each point along the path. Furthermore, the northern and southern limits of the umbral path are actually paralleled by a relatively narrow zone where the eclipse is neither penumbral nor umbral. An observer positioned here will witness a solar crescent which is fragmented into a series of bright beads and short segments whose morphology changes quickly with the rapidly varying geometry of the Moon with respect to the Sun. These beading phenomena are caused by the appearance of photospheric rays which alternately pass through deep lunar valleys and hide behind high mountain peaks as the Moon's irregular limb grazes the edge of the Sun's disk. The geometry is directly analogous to the case of grazing occultations of stars by the Moon. The graze zone is typically five to ten kilometers wide and its interior and exterior boundaries can be predicted using the lunar limb profile. The interior boundaries define the actual limits of the umbral eclipse (both total and annular) while the exterior boundaries set the outer limits of the grazing eclipse zone.

Table 6 provides topocentric data and corrections to the path limits due to the true lunar limb profile. At five minute intervals, the table lists the Moon's topocentric horizontal parallax, the semi-diameter, the relative angular velocity of the Moon with respect to the Sun and lunar libration in longitude. The center line altitude and azimuth of the Sun is given, followed by the azimuth of the umbral path. The position angle of the point on the Moon's limb which defines the northern limit of the path is measured counter-clockwise (i.e. - eastward) from the north point on the limb. The path corrections to the northern and southern limits are listed as interior and exterior components in order to define the graze zone. Positive corrections are in the northern sense while negative shifts are in the southern sense. These corrections [minutes of arc in latitude] may be added directly to the path coordinates listed in Table 3. Corrections to the center line umbral durations due to the lunar limb profile are also included and they are all negative. Thus, when added to the central durations given in Tables Table 3, Table 4, Table 5, and Table 7, a slightly shorter central annular phase is predicted.

Next section NASA RP 1301: Eclipse Predictions: Saros History

SAROS HISTORY

The annular eclipse of 10 May 1994 is the fifty-seventh member of Saros series 128, as defined by van den Bergh (1955). All eclipses in the series occur at the Moon's descending node and gamma[8] increases with each member in the series. The family began on 29 Aug 984 with a partial eclipse in the southern hemisphere. During the next four centuries, a total of twenty-four partial eclipses occurred with the eclipse magnitude of each succeeding event gradually increasing. Finally, the first umbral eclipse occurred on 16 May 1417. The event was a total eclipse of short duration which was followed by three more eclipses with similar characteristics. The twenty-ninth event occurred on 28 Jun 1489 and was of annular/total nature. The ensuing three members were also annular/total eclipses of monotonically decreasing duration. This was a direct consequence of the Moon's increasing distance with each event. Eventually, the character of the series changed to pure annular with the thirty-third member on 11 Aug 1561.

For almost three centuries, Saros 128 continued to produce annular eclipses where each event was of progressively smaller magnitude and increasing duration. The trend culminated with the annular eclipses of 1 Feb 1832 and 12 Feb 1850, each of which was characterized by an eclipse magnitude of 0.934 and a greatest duration of 8m 35s. Having reached its orbital apogee, the Moon's distance began to decrease with each succeeding eclipse, resulting in annular eclipses of increasing magnitude and decreasing duration. Although the annular eclipse of 10 May 1994 still reaches a magnitude of 0.943 and a maximum duration of 6 minutes 14 seconds, each subsequent event is of rapidly diminishing maximum duration. To illustrate, the eclipses of 20 May 2012, 1 Jun 2030 and 11 Jun 2048 will exhibit maximum durations of 5m 46s, 5m 21s and 4m 58s respectively as the path of each event shifts northward. Member sixty-four is the last central eclipse of the series and occurs on 15 Jul 2120. The remaining nine events are partial in the northern hemisphere with the last and seventy-third member occurring on 1 Nov 2282.

In summary, Saros series 128 includes 73 eclipses with the following distribution: 

                   Partial   Annular   Ann/Tota  Total
                   -------   -------   --------  -----
Non-Central           33        0          0       0         
Central               --       32          4       4
Next section NASA RP 1301: Weather Prospects for the Eclipse: Overview WEATHER PROSPECTS FOR THE ECLIPSE

OVERVIEW

The mid latitude track of the May 1994 eclipse takes it across some of the more active weather regions of the Northern Hemisphere. At its southernmost extent over Mexico, weather patterns are regular and reliable, with relatively small variation from season to season. At the apex of its path over Nova Scotia, weather is cloudy and changeable. And at sunset over Morocco, there is a combination of both - the sunny disposition of the sub tropics combined with the vagaries of passing temperate zone lows and highs.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Mexico

MEXICO

The eclipse track crosses one of the driest and sunniest parts of Mexico, in spite of a jumbled terrain which includes cool beaches, deserts, 3000 meter peaks and a broad 1500 meter plateau. Each of these features has an influence on the weather, but the moisture supply is so low in most areas that, with only one exception, cloud cover is sparse and sunshine plentiful. The main control on the weather is a large and permanent high pressure cell which resides in the eastern Pacific about half way between Hawaii and San Francisco. This semi-permanent anticyclone suppresses rain bearing weather systems along the California and Baja coasts, bringing the dry summers for which the area is well known.

