"A-ha" Moments

I love it when one of my students has an epiphany: one of those "aha" moments when everything clicks and all of the sudden the world makes a little more sense. Recently I was with some astronomy students at a local observatory, and I was showing them how to find the ecliptic in the night sky (the plane that contains the sun, the earth, and most of the other planets). As I gestured to the crescent moon, I mentioned that the bright side of the moon would "point" to where the sun had disappeared over our horizon. Then I mentioned that earth's north pole points toward Polaris, the North Star, and pointed out Jupiter and Saturn, high in our night sky. Just then, one of the students exclaimed, "Oh, then we're tilted!", meaning that our whole solar system is "tilted" relative to what we perceive as vertical in our little part of the world! Once I figured out what she was talking about (sometimes I take these concepts for granted), it made my night.