Welcome to today’s exciting episode of “How Big a Dork Am I?” Today, we’ll be discussing the making of unnecessary models:

In this