During the winter months, weather systems arrive over the eclipse track on upper level westerly winds. During the summer, easterly low level trade winds carry the moisture which builds thunderstorms and brings the rainy season or "tiempo des aguas". May is the intermediate season, too soon for the moist easterlies, and getting very late for westerly disturbances. Still, what weather occurs on eclipse day is likely to come with the last westerly troughs moving in from the Pacific.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Western Baja

WESTERN BAJA

Although its one of the drier places in the world, the west coast of the Baja Peninsula is plagued by a persistent low level cloudiness and fog. The dull grey skies, mostly in the morning, come courtesy of the high pressure system which camps in the eastern Pacific. Wind circulations around the high build a strong temperature inversion which traps moisture in the lowest 2000 meters of the atmosphere.

A cold California Current flows southward along the coast, lowering the air temperature, and bringing the atmosphere to saturation. Winds, mostly out of northwest, carry the cloud onshore to plague eclipse chasers (as many discovered in July 1991). The sun is usually able to burn this cloud away by noon, but that will be much too late for this eclipse. Depending on the lie of the coast, some areas are more prone than others to intercept the flow of moist air from the ocean. First among these is the prominent fishhook peninsula jutting from the Baja coast, terminating at Punta Eugenia. The hook creates a large bay - Bahia Sebastian Vizcaino - which scoops the moist northwest flow from the ocean and directs it inland. And it's here that the eclipse first comes ashore.

Satellite pictures show that low cloud and fog often fill the entire Desierto de Vizcaino which lies at the bottom of the Bay. Statistics collected over a 30 year period show that the cloud does not usually penetrate as far as San Ignacio but it doesn't miss by much. Nearby El Alamo records fog nearly 6 days of the month. Some of the cloudiest areas along the Baja coast report fog on one day out of three. If there were a station on the coast of the Bahia Sebastian Vizcaino it is likely that it would be a strong challenger for the foggiest location.

Those who wish to challenge the statistics and be the first to greet the ringed sun on the west side of the Baja should keep a weather eye peeled for evidence of impending cloudiness. While fog and low cloud are obvious, even a feeling of humidity or mugginess may signal that cloud will form once the sun rises. Be wary of cloud and fog in the distance, for the rising sun will quickly warm the ground and strengthen the onshore breezes which will carry the cloud inland.

All-in-all, eclipse chasers would do well to avoid much of western Baja, and seek better weather prospects elsewhere. And better prospects are only a short distance away, on the east slopes of the peninsula and along its mountain spine.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Along the Gulf of California


ALONG THE GULF OF CALIFORNIA

The sunniest skies along the entire eclipse track can be found on the eastern slopes of the Baja Peninsula and the western coast of mainland Mexico. Figure 8 shows that the frequency of clear skies (less than 1/3 cloud cover) in May ranges from 80 to 90 percent[9]. The Gulf of California is protected in the east by the Sierra Madre Occidental and in the west by the mountain backbone of the Baja Peninsula. Winds arriving from nearly every direction have to travel downslope - drying and losing what little cloud might remain. Only high level disturbances can cross the mountains undisturbed and the climatological record shows that most of the cloudiness comes from ice crystal cirrus clouds. These clouds tend to be thinner than their water vapor cousins. The eclipse should be visible through cirrus cloud, and the cloud might even add an attractive element to the sky.

Roads along the eastern side of the Baja Peninsula are limited and mostly unpaved. Fortunately it's only necessary to travel just far enough inland to get away from the Pacific marine cloud. El Arco, just south of the center line and on the main highway is probably blessed with good prospects. For those who want to capture Baily's beads from the north limit, the skies around Punta Prieta are very promising.

On the east side of the Gulf of California access is almost unlimited and the weather is excellent. Hermosillo and Guaymas show clear skies or scattered cloud on 77% of the days in May. Prospects are even better along the beaches of the Gulf, with the coastal pueblo of Bahia Kino likely offering the best weather prospects of any position along the entire eclipse track. It's also very close to the center line.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Mainland Mexico

MAINLAND MEXICO

Climbing the Sierra Madre Occidental, the eclipse track moves onto the Interior Plateau of mainland Mexico. The height of the Sierra, 3200 meters high, keeps all but the largest Pacific systems from bringing precipitation. These Pacific disturbances, borne on westerly winds in the upper atmosphere, are primarily a winter feature, and in May are becoming increasingly rare. Cloud cover increases slowly as the track travels from Hermosillo to El Paso in Texas. Some of this increase in cloud cover is a result of heating of the eastward facing mountain slopes. Bubbles of warm air cool as they rise, becoming saturated and turning into puffy cumulus. At worst, only scattered cumulus can be expected since eclipse time is around 10:15 AM CST in northern Mexico. Cloud development doesn't peak until 2 PM when temperatures are approaching their maximum.

