Thursday, May 18, 2017

Apparent Solar Motion in the Southern hemisphere.

It is often taken for granted in the Australian pagan/neopagan scene that circle-casting in the southern hemisphere should be done anti-clockwise. The usual justification for this is that the circle should be cast in the same direction as the apparent motion of the Sun (and all the other heavenly bodies) across the sky, and while that motion is clockwise in the northern hemisphere, it's anti-clockwise in the southern hemisphere, so we need to reverse the traditional circle-casting direction when south of the equator. I shall examine the “following the Sun” concept by assuming it is true, and determining what it means for practitioners at different latitudes.

The trouble with using these assumptions is that it is simply not true that the Sun always follows an anti-clockwise path through the sky in the southern hemisphere (nor does it always follow a clockwise path in the northern hemisphere). It is true that the sun's apparent motion is always in the same direction when viewed from north of the Tropic of Cancer or south of the Tropic of Capricorn, but it is not true of any point within the tropics.

To visualise the reasons for this, we start with a simplified model of the situation by assuming that the Earth is not tilted on its rotational axis relative to its orbit around the Sun. Later we will build on that model to arrive at a correct understanding of the Sun's actual motion through the sky (within reason; I'm not going to go into more arcane matters such as the precession of the equinox, only what we need to determine the Sun's true apparent motion with regard to direction).

Let's start by imagining we're standing on the North Pole. Before us is the Sun, burning with attenuated light right on the horizon, appearing to be half set. If we remain there for a full 24 hours, the Sun will seem to move clockwise around the horizon through a full circle and return to its starting point.

Now imagine us travelling south from the north pole. The Sun rises as we move south, soon clearing the horizon altogether. If we stop at various points on our journey and observe the Sun through a 24 hour cycle, it still travels through a full circle to return to its starting point, but that circle is no longer identical to the circle of the horizon. The southernmost edge of the Sun's path is now above the horizon by as many degrees as the degrees of latitude we have moved south from the north pole. No matter where we are in our journey from the pole, the Sun will always rise precisely in the east and set precisely in the west. The Sun's path acts as if it's a great circular hoop attached at two points to the horizon, directly to our east and west, with the hoop being tilted further up into the sky to the south (and down below the horizon to the north) the further south we go. As we continue our journey south across the northern half of the planet, the Sun's apparent motion remains clockwise.

Eventually we find ourselves arriving at the equator. The Sun, which was previously due south at local midday is now directly overhead. We have reached a critical boundary in our journey, for there is now no objective way to ascribe either clockwise or anti-clockwise motion to the Sun's path. To do so would require selecting which direction along the north-south path you're taking to 'face' the Sun from, and there's no objective reason for either choice. This is why some practitioners who accept the 'Sun-wise' casting paradigm will often state that the equator is an exceptional place in this respect.

We continue our journey south of the equator, and once again it makes sense to speak of the Sun going around in a particular direction, but now that direction is the opposite of that for the northern hemisphere. From the southern hemisphere, the Sun appears to go around anti-clockwise. This evolution continues until we reach the south pole, and we once more see the sun half-sunken beneath the horizon and moving around it once every 24 hours, but this time it is clearly appearing to move in the opposite direction to its motion at the north pole, anti-clockwise instead of clockwise. Of course, the Earth is still spinning in the same direction as before, but we are seeing the results from a new perspective. We are effectively standing upside down relative to our orientation at the north pole.

Imagine that Earth is at the centre of a very large hollow sphere and the sky above is the inner surface of the shell. Directly above the north pole is a point on that imaginary sphere called the north celestial pole, and above the south pole lies the south celestial pole. A point above the equator will trace out a great circle across the celestial sphere over a 24 hour period called the celestial equator. In our simplified model, the sun always remains exactly on the celestial equator, and if that were true in reality, the claim that northern hemisphere = clockwise solar motion and southern hemisphere = anti-clockwise solar motion would always be true, regardless of our latitude or the calendar date.
Because the Earth's rotational axis is tilted away from a right angle to its orbital plane, the true situation is more complicated. The Sun spends some time close to the celestial equator, but it's usually perceptibly removed from it, and reaches 23.5 degrees north or south of it during solstices. When it is some distance away, it's path is not a great circle, but a nearly circular spiral sweep at some particular celestial latitude in the northern or southern tropics. Once again, anyone north of that path (i.e., the point on the celestial sphere directly overhead from them is north of that path) will see the Sun moving clockwise and anyone south of it will reckon the Sun to be moving anticlockwise, but that path could be as far south as Rockhampton or nearly to Alice springs, or a bit further north than Hawaii. The closer a tropical location is to the equator, the more evenly the time is divided between being north or south of the Sun's path. Darwin is over halfway to the equator from the Tropic of Capricorn, and so spends about 25% of the time being north of the Sun's path, whereas we would need to drive a few dozen kilometres north of Rockhampton to ensure at least one full day of seeing the sun passing to our south at southern midsummer. Residents of Honolulu might get several days of seeing the Sun pass to their north around midsummer for the northern hemisphere.

Practitioners living in the tropics who adhere to 'Sunwise' casting may want to learn about how the Sun's apparent motion varies throughout the year, and cast in the direction indicated by local astronomical conditions. What is correct one day might not be on the next. People who live in the tropics and wish to experiment with the results of casting the circle this way or that relative to the Sun's apparent motion have an interesting opportunity to check an extended range of possibilities.

No comments:

Post a Comment