Eclipse Notes
Mark Pottenger
The solar eclipse coming on August 11, 1999 seems to be getting an unusual amount of attention from the astrological community. Below are expansions of answers to questions I have received in the last few weeks.
The first question was: “Why does the eclipse path move from west to east rather than east to west?”
A total solar eclipse is caused by the Moon passing directly between the Earth and the Sun and casting a shadow on the Earth.
Think of the geometry (NOT TO SCALE!):
The cone coming to a point on Earth is the umbra (full eclipse shadow). A perfect line-up is the height of the eclipse. The double cone getting wider around the Earth is the penumbra (partial eclipse shadow).
Now think of the motions (grossly simplified, umbra only) (NOT TO SCALE!):
This is drawn from a horoscope perspective with East left and West right, with a centerline locked to Sun-Earth so only the Moon & shadow relative motion shows.
The Sun and Moon both have apparent diameters of about 30 minutes of arc (half a degree). On August 11, 1999, the Moon will be moving about 13 degrees per day faster than the sun zodiacally. The zodiacal motion is opposite apparent diurnal motion caused by rotation of the Earth. The zodiacal (or Right Ascension for astronomical purposes) motion determines the duration of the eclipse. The partial eclipse is from the first bit of the Moon hiding the first bit of the Sun to the last bit of each. This is roughly 30’ Moon motion from first contact to full coverage and another 30’ motion to last contact. With the Moon moving about 13 degrees per day faster than the Sun, 1 degree of motion is about 1/13 of a day or about 1.85 hours. If the Earth were a point, that would be the total duration of an eclipse. Since the Earth is actually several thousand miles across (think of parallax corrections), the full duration is longer than the duration viewed from a single point, but it is still only a few hours. The total eclipse lasts only as long as the Moon fully hides the Sun from a given observer, a number requiring much more exact figures than the approximations I am giving here. The apparent diurnal motions, while 360 times greater than the Sun’s zodiacal motion and about 26 times greater than the Moon’s zodiacal motion, are almost irrelevant to determining eclipse motions because they affect the apparent positions of the Sun and Moon equally. It is the real, separate zodiacal motions that matter.
You can see from this diagram that the Moon’s west to east zodiacal/RA motion produces a shadow that sweeps into, over and past the Earth from west to east. The Earth will rotate under that moving shadow, but a few hours of rotation won’t overpower the zodiacal/RA motion shown above. Full eclipse calculations take in a lot more work: exact sizes & distances, shape of the Earth, declinations of Sun and Moon, etc.
Going to a reference book by someone who did all the detailed calculations, I found the following values. Umbra start 9:29:52.1 UT, greatest eclipse 11:03:04.9 UT, umbra end 12:36:24.0 UT, all using a delta t value of 64.5 seconds. The actual umbra period is just over 3 hours, so the earth’s rotation under the moving shadow in the period is about 47 degrees. If the Earth was not rotating as the shadow passed and if the eclipse path was exactly along the equator, the path of the shadow would cover the full 180 degrees of longitude of the side of Earth facing the Moon. Since eclipse paths are rarely exactly equatorial, there is also a latitude component in the actual paths. For the eclipse this August, the actual path is about 155 degrees of longitude and about 25 degrees of latitude (eyeballing from a map).
For anyone interested, here is an address for a map of the August 1999 eclipse:
http://riemann.usno.navy.mil/AA/data/docs/eclipse/aug99se.html.
The second question about the August eclipse related to aspects. There will be a grand cross at the time of the eclipse, and I was asked how common this is.