Morning fog and stratus is more likely to be a problem in the jumble of mountainous terrain. High and dry elevations cool rapidly overnight. Cool air collects in the valleys where temperatures may fall low enough to allow the air to become saturated. Overnight lows average 59 F at Hermosillo in May. In comparison to the frequency of foggy mornings along the outer Baja coast, it's a minor problem in the mountains, and can be avoided by moving a short distance. Most overnight fogs will have likely burned off by eclipse time. Fog may redevelop as the ground cools during the eclipse, but the temperature decline in an annular eclipse will be smaller than that during a total. The outcome will depend on the moisture available.

Whether in dry or wet climates, mountains generate cloudiness. The Interior Plateau is no exception. Satellite images from May of 1992 show that the Sierra Madres are often spotted with patchy morning clouds, though usually not too heavily. These clouds are often at middle and high levels - 6000 feet or more above ground. Flatter areas away from the mountains (i.e. - up toward Ciudad Juarez and El Paso, Texas) are probably better sites, but for the most part the cloud which forms over the Sierra will blow toward them anyway. The effects of this cloud can be seen in Figure 8 as the area within the 50% contour which surrounds Temosachic.

During the spring months the sub-tropical jet stream can usually be found over northern Mexico, arcing across the Baja Peninsula and into the southern United States. The jet stream is occasionally marked by a band of cirrus and altostratus cloud, sometimes thick, but usually thin and wispy. Depending on the weather patterns of the day, the jet may lie south of the eclipse track, or a little to the north, though the former is more likely. In general, it's found close to the track, and may be difficult or impossible to avoid.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Across the United States and Canada

ACROSS THE UNITED STATES AND CANADA

As the eclipse track moves northeastward, it encounters higher latitude weather systems where cloudiness increases steadily. Figures 10 and 11 show the frequency of clear skies (less than 1/3 cloud cover) in May for the U. S. and Canada. Excellent weather greets the umbra as it enters the U. S.. Discouraging statistics bid it farewell over the Atlantic, the Azores and Africa. Even under conditions of scattered cloudiness (<50% sky coverage), the annular eclipse should be visible. Based on climatology only, New Mexico, southeast Arizona and El Paso are the best destinations. May 1992 satellite photos show that the El Paso area had favorable conditions at eclipse time on 21 days. Areas in Mexico faired even better.

The Gulf of Mexico supplies most of the moisture which fuels the weather systems of spring. In May, low level winds have turned to the south across much of the Gulf coast and Great Plains. Warm humid air floods northward to mark the beginning of summer. Thunderstorms often erupt across the States as weather disturbances and frontal systems collide with the humid air. The westward flow of Gulf air is blocked by the Rocky Mountain chain, and is re-directed into Oklahoma, Kansas, Missouri, and eastward to envelop the lower Great Lakes. The Appalachians block the flow to some extent, but the Atlantic Ocean, another moisture source, is ready to fill in when winds turn easterly.

The western edge of this giant atmospheric river lies very nearly along the eclipse track. Upper level westerlies carry high altitude disturbances over the humid air where they trigger the giant thunderstorms which characterize springtime American weather. Afterwards the westerlies push the humidity and cloud eastward for a short time, returning dry and sunny skies to the Plains for a few days. Inexorably, southerly flow begins again and the Gulf moisture returns to fuel yet another disturbance.

Over northern sections, along the Great Lakes, New England States and over southern Canada, occasional polar air masses make a sortie southward. Marked by low pressure systems, and strong warm and cold fronts, these systems come with extensive cloud shields and usually rain. The lows pause briefly along the west slopes of the Appalachians, gathering resources to push over the peaks and into New England. Its a cloudy area, because of the lingering polar lows, the mountains, the Atlantic Ocean and the Gulf moisture. Figure 11 shows that the frequency of good eclipse weather drops below 30% from West Virginia to Maine, and again over Nova Scotia. The cloudiest area of all lies over New Hampshire and Vermont.

Since thunderstorms usually form in the afternoon and evening, a morning eclipse will escape the greatest threat of heavy weather. Cloud cover also increases during the day, reaching a maximum in the late afternoon. Figures 10 and 11 are drawn from morning cloud statistics, better reflecting the climatology that applies to the eclipse. Humid Gulf air masses also bring hazy polluted skies to areas east of the Mississippi. However, it's not likely to be much of a problem for an annular eclipse.

In western regions [Texas and Oklahoma], the dust storm season ends by May 10. Strong surface winds may whip up the dirt in small areas downwind from bare fields, but growing crops will bind the soil and tame more widespread storms. May is the month for tornadoes and hail across much of the mid west and through the Great Lakes, but is still a month or more away from the start of the hurricane season.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Strategies to Cope with the Weather

STRATEGIES TO COPE WITH THE WEATHER

Outside of the southwestern U. S. and Mexico, weather becomes much more variable. Cloudiness changes with each passing high and low. Fortunately North America is blessed with a profusion of weather forecasting services. Forecasts suitable for initial planning should be available 5 to 6 days before the eclipse. By the third day - May 7 - forecasters should be able to zero in more accurately and chasers can begin to plan their final site. Look for a dry westerly flow behind a strong cold front, if possible. In May 1984 those conditions brought clear skies across the southern states and a fine annular eclipse was enjoyed by millions from Georgia to the Carolinas. The motion of these systems can be forecast quite accurately about 36 to 48 hours ahead of time, allowing lots of time for planning and travel.

