astronomymagnetic fieldsplasma-physicssolar-windsun
Yesterday I saw online a lot of people seeing auroras both in the North and in the South of the globe. Unfortunately, I wasn't one of these people, and this got me curious about how much we can predict solar activity and the appearance of auroras on Earth. For example, I know we can make accurate predictions of eclipses, and weather forecasts on Earth are very common (within limitations).
In short, can we predict the appearance of auroras on Earth? If so, how good are these predictions?
The excitement behind various claims is somewhat excessive.
First, the Mayan astronomers, see e.g. Mayan astronomy at this page, didn't use any armillary spheres or sextants as others did. Their observations were made with naked eye and they were depicting positions of planets with crosses. The accuracy of the Venus' position after a synodic 584-day cycle was off by 2 hours.
It's good but it isn't unbelievably accurate in any sense. It just means that the moment when the Venus "returns to the original place" was measured with a 2-hour accuracy. As far as I know, all the Mayan models for the orbits were periodic and the imagined trajectories were circular. They have just played with lots of periods which is why they ended with lots of these baktuns and pictuns (cycles) and parallel calendars. But it was numerology based on the known periodicities, not really a precise framework to predict the positions. Let me also emphasize that there was no "dogmatism" concerning the identity of the "center of the Universe".
The Babylonians did all the astronomy with the tables. Lots of tables. Of course, they could do things much more accurately than the Mayans. It was a phenomenological approach with a lot of hard work whose basic logic only depended on arithmetics applied to measured data adjusted so that the agreement with all the data is reached. They were mapping the trajectories of the Sun and the planets in some coordinates, observed some periodicities, and were ready to calculate all the required corrections by some arithmetic formulae that were simply a good fit.
They didn't have any prejudices about the circular shape of any orbits, centers of the Universe, relationships between planets and cosmology (birth of the Universe), and so on. It was a heavily empirical approach. You could say that it was modern science but you would be missing the fact that they were simply not looking for the laws of physics that explain all the patterns and they were not attempting to reduce the amount of the independent mess. The mess was immense, the trajectories looked rather general. Effectively, the success and precision of their predictions for the locations boiled down to their having very complicated "laws of physics", laws with tons of (measured) corrections and special rules for individual planets and individual situations.
That's why the Greek astronomy represented dramatic progress because they were actually trying to make things simple, to see a rational explanation of the causes behind the particular trajectories. They were not satisfied with the empirical side of the story and that's why it was such a breakthrough. They were building mechanical models. When it comes to the accuracy, whether the orbits were thought of in the geocentric or heliocentric frame is an irrelevant technicality. The heliocentric frame is closer to allowing us to write Newton's equations as the full classical explanation which is a "culmination" of non-relativistic celestial mechanics. However, one has to do lots of other things before these final steps in order to represent the observed positions on the two-sphere by some actual trajectories in the 3D space which have a cause.
So the Babylonian models were "overfitted", using an immense amount of observed data that weren't independent from each other. Greeks wanted simple enough models that account for the facts. Circular motion is the most symmetric one so they started with it and tried to match the observations in various ways. It didn't work quite exactly so they began to build the epicycles (smaller rotating circles) on top of the deferents (main circles that carry the objects).
Epicycles are often talked about in a negative light but they represented (and similar methods represent) a very progressive intermediate phenomenological description in between the "Babylonian tables" and "simple models of trajectories given by simple equations". The idea that one circle carries another which carries the planet is pretty much equivalent to some kind of a Fourier expansion of $\vec r(t)$ and the Greek astronomers were picking several leading coefficients of this expansion (by observing them). I am sure that most people who talk dismissively about epicycles wouldn't be capable of doing anything of the sort – and anything superior, either.
Ptolemy's model was finally a very accurate description. It was a geocentric model – not only the Sun but also the other planets (and, correctly, the Moon) – were directly orbiting around the Earth. But that didn't hurt the accuracy because the orbits were described in such a way that the Sun-Earth separation was correctly subtracted, anyway.
Now, note that if the exact distances of the planets were known one could notice that in the case of all planets, we are suspiciously subtracting the same periodic function with the period of 1 year, namely the Sun-Earth separation, and we could figure out that in the heliocentric frame, things get more natural. However, when you don't know the absolute distances, things are a bit tougher. They were not aware of the possible task "get simpler by going heliocentric" so they didn't pursue it. It wasn't a problem. Even in Newton's physics, we may describe things in the Earth's frame (even a spinning, non-inertial frame) as long as all the fictitious forces are correctly added.
It's another myth when people believe that the heliocentric model implies that it has no epicycles. Instead, the Copernical model had an even greater number of epicycles than Ptolemy's model because some of the new ones replaced the equants. Ptolemy's equants were actually a rather clever observation that played a similar (although not quite as accurate) role as Kepler's observation that the Sun sits at a focus of the elliptical orbits. Of course, Kepler's precise observations about the ellipses were not known to Copernicus and they don't directly follow from heliocentrism.
Just to confirm that CuriousOne is correct as regards direct radiation damage to your body.
From Solar Flares
Solar flares are gigantic explosions associated with sunspots, caused by the sudden release of energy from “twists” in the sun’s magnetic field. They are intense bursts of radiation that can last for anywhere from minutes to hours. Solar flares and CMEs pose no direct threat to humans—Earth’s atmosphere protects us from the radiation of space weather. (If an astronaut out in space is bombarded with the high-energy particles from a CME, he or she could be seriously injured or killed. But most of us won’t have to worry about that situation.) We could, however, feel the effects of CMEs indirectly, through the disruptions to our technology—some of which could have devastating and lingering effects on civilization.
As an example of this, you could read Quebec Blackout and as we become more reliant on satellites, we spend a lot of effort hardening their electronic components against radiation. We also try to predict Solar weather, so we can turn things off before the flare affects us.
However, taking into account what I have learned from @RobJefferies comments below, your best chance of minimising indirect effects are, as you say in your post, near the equator.
Best Answer
Approximately yes, as follows.
Ham radio guys monitor solar activity closely because of the effects that it has on radio communications on earth. In this context, large numbers of sunspots are well-correlated with favorable conditions on earth for long-distance radio contacts- and the connecting mechanism is that large numbers of sunspots are correlated with the occurrence of mass ejections of charged particles from the sun. Those charged particles energize the layers of the atmosphere responsible for deflecting radio beams back to earth, thereby allowing them to carom back and forth between the earth's surface and the ionosphere and thereby circle the globe.
So you can estimate the prevalence of intense auroral activity with sunspot count.
That said, we are now at the maximum in the current 11-year sunspot cycle, which makes the coronal mass ejection responsible for last night's aurora an usual event, and demonstrates the utility of predicting auroras on the basis of sunspot count.