★ APPLICATIONS ★ DIVERS ★ Aleatoire presents a program to predict total eclipses of the sun ★ |
| Eclipse Predictor (Computing with the Amstrad) | Applications Divers |
ASTRONOMY is the oldest science and it is said that in 2159 BC, which is over 4000 years ago, two Chinese astonomers, Hi and Ho, were executed for failing to predict an eclipse. Actually it is more likely that they made an error in preparing the official calendar. Nevertheless the Chinese were definitely predicting eclipses during the Shang dynasty, circa 1766-1123 BC, but it is the Babylonians who are credited with the discovery of the Saros period. Very briefly, what the Babylonian records revealed was that if a solar eclipse, be it partial, annular or total, occurred at a certain location then a similar eclipse would occur again in that location in exactly 18 years, 10 days and 8 hours. Figure I: Diagram of good total eclipse conditions >> To explain this constant Saros period and predict eclipses it is convenient to consider the Earth as fixed and to suppose the observer to be at the centre of the Earth. To this observer the sun and moon appear to move against a celestial sphere - the star background. Looking down onto its North Pole the sun moves anti-clockwise round this sphere once a year in a path called the ecliptic and the moon moves round in the same direction about 12 times faster, that is once a month. We have partial eclipses because the moon's orbit is tilted to the ecliptic by five degrees. This means there are only two places in its orbit where the moon could overlap and hide the sun if the sun were there. Usually, though, the moon appears to sail above or below the sun. These intersections are called the nodes (ascending and descending) and, because the Earth is 8000 miles in diameter, the moon has only to be within about 13 degrees of a node for it to produce an annular or total eclipse somewhere on the Earth. We have annular eclipses because the moon s orbit is so elliptical that for most of the time it appears to be slightly smaller than the sun and so, for a total eclipse, we need to define the apsides, that is that part of the orbit where the moon is close enough to appear larger than the sun. The apsides cover about 144 degrees of the 360 degree orbit. Therefore, to get a very long total eclipse, we need the sun, the moon, the centre of one of the nodes and the centre of the apsides to be lined up as shown in Figure I. Now the Greeks were aware of the nodes and apsides in the second century BC and also aware that these imaginary points are moving. The reason for this is mainly due to the sun s gravity and can be explained by Newton's theory of gravitation. Suffice it to say that the apsides To be more figurative, the time taken by the moon to complete one orbit in relation to the sun. that is from new moon to new moon or the synodic month, is 29.5306 days. The time for the moon to complete one orbit in relation to the apsides is the anomolistic month = 27.5306 days and finally we have the nodal month = 27.2122 days. Now there was a 7.2 minute total eclipse (almost the maximum possible time) on June 20 1955. Therefore we can assume that the sun, moon, nodes and apsides were very close to the line-up shown in Figure I. Type in Listing I and it should predict total eclipses between that starting date and September 12 2053. Note that it does this by counting in svnodic months (line 190) - that is, from new moon to new moon - then calculating if this vital junction is also close enough to the centre of the apsides (line 200) and also to the centre of one of the nodes (lines 210 and 220) to produce a total eclipse. If close enough it calls the subroutine in line 300 to print the current date. Finally it increments the number of degrees that the nodes and apsides have moved per synodic month in lines 250 and 260. Although the output may appear a random sequence you should find many dates related by the Saros period (each date being 18 years 10 days 8 hours apart) particularly the sequence: JUN 20 1955 As a final check that your program is working note that August 11 1999 is the next, and only, date of a total eclipse that will be visible in England this century. It will occur in Cornwall but predicting exactly where (rather than just when) requires a much more complex program.
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