If weather systems expected for eclipse day are weak or poorly defined, forecasts will be less accurate and inclined to change as the day approaches. Chasers may have to travel over greater distances to reach areas where forecasters are more certain of events on eclipse day. Staying closer to home and using the satellite imagery shown on commercial television to plan at short notice is another alternative. A few hours driving may place you in an opening in an otherwise unpromising sky. Be careful when using such images, since many television stations process the pictures for a more attractive display and may lose some of the finer and smaller cloud details. The larger weather systems with the greatest amount of cloud are always visible. Watch the various forecasts from several different channels, or contact the U. S. National Weather Service or Environment Canada to allay any doubts.

Next section NASA RP 1301: Weather Prospects for the Eclipse: The Azores


THE AZORES

A few rocky islands in the eastern Atlantic offer a landsman's perch from which to watch the eclipse as it speeds to Africa. The islands are located under a strong and permanent high pressure anticyclone, but skies are anything but clear in the humid air. Santa Maria Island shows only a 15% frequency of scattered cloud at eclipse time. Clear skies have a frequency of zero! However, this altogether dismal statistic may not be entirely representative of the eclipse prospects. Oceanic islands often have a considerable variation in cloudiness between leeward and windward sides. In this case the improvement is probably meager. Table 15 shows that none of the sites in the Azores have promising statistics.

Next section NASA RP 1301: Weather Prospects for the Eclipse: Morocco

MOROCCO

As the golden-ringed sun settles toward the horizon it reaches the shores of Morocco and the city of Casablanca. It's not an auspicious ending. Casablanca is a fairly cloudy city, with a climate that resembles that in the Baja. As in Mexico, the controlling influence on cloudiness in northwest Africa is a large and permanent high pressure cell - the same one which controls the weather of the Azores. Strong northerly winds circulating around this high push the cool Canary Current southward along the coast of Morocco. The by now familiar combination of cool ocean breezes and moist air trapped beneath a temperature inversion conspire to cloak the coast in low clouds and occasional fogs. The eclipse ends in much the same weather as it began.

Inland regions usually escape the marine cloudiness, especially on the rising slopes of the towering Atlas mountains. The probability of a sunny sunset increases from a dismal 30% on the Atlantic shores to a promising 50% near the end of the track ( Figure 9). Cloud seems to pile up against the mountains in the neighborhood of Ifrane, which reports fewer sunshine hours than any other Moroccan location in Table 15. Cloudiness in the interior comes from a variety of sources. The most likely is a low pressure depression related to more intense systems moving over Europe. Another is a passing low pressure disturbance which travels eastward into the Mediterranean. Sometimes the latter originate in the Atlantic, and pass through the Straits of Gibraltar. At other times they form on the east side of the Atlas Mountains and move across the northern reaches of the Sahara Desert through Algeria and Libya.

If the track is just right, these lows can draw hot oppressive dusty air from the desert, a wind known as the sahat in Morocco and the scirocco elsewhere in north Africa. The scirocco is not usually as intense over Morocco as other parts of the Mediterranean, but the dust can be a considerable problem for eclipse chasers. One description, though not over Morocco, confesses to a yellowish leaden sky "through which the sun can be seen only as pale disk, if at all." Satellites have traced Saharan dust all the way to the Caribbean. From Tangier eastward about 5 scirocco days per month are reported in May.

As the scirocco lows move eastward, winds turn northerly again and moist air is drawn inland against the Atlas Mountains. Lifted by the terrain, clouds build deeply, bringing the occasional rains and thundershowers of spring. These variable weather systems are especially favored in May. Even so, sunshine is the dominant element, with most inland areas receiving an amount comparable to northern Mexico.

One of the major problems for sunset eclipses is the apparent thickening of cloud near the horizon due to perspective effects. Skies must be fairly clear to hold promise of an open horizon, as many discovered in southern California in 1992. Haze may obscure the horizon, hiding low cloud layers until silhouetted by the declining sun, leaving only a half hour or less for movement to a more promising location. Since the terminus of the eclipse is on the Sahara side of the Atlas Mountains, the horizon view to the west will be blocked by the terrain. These are significant peaks with some summits reaching over 3500 meters along the center line. The most promising chances are likely to be found about 150 kilometers inland, perhaps somewhere along the road joining Marrakech and Meknes where the view to the setting sun is unobstructed. Another promising route is along the highway from Casablanca to Khouribga and beyond, climbing steadily upward from the coastal plain.

Chasers will have the best chance of success if they've scouted a few locations beforehand. Up-to-date weather information and a commitment to mobility will also help. Luckily the eclipse is late in the day, affording considerable time and daylight for planning and decisions.

