Ancient astronomers got pretty good at predicting lunar eclipses and had trouble predicting solar eclipses.
One person was said to have predicted a solar eclipse in 585 BC, but his method was abandon since it was not reliable.
In 1715 Sir Edmund Haley was able to predict a solar eclipse. I will not tell you how, but he used something rhyming with mewton's slaw of fravity.
Creating a map that people could navigate with has been proposed. Unfortunately it is something beyond the current capabilities of FES.
I trip to Antarctica is out of the question. Who ever went would be meet by a naval blockade and if they managed to slip by them would die horrible deaths in the harsh environment.
Buying a ticket for any flight between Australia to South America and verifying the flight time seems something beyond reach.
Why not just work on a FE model where you can predict lunar eclipses? Seems kind of where our ancient ancestors started. Once you get a reliable model with that you can use it as a foundation to build on and figure out other stuff.
http://www.timeanddate.com/eclipse/list.htmlOnce you can do something like what is in the link you will know you are on the right track.