Angular Diameter, Sect, the 5-degree rule and the Aries Ingress

Modern practitioners of Hellenistic astrology have noticed that when the Sun is very close to the Ascendant, it can sometimes be difficult to judge the sect (diurnal or nocturnal) of a chart when delineating it using Hellenistic methods. Technically speaking, a day chart is defined as one with the Sun above the horizon, and a night chart as one with the Sun below the horizon. The problem is that the Sun does not suddenly jump from below to above the horizon. It takes some time for the body of the Sun to cross over Ascendant. To complicate matters, there is also an issue of refraction of the sun’s rays by the Earth’s atmosphere, which causes the sun to appear to be in a place other than it is in reality.

Let’s start with the angular diameter of the Sun. The following diagram from wikipedia makes this clear:

Modern measurements of the angular diameter of the Sun give a figure of about 32 minute of arc, or about half a degree. Because the Ascendant takes about 4 minutes to change by 1 degree, we can estimate that the body of the Sun will take about 2 minutes to cross over the horizon.

But now the interesting part. To an observer on Earth, the sun appears to rise before the body of the sun even reaches the horizon due to the refraction of the sun’s light by the Earth’s atmosphere. The following diagram from wikipedia makes this clear:

Due to refraction the sun appears to have an angular diameter of 34 minutes of arc, a figure often found in older astrological texts which were based on observation. This is why cazimi is defined as being within 17′ of arc of the center of the Sun.

In addition, the Sun appears to rise while its body is still beneath the horizon. As can be seen in the diagram, the center of the Sun lies about 50 arc-minutes below the horizon when the upper tip of the sun first appears on the horizon, and the lower tip of the body of the sun lies about 50′ + 17′ or 67′ below the horizon. It takes the Ascendant a little over 4 minutes to traverse 67 minutes of arc, so that during this roughly 4-minute period we are in a gray zone about whether to consider the chart to be of the diurnal or nocturnal sect.

I wondered if Ptolemy, who was an astronomer and natural scientist, allowed these observations about sunrise and the refraction of the sun’s light by the Earth’s atmosphere to influence his thinking about the 5-degree rule in astrology. With this in mind I calculated the time it would take for the Ascendant to traverse 67′ of arc in Alexandria, Egypt, around sunrise for the cardinal solstices and some dates in between. Here are the results.

Time to traverse 67′ of arc in Alexandria around sunrise:

As you can see, the average duration was about four and a half minutes with a range from a low of just over 3 minutes to a high of just over 5 minutes. My hypothesis is that Ptolemy, knowing that the symbolism of the Ascendant in astrology is based on the rising of the sun, applied his astronomical observations of the duration of the sun’s rising as one consideration in the development of his 5-degree rule for the Ascendant in astrology. In other words, could Ptolemy have had in mind, as astrologers sometimes do, an equivalence of 1 minute of clock time to 1 degree on the ecliptic? At the very least during these 3 to 5 minutes of duration of the rising of the sun, the chart remains somewhat ambiguous about its sect, that is, whether it should be interpreted as a day or night chart.

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A related issue comes up with regard to the timing of the Aries ingress (or any other ingress of the Sun). The Sun travels about one degree every day and half a degree in 12 hours.

Do we time the ingress from the moment the tip of the body of the Sun touches 0 Aries, or when the center of the Sun conjoins 0 Aries, or when the final edge of the Sun crosses over 0 Aries so that the entire body of the Sun lies in the sign Aries. The crossing of the body of the Sun from Pisces fully into Aries lasts a span of about 12 hours.

This issue poses a potential conundrum for astrologers who use Whole Sign houses. If the body of the Sun is partly in Pisces and partly in Aries, it must be simultaneously in two whole sign houses, somewhat like a person standing at the Equator with one foot in the northern hemisphere and one foot in the southern hemisphere. How does one interpret a planet that is partially in two houses at once?

I think the convention in modern astrology programs is to cast the ingress for the moment that the center of the Sun conjoins 0 Aries, but at that moment part of the Sun has been in Aries for about 6 hours  and part of the Sun will remain in Pisces for the next 6 hours.

It would be interesting to cast a chart for the Aries ingress for the moment that the forward edge of the body of the sun first touches 0 Aries to see if this convention produces a more meaningful astrological chart. To use a human analogy, am I at your house when my foot first enters the threshold, when the center of my body is exactly centered in the threshold, or when my entire body is just inside the front door?