Next section NASA RP 1301: Observing the Eclipse: Eye Safety during Solar Eclipses

OBSERVING THE ECLIPSE

EYE SAFETY DURING SOLAR ECLIPSES

The Sun can be viewed safely with the naked eye only during the few brief minutes of a total solar eclipse. Annular and partial solar eclipses are never safe to watch without taking special precautions. Although more than 88% of the Sun's surface is obscured during May's annular phase, the remaining photospheric annulus is intensely bright and cannot be viewed directly without eye protection. Do not attempt to observe the partial or annular phases of the eclipse with the naked eye. Failure to use appropriate filtration may result in permanent eye damage or blindness!

Generally, the same equipment, techniques and precautions used to observe the Sun outside of eclipse are required [Chou, 1981; Marsh, 1982]. There are several safe methods which may be used to watch the partial and annular phases. The safest of these is projection, in which a pinhole or small opening is used to cast the image of the sun on a screen placed a half-meter or more beyond the opening. Projected images of the sun may even be seen on the ground in the small openings created by interlacing fingers, or in the dappled sunlight beneath a tree. Binoculars can also be used to project a magnified image of the sun on a white card, but you must avoid the temptation of using these instruments for direct viewing.

Direct viewing of the sun should only be done using filters specifically designed for this purpose. Such filters usually have a thin layer of aluminum, chromium or silver deposited on their surfaces which attenuates both the visible and the infrared energy. Experienced amateur and professional astronomers may use one or two layers of completely exposed and fully developed black-and-white film, provided the film contains a silver emulsion. Since developed color films lack silver, they are unsafe for use in solar viewing. A widely available alternative for safe eclipse viewing is a number 14 welder's glass. However, only mylar or glass filters specifically designed for the purpose should used with telescopes or binoculars.

Unsafe filters include color film, smoked glass, photographic neutral density filters and polarizing filters. Deep green or grey filters often sold with inexpensive telescopes are also dangerous. They should not be used for viewing the sun at any time since they often crack from overheating. Do not experiment with other filters unless you are certain that they are safe. Damage to the eyes comes predominantly from invisible infrared wavelengths. The fact that the sun appears dark in a filter or that you feel no discomfort does not guarantee that your eyes are safe. Avoid all unnecessary risks. Your local planetarium or amateur astronomy club is a good source for additional information.

Next section NASA RP 1301: Observing the Eclipse: Sky at Maximum Eclipse

SKY AT MAXIMUM ECLIPSE

Since annular eclipses are not accompanied by the twilight skies seen during total eclipses, they do not present an especially good opportunity to view planets in the daytime sky. Nevertheless, Venus can be observed in broad daylight provided that the sky is cloud free and of high transparency (i.e. - no dust or particulates). During the May 1994 eclipse, Venus will be located 27.7deg. east of the Sun. Look for the planet by first covering the eclipsed Sun with an extended hand. Other planets may be attempted but chances of successful detection are quite small. The following ephemeris [using Bretagnon and Simon, 1986] gives the positions of the naked eye planets during the eclipse. Delta is the distance of the planet from Earth (A.U.'s), V is the apparent visual magnitude of the planet, and Elong gives the solar elongation or angle between the Sun and planet. Note that Jupiter is near opposition and will be below the horizon during the eclipse for all observers.

   Planetary Ephemeris: 10 May 1994 17:00:00 UT    Equinox of Mean Date
 
   Planet       RA    Declination    Delta     V   Diameter Phase   Elong(deg)
  
   Sun        3h 9m25s  17d41'14"   1.0099  -26.7  1900.5"     -      -
   Mercury    3 57  1   21 56 39    1.2204   -1.2     5.5    0.87   12.0 E
   Venus      5  5 20   23 58 50    1.4370   -3.4    11.6    0.88   27.7 E
   Mars       1 15 15    6 58 12    2.1730    1.4     4.3    0.97   29.8 W
   Jupiter   14 26 11  -13 -1 -5    4.4349   -2.0    44.4    1.00  168.6 E
   Saturn    22 51 57   -8-57-48   10.0626    0.4    16.4    1.00   68.9 W

Next section NASA RP 1301: Observing the Eclipse: Eclipse Photography

ECLIPSE PHOTOGRAPHY

The eclipse may be safely photographed provided that the above precautions are followed. Almost any kind of camera with manual controls can be used to capture this rare event. However, a lens with a fairly long focal length is recommended to produce as large an image of the Sun as possible. A standard 50 mm lens yields a minuscule 0.5 mm image, while a 200 mm telephoto or zoom produces a 1.9 mm image. A better choice would be one of the small, compact catadioptic or mirror lenses which have become widely available in the past ten years. The focal length of 500 mm is most common among such mirror lenses and yields a solar image of 4.6 mm.  Adding 2x tele- converter will produce a 1000 mm focal length which doubles the Sun's size to 9.2 mm. Focal lengths in excess of 1000 mm usually fall within the realm of amateur telescopes. If full disk eclipse photography on 35 mm format is planned, the focal length of the telescope or lens must be 2600 mm or less. Longer focal lengths will only permit photography of a portion of the Sun's disk. For any particular focal length, the diameter of the Sun's image is approximately equal to the focal length divided by 109.

