Peanut Earth

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).

For a perfect sphere three perpendicular lines from the center to the surface all have the same distance a (top) while for a spheriod only two of the three perpendicular lines have the same distance from the center (bottom right). If all three perpendiculars are different then we have something called a triaxial spheroid [Adapted from WikiPedia].

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.

The colors in this image represent the gravity anomalies measured by GRACE. One can define standard gravity as the value of gravity for a perfectly smooth ‘idealized’ Earth, and the gravity ‘anomaly’ is a measure of how actual gravity deviates from this standard. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker. [Credit: NASA/JPL/University of Texas Center for Space Research]

One response to “Peanut Earth

  1. Very well put Andreas, and bearing in mind additional thinking on the subject of ice ages, for example, (but not only), Earth’s Shifting Crust by Charles H Hapgood; where he and others postulate, that ice ages are the result of imbalances in the dynamics of rotation of the “peanut” caused by ice deposited above sea level; we may be about to observe the result of both the removal of vast quantities of mass from below the surface, (Oil comes to mind), and the ongoing changes to above sea level ice deposits. Food for thought?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.