Glad to hear that your Greek/Olympics Girl Scout camp went so well, PL. Here is a game for your next one. (Who says book larnin' has no practical uses?)
Your task is to figure out how much the Earth weighs. You are allowed to select two tools to help you. Naturally, you choose a pair of scissors and a shovel.
Point one blade of the scissors at the North Star, the other blade at the horizon and measure the angle between them. This is your latitude. (I just did this in my back yard. The latitude of Detroit is 42 and a quarter degrees.)
Now go a few miles to the South and do it again. (I drove 52 miles to Toledo. According to my scissors, Toledo is located at 41 and a half degrees North latitude.)
OK, this is a difference of three-quarters of a degree. Now we can find the circumference (C) of the Earth by the ratio
.75 degrees / 360 degrees = 52 miles / C
So the circumference of the Earth is 25,000 miles.
Step 2. Now take your shovel and dig a tunnel through the center of the Earth, all the way to the other side. When I did this last night, the length of my tunnel (= the diameter of the Earth) was
D = 25000/pi miles plus 3 millimeters.
But according to Euclid (C = pi D), this is three millimeters too long! This excess is due to the local warping of space by the Earth's gravitational field. Einstein says the extra length should be about .00000000000000000000005 cm. per metric ton of mass. So the Earth weighs
.3 cm / .00000000000000000000005 cm/ton = 6,000,000,000,000,000,000,000 tons.
Your friend, Mathman
(I can't believe I wrote that.)