Eclipses

Late in 2004 I wrote some software that calculates lunar eclipses. The software is based on eclipse code written by Fred Espenak and printed as Appendix B in his reference book, the Fifty Year Canon of Lunar Eclipses: 1986–2035. This code is in turn based on algorithms published in “Astronomical Formulae for Calculators” by Jean Meeus.

I have modified the software so it can also predict eclipses for fictictious satellites located at the L4 and L5 Lagrangian points of the moon’s orbit. Like lunar eclipses, these eclipses occur when the satellites enter the Earth's shadow. These eclipse predictions are for hypothetical satellites that share the moon’s motion, but are offset from the moon’s position by 60 degrees. These eclipses are the most important because the hypothetical satellites would be in the Earth’s shadow, and thus would not have access to solar power. These hypothetical eclipses would be most useful for writers of science fiction.

There are other Lagrangian eclipses that are possible, but these are less important for various reasons. These eclipses are:

• Sun – Moon – Satellite. These are important, but not especially so. The satellite would only be in darkness for a few minutes at most.
• Sun – Satellite – Earth. These are not important because sunlight is not obscured for the satellite.
• Sun – Satellite – Moon. These are not important because sunlight is not obscured for the satellite.
• Sun – Satellite – Satellite. These are not important because the sunlight dimming is negligible.

Accuracy

The eclipse tables are reasonably accurate, but some inaccuracies do exist. Don’t use these tables if accurate timings are required. Consult an astronomical almanac instead.

• The various contact times for the eclipses appear to vary by a few minutes when compared against eclipse tables.
• The eclipse times include a fudge factor called Delta-T, which is basically a count of leap seconds. The values for Delta-T should not be treated as accurate, especially for values in the more distant future.
• When compared against accurate references, eclipses may be classified as the wrong type. Borderline total eclipses may be listed as partial, borderline partial eclipses may be listed as penumbral, and borderline penumbral eclipses may not be listed at all. This is due in part to the different constants used for the width of the Earth’s shadow. The Earth’s atmosphere contributes appreciably to the width of the Earth’s shadow and its effects cannot be predicted with perfect accuracy.
• I have no way to verify the accuracy of the predictions for the Lagrangian orbits. I can find nothing on the Web where anyone else has calculated eclipses for the Lagrangian points.

A comparison with NASA predictions

Here is a comparison of some of these eclipses with NASA predictions. The comparisons show that the predictions are good enough to know within a few minutes when the eclipse takes place, but not accurate enough for precise timings. The differing shadow widths also show up for some eclipse as disagreements over the eclipse type and whether an eclipse takes place. For penumbral eclipses, whether they are predicted to take place is academic because shallow penumbral eclipses are essentially unobservable. For the transition between penumbral and partial, and between partial and total, the difference is more obvious.

Eclipse Tables

Below are some eclipse predictions made with the software. Each of these files is about 120kb.

Long Total Lunar Eclipses

These tables show the ten longest total lunar eclipses between 2000 BC and 5000 AD, and the ten longest lunar eclipses in the twenty-first century, as computed by me. Dates before October 15, 1582 use the Julian calendar.

The longest lunar eclipses take place when the moon is at apogee, and the Earth is at aphelion. The lunar apogee increases the length of time it takes for the Moon to pass through the Earth’s shadow, and Earth’s aphelion increases the width of the Earth’s shadow at the distance of the moon. Because the Earth currently reaches aphelion in early July, the longest lunar eclipses occur in the middle of the year. At this time of the year, the full moon is highest in the sky as seen from the Southern Hemisphere, thus the Southern Hemisphere is the best place from which to observe these long lunar eclipses.