The author also seems to have an interesting course on astronomy and culture:

We will look at questions like: How is the date of Chinese New Year determined? Why do the Muslim and Chinese months start on different days? Will the Moon ever look like it does on the Singapore flag? What date of the year is the earliest sunrise in Singapore? How did ancient sailors navigate?

http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html

The key to really getting this for me was:

You may also want to remember that it is the barycenter of the Earth-Moon system that moves in an ellipse around the Sun, and that the orbits of both the Earth and the Moon are perturbations of this ellipse.

what about other planets & satellites in our solar system??

this is something i need a video to understand properly

Not a video, but a helpful image:

http://upload.wikimedia.org/wikipedia/commons/1/1d/Moon_traj...

mm... nope. that didn't help

between the quote below from the article and the excellent picture above, you should be able to see it....Try again, cuz it's really interesting.

"Imagine you're driving on a circular race track. You overtake a car on the right, and immediately slow down and go into the left lane. When the other car passes you, you speed up and overtake on the right again. You will then be making circles around the other car, but when seen from above, both of you are driving forward all the time and your path will be convex."

When I first saw the article on reddit, I tried to see if I could figure it out myself, by trying to imagine motion of moon and Earth. But I couldn't.

Then I went to the article and was skimming through it. Just gave up when I hit this imagine "race track" thing. Was too lazy at that point in time.

However the wikipedia picture did it in seconds. I didn't even have to read the above quote :) Just proves that "a picture is worth a thousand words"

That works actually, thanks