My major retirement project has been education -- mentoring students at a local high school and more recently at UCSD. I think a lot about simple experiments to demonstrate basic principles of physics. For example, you can connect a resistor to a sensitive radio receiver, dunk the resistor into liquid nitrogen and have the students hear for themselves the sudden drop in noise level. It's hard to think of a more vivid demonstration of thermally vibrating molecules.

We fly high altitude balloons with cameras, and I'm always having to caution the students that they are *not* seeing the curvature of the earth. This usually becomes obvious enough when the camera swings back and forth and the horizon goes from being convex to concave. It's just an artifact of the camera lens.

But there is a way we might actually do it and even come up with a reasonable estimate of the earth's size. I read an airline pilot saying that he often sees other planes above the apparent horizon even when he knows them to be at lower altitudes than his own. The reason, of course, is that his sight line to the horizon is not perpendicular to his local vertical; it's lowered because of the earth's finite size.

This suggests a way to demonstrate and even measure the curvature of the earth from a high altitude balloon: mount two cameras looking horizontally exactly 180 degrees apart, then show that the actual angle between the horizon lines in opposite directions isn't 180 degrees. If you can calibrate the cameras and lenses, it should be possible (by counting pixels in the images) to measure the actual angle, and from that and your known altitude, estimate the diameter of the earth. I'll have to work on this one...

I've also been thinking of demonstrating that gravity decreases with altitude according to Newton's inverse square gravity formula. The problem is that the decrease at altitude is only about 1%, roughly the limit of what you can measure with those cheap and ubiquitous MEMS accelerometers, and they are probably also affected by temperature variations. But if I can figure out how to do it accurately, we could again estimate the diameter of the earth from the measured gravity reduction and the known altitude of the measurement.