I keep on hand a chart file with daily 0 UT charts for just over a century (36,526 charts from January 1, 1900 through January 2, 2000). A file like this can be handy for occasional astronomical questions. I set orbs of 5 degrees for squares and oppositions. I did a query to copy any charts with Sun opposite any of the outer planets (Mars, Jupiter, Saturn, Uranus, Neptune and Pluto—I did not look at asteroids and Mercury and Venus can't reach a square or opposition to the Sun) to a subset file. This query extracted 4,702 charts. I did another query to copy any charts with Sun square any of the outer planets from the subset file to a new subset file. This query got 962 charts. These have at least a T-square. I did 6 queries from the new subset to get the charts with at least two planets square the Sun. Separate queries were needed to handle the mixture of AND and OR logic. The 6 queries and the number of charts each found were:
Sun square Mars and square (Jupiter or Saturn or Uranus or Neptune or Pluto): 47
Sun square Jupiter and square (Mars or Saturn or Uranus or Neptune or Pluto): 60
Sun square Saturn and square (Mars or Jupiter or Uranus or Neptune or Pluto): 48
Sun square Uranus and square (Mars or Jupiter or Saturn or Neptune or Pluto): 37
Sun square Neptune and square (Mars or Jupiter or Saturn or Uranus or Pluto): 26
Sun square Pluto and square (Mars or Jupiter or Saturn or Uranus or Neptune): 21
Doing the 6 overlapping queries produced duplicate charts. I might have avoided duplicates by combining all six queries into one, but it would have been very awkward to set up. I manually deleted 118 duplicates & 3 triplicates. This left 118 unduplicated charts with 5-degree orb grand crosses or double T-squares involving the Sun. This number (118) is the final answer if the question is "how many days this century was the Sun in a 5-degree opposition and at least two 5-degree squares with major planets at 0 UT". This doesn’t guarantee crosses, since the two planets square the Sun could be conjunct each other rather than opposite (making a double T-square). It is also possible that this technique will have missed a few crosses that crossed orb boundaries between one day and the next, but since the orbs are arbitrary anyway it isn't a big concern.
This table summarizes the queries described so far.
|
Sun |
Mars |
Jupiter |
Saturn |
Uranus |
Neptune |
Pluto |
Unduplicated Total |
|
Opposite from 36526 |
350 |
826 |
914 |
968 |
979 |
961 |
4702 |
|
Square from 4702 |
188 |
209 |
218 |
182 |
162 |
124 |
962 |
|
Cross or T involving |
47 |
60 |
48 |
37 |
26 |
21 |
118 |
Since my queries up to this point were based on once-a-day (0 UT) charts and 5-degree orbs, none used the Moon. I changed my orb definition for conjunction and opposition to 15 degrees, then did two queries to get the charts with the Moon within a day's motion of conjunct or opposite the Sun. These are eclipse candidates during grand crosses or double T-squares involving the Sun. The result was 24 dates (18 potential Sun-Moon conjunctions & 6 potential Sun-Moon oppositions). These dates are not isolated, but are actually just 12 sets of date ranges captured by the 15-degree orb I used to make sure I wouldn’t miss any (9 conjunctions and 3 oppositions). Rather than enter another complex query to see if these are all grand crosses, I manually checked 12 dates and found that 2 are double-T rather than cross. The dates are:
Conjunctions (15-degree orb):
October 13, 1909 October 14, 1909 October 15, 1909
January 11, 1910 January 12, 1910
July 26, 1911
October 26, 1916 October 27, 1916 October 28, 1916 (double T: Saturn conj. Neptune)
May 12, 1926 May 13, 1926
October 12, 1931
January 15, 1934 January 16, 1934
January 27, 1941 January 28, 1941 (double T: Jupiter conjunct Saturn)
August 11, 1999 August 12, 1999
Oppositions (15-degree orb)
February 23, 1959 February 24, 1959
May 9, 1963 May 10, 1963
July 28, 1999 July 29, 1999
If anyone wants to do similar queries for other centuries or wants to filter grand crosses at the earlier step where I got 118 charts, the 6 queries above should be revised on the following model: Sun square Mars and square (Jupiter or Saturn or Uranus or Neptune or Pluto) and Mars opposite (Jupiter or Saturn or Uranus or Neptune or Pluto).
I don't have eclipse data in my program, so the 12 date ranges (9 possible solar & 3 possible lunar eclipses) had to be checked against a source with eclipse data. I found the following in eclipse canon books:
Partial Solar Eclipse October 11, 1931 12:55:37 ET
Total Solar Eclipse August 11, 1999 11:04:09 ET
Partial Lunar Eclipse July 28, 1999 11:33.7 UT
Based on my queries, it looks like the August 1999 eclipse is the only total solar eclipse this century that occurs with the Sun in a 5-degree orb grand cross with the outer planets. It is also the first Sun conjunct Moon grand cross with the outer planets in 65 years.