I got in trouble in class today. When the earth was introduced as a sphere, I disagreed and stated that the earth was shaped like a peanut instead. While it got me laughs from some students, not everyone was amused. And yet, I am serious on two counts:
First, a sphere is a well defined shape that depends only on its radius. A sphere is a perfect mathematical idealization without a blemish such as a scratch, a bump, or a hole. It is also perfectly symmetric in two angles that I call longitude and latitude.
Second, a peanut eludes definition, because each peanut differs slightly from the next. It approximates a sphere poorly. Perhaps a spheroid is better approximation. It results when an air-filled beach ball is squished at its North-Pole. Still this does not look like a peanut, but instead of one parameter (its radius a), we now use two parameters (a and b) to describe it better. Or better yet, let us use three parameters (a and b and c).
We can keep going like this for many, many more parameters by fancy sounding mathematical constructs. Still, neither peanut nor earth will ever be defined by perfectly defined mathematical objects, but a finite sum of them may approximate a true shape well enough. Both peanut and earth occur in nature and thus reflect physics, biology, and chemistry. As such our peanut earth can only be approximated by something mathematical, but the mathematics are always off by an amount that we can always make smaller by adding more parameters to describe the shape. In my glacier work off Greenland I use about 2200 such parameters to describe the shape of the earth to accurately represent its floating ice shelf.
Closing my argument, I find that the little peanut has more in common with our planet earth than a sphere. Peanut and earth may look different from a distance, but the closer we look, and the better our sensors become, and the more accuracy we require, the closer our approximation of earth resembles our approximation of the peanut. The sphere is just the first of many approximations of the real thing. The real thing has a name and the Smithonian Institution defines and describes geoid much better than I do here calling it peanut earth.