A mylar or glass solar filter must be used on the lens at all times for both photography and safe viewing. Such filters are most easily obtained through manufacturers and dealers listed in Sky & Telescope and Astronomy magazines. These filters typically attenuate the Sun's visible and infrared energy by a factor of 100,000. However, the actual filter attenuation and choice of ISO film speed will play critical roles in determining the correct photographic exposure. A low to medium speed film is recommended (ISO 50 to 100) since the Sun gives off abundant light. The easiest method for determining the correct exposure is accomplished by running a calibration test on the uneclipsed Sun. Shoot a roll of film of the mid-day Sun at a fixed aperture [f/8 to f/16] using every shutter speed between 1/1000 and 1/4 second. After the film is developed, the best exposures are noted and may be used to photograph the partial and annular phases since the Sun's surface brightness remains constant throughout the eclipse.

Another interesting way to photograph the eclipse is to record its various phases all on one frame. This is accomplished by using a stationary camera capable of making multiple exposures (check the camera instruction manual). Since the Sun moves through the sky at the rate of 15 degrees per hour, it slowly drifts through the field of view of any camera equipped with a normal focal length lens (i.e. - 35 to 50 mm). If the camera is oriented so that the Sun drifts along the frame's diagonal, it will take over three hours for the Sun to cross the field of a 50 mm lens. The proper camera orientation can be determined through trial and error several days before the eclipse. This will also insure that no trees or buildings obscure the camera's view during the eclipse. The Sun should be positioned along the eastern (left) edge or corner of the viewfinder shortly before the eclipse begins. Exposures are then made throughout the eclipse at five minute intervals. The camera must remain perfectly rigid during this period and may be to clamped to a wall or fence post since tripods are easily bumped. The final photograph will consist of a string of Suns, each showing a different phase of the eclipse.

Finally, an eclipse effect which is easily captured with point-and-shoot or automatic cameras should not be overlooked. During the eclipse, the ground under nearby shade trees is covered with small images of the crescent Sun. The gaps between the tree leaves act like pinhole cameras and each one projects its own tiny image of the Sun. The effect can be duplicated by forming a small aperture with one's hands and watching the ground below. The pinhole camera effect becomes more prominent with increasing eclipse magnitude. Virtually any camera can be used to photograph the phenomenon, but automatic cameras must have their flashes turned off since this will obliterate the pinhole images.

For more information on eclipse photography, observations and eye safety, see FURTHER READING in the BIBLIOGRAPHY.

Next section NASA RP 1301: Observing the Eclipse: Contact Timings from the Path Limits

CONTACT TIMINGS FROM THE PATH LIMITS

Precise timings of second and third contacts, made near the northern and southern limits of the umbral path (i.e. - the graze zones), are of value in determining the diameter of the Sun relative to the Moon at the time of the eclipse. Such measurements are essential to an ongoing project to monitor changes in the solar diameter. Due to the conspicuous nature of the eclipse phenomena and their strong dependence on geographical location, scientifically useful observations can be made with relatively modest equipment. Inexperienced observers are cautioned to use great care in making such observations. The safest timing technique consists of the inspection of a projected image of the rather than direct viewing of the solar disk. The observer's geodetic coordinates are required and can be measured from USGS or other large scale maps. If a map is unavailable, then a detailed description of the observing site should be included which provides information such as distance and directions of the nearest towns/settlements, nearby landmarks, identifiable buildings and road intersections. The method of contact timing should also be described, along with an estimate of the error. The precisional requirements of these observations are +/-0.5 seconds in time, 1" (~30 meters) in latitude and longitude, and +/-20 meters (~60 feet) in elevation. The International Occultation Timing Association (IOTA) coordinates observers world-wide during each eclipse. For more information, contact:

				Dr. David W. Dunham/IOTA
				7006 Megan Lane
				Greenbelt, MD 20770-3012
				U. S. A.
Send reports containing graze observations, eclipse contact and Baily's bead timings, including those made anywhere near or in the path of totality or annularity to:

				Dr. Alan D. Fiala
				Orbital Mechanics Dept.
				U. S. Naval Observatory
				3450 Massachusetts Ave., NW
				Washington, DC 20392-5420
Next section NASA RP 1301: Plotting the Path on Maps

PLOTTING THE PATH ON MAPS

If high resolution maps of the umbral path are needed, the coordinates listed in Table 7 are conveniently provided at 1 degree increments of longitude to assist plotting by hand. The path coordinates in Table 3 define a line of maximum eclipse at five minute increments in Universal Time. It is also advisable to include lunar limb corrections to the northern and southern limits listed in Table 6, especially if observations are planned from the graze zones. Global Navigation Charts (1:5,000,000), Operational Navigation Charts (scale 1:1,000,000) and Tactical Pilotage Charts (1:500,000) of many parts of the world can be obtained from the Defense Mapping Agency. For specific information about map availability, purchase prices, and ordering instructions, call DMA at 1-800-826-0342 (USA) or (301) 227-2495 (outside USA). The address is: 

				Defense Mapping Agency CSC
				Attn: PMA
				Washington, DC 20315-0010, USA
Topographic maps of the United States at various scales (1:24,000, 1:62,500, 1:100,000, 1:250,000) can be ordered from:

U. S. Geological Survey for Alaska: U. S. Geological Survey

	Map Sales				Map Sales
	Box 25286				101  12th Ave., #12
      	Denver, CO 80225, U. S. A.		Fairbanks, AK 99701, U. S. A.
Topographic maps of Canada at various scales can be ordered from:

					Canada Map Office
					615 Booth St.
					Ottawa, ON K1A 0E9
					Canada.
It's also advisable to check the telephone directory for any map specialty stores in your city or metropolitan area. They often have large inventories of many maps which available for immediate delivery.

Next section NASA RP 1301: Algorithms, Ephemerides, and Parameters

ALGORITHMS, EPHEMERIDES AND PARAMETERS

Algorithms for the eclipse predictions were developed Espenak primarily from the Explanatory Supplement [1974] with additional algorithms from Meeus, Grosjean and Vanderleen [1966]. The solar and lunar ephemerides were generated from the JPL DE200 and LE200, respectively. All eclipse calculations were made using a value for the Moon's radius of k=0.2722810 for umbral contacts, and k=0.2725076 [adopted IAU value] for penumbral contacts. Center of mass coordinates were used except where noted. An extrapolated value for Delta_T of 59.5 seconds was used to convert the predictions from Terrestrial Dynamical Time to Universal Time.

The primary source for geographic coordinates used in the local circumstances tables is The New International Atlas (Rand McNally, 1991). Elevations for major cites were taken from Climates of the World (U. S. Dept. of Commerce, 1972).

Next section NASA RP 1301: Acknowledgments

ACKNOWLEDGMENTS

Most of the predictions presented in this publication were generated on a Macintosh IIfx. Additional computations, particularly those dealing with Watts' datum and the lunar limb profile were performed on a DEC VAX 11/785 computer. Word processing and page layout for the publication were done on a Macintosh using Microsoft Word v5.1. Figure annotation was done with Claris MacDraw Pro.

Translation into html was accomplished with the freeware rtftohtml 2.5 for the Macintosh by Chris Hector on a PowerBook 180c.

We thank Francis Reddy who helped develop the data base of geographic coordinates for major cities used in the local circumstances predictions. Dr. Wayne Warren graciously provided a draft copy of the IOTA Observer's Manual for use in describing contact timings near the path limits. We also want to thank Dr. John Bangert for several valuable discussions and for sharing the USNO mailing list for the eclipse Circulars. The format and content or this work has drawn heavily upon over 40 years of eclipse Circulars published by the U. S. Naval Observatory. We owe a debt of gratitude to past and present staff of that institution who have performed this service for so many years. In particular, we would like to recognize the work of Julena S. Duncombe, Alan D. Fiala, Marie R. Lukac, John A. Bangert and William T. Harris. The support of Environment Canada is acknowledged in the acquisition and arrangement of the weather data. Finally, the authors thank Goddard's Laboratory for Extraterrestrial Physics for several minutes of CPU time on the LEPVX2 computer.

The names and spellings of countries, cities and other geopolitical regions are not authoritative, nor do they imply any official recognition in status. Corrections to names, geographic coordinates and elevations are actively solicited in order to update the data base for future eclipses. All calculations, diagrams and opinions presented in this publication are those of the authors and they assume full responsibility for their accuracy.

Next section NASA RP 1301: Bibliography

BIBLIOGRAPHY

REFERENCES

Bretagnon, P. and Simon, J. L., Planetary Programs and Tables from -4000 to +2800, Willmann-Bell, Richmond, Virginia, 1986.

Chou, B. R., "Safe Solar Filters", Sky & Telescope, August 1981, p. 119.

Climates of the World, U. S. Dept. of Commerce, Washington DC, 1972.

Dunham, J. B, Dunham, D. W. and Warren, W. H., IOTA Observer's Manual, (draft copy), 1992.

Espenak, F., Fifty Year Canon of Solar Eclipses: 1986 - 2035, NASA RP-1178, Greenbelt, MD, 1987.

Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Her Majesty's Nautical Almanac Office, London, 1974.

Herald, D., "Correcting Predictions of Solar Eclipse Contact Times for the Effects of Lunar Limb Irregularities", J. Brit. Ast. Assoc., 1983, 93, 6.

Marsh, J. C. D., "Observing the Sun in Safety", J. Brit. Ast. Assoc., 1982, 92, 6.

Meeus, J., Grosjean, C., and Vanderleen, W., Canon of Solar Eclipses, Pergamon Press, New York, 1966.

Morrison, L. V., "Analysis of lunar occultations in the years 1943-1974...", Astr. J., 1979, 75, 744.

Morrison, L.V. and Appleby, G.M., "Analysis of lunar occultations - III. Systematic corrections to Watts' limb-profiles for the Moon", Mon. Not. R. Astron. Soc., 1981, 196, 1013.

The New International Atlas, Rand McNally, Chicago/New York/San Francisco, 1991.

van den Bergh, Periodicity and Variation of Solar (and Lunar) Eclipses, Tjeenk Willink, Haarlem, Netherlands, 1955.

Watts, C. B., "The Marginal Zone of the Moon", Astron. Papers Amer. Ephem., 1963, 17, 1-951.

FURTHER READING

Allen, D. and Allen, C., Eclipse, Allen & Unwin, Sydney, 1987.

Astrophotography Basics, Kodak Customer Service Pamphlet P150, Eastman Kodak, Rochester, 1988.

Brewer, B., Eclipse, Earth View, Seattle, 1991.

Covington, M., Astrophotography for the Amateur, Cambridge University Press, Cambridge, 1988.

Espenak, F., "Total Eclipse of the Sun", Petersen's PhotoGraphic, June 1991, p. 32.

Fiala, A. D., DeYoung, J. A. and Lukac, M. R., Solar Eclipses, 1991-2000, USNO Circular No. 170, U. S. Naval Observatory, Washington, DC, 1986.

Littmann, M. and Willcox, K., Totality, Eclipses of the Sun, University of Hawaii Press, Honolulu, 1991.

Lowenthal, J., The Hidden Sun: Solar Eclipses and Astrophotography, Avon, New York, 1984.

Mucke, H. and Meeus, J., Canon of Solar Eclipses: -2003 to +2526, Astronomisches Büro, Vienna, 1983.

North, G., Advanced Amateur Astronomy, Edinburgh University Press, 1991.

Oppolzer, T. R. von, Canon of Eclipses, Dover Publications, New York, 1962.

Pasachoff, J. M. and Covington, M., Cambridge Guide to Eclipse Photography, Cambridge University Press, Cambridge and New York, 1993.

Pasachoff, J. M. and Menzel, D. H., Field Guide to the Stars and Planets, 3rd edition, Houghton Mifflin, Boston, 1992.

Sherrod, P. C., A Complete Manual of Amateur Astronomy, Prentice- Hall, 1981.

Sweetsir, R. and Reynolds, M., Observe: Eclipses, Astronomical League, Washington, DC, 1979.

Zirker, J. B., Total Eclipses of the Sun, Van Nostrand Reinhold, New York, 1984.

Return to the 1994 May 10 eclipse bulletin description NASA RP 1301: Figures

Figures

NASA RP 1301: Tables

Tables

NASA RP 1301: Maps

Maps

Note that these JPEG files of sections of the Defense Mapping Agency Global Navigation Charts are fairly large (> 300 Kbyte each).

NASA RP 1301: Footnotes [1] The instant of greatest eclipse occurs when the distance between the Moon's shadow axis and Earth's geocenter reaches a minimum. Although greatest eclipse differs slightly from the instants of greatest magnitude and greatest duration (for total eclipses), the differences are usually negligible.

[2] Eclipse magnitude is defined as the fraction or percentage of the Sun's diameter occulted by the Moon. It's usually expressed at greatest eclipse. Eclipse magnitude is strictly a ratio of diameters and should not be confused with eclipse obscuration which is a measure of the Sun's surface area occulted by the Moon.

[3] Delta_T is the difference between Terrestrial Dynamical Time and Universal Time

[4] Eclipse obscuration is defined as the fraction of the Sun's surface area occulted by the Moon.

[5] First contact is defined as the instant of external tangency between the Sun and Moon; it marks the beginning of the partial eclipse.

Second and third contacts define the two instants of internal tangency between the Sun and Moon; they signify the commencement and termination of the umbral (total or annular) phase.

Fourth contact is the instant of last external contact and it marks the end of the partial eclipse.

[6] P is defined as the contact angle measured counter-clockwise from the north point of the Sun's disk.

V is defined as the contact angle measured counter- clockwise from the zenith point of the Sun's disk.

[7] For partial eclipses, maximum eclipse is the instant when the greatest fraction of the Sun's diameter is occulted. For umbral eclipses (total or annular), maximum eclipse is the instant of mid- totality or mid-annularity.

[8] Gamma is measured in Earth radii and is the minimum distance of the Moon's shadow axis from Earth's center during an eclipse. This occurs at and defines the instant of greatest eclipse. Gamma takes on negative values when the shadow axis is south of the Earth's center.

[9] This figure is derived from data collected at selected intervals during the daylight hours. The chart is not directly comparable with Figures 9 to 11 because of national differences in data collection. However the patterns of heavy and light cloudiness are similar. <\body> <\html> NASA RP 1301: Request Form for NASA Eclipse Bulletins




REQUEST FORM FOR NASA ECLIPSE BULLETINS

NASA eclipse bulletins contain detailed predictions, maps and meteorology for future central solar eclipses of interest. Part of NASA's Reference Publication (RP) series, the bulletins are provided as a service to the international astronomical community in the planning and execution of successful eclipse expeditions. They should also be useful to educators, the media and the lay community as a source of concise eclipse information. Comments, suggestions and corrections are solicited to improve subsequent eclipse bulletins.

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Permission is freely granted to reproduce any portion of this NASA Reference Publication All uses and/or publication of this material should be accompanied by an appropriate acknowledgment of the source.

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Return Requests		Fred Espenak		or		Jay Anderson		

and Comments to:	NASA/GSFC				Environment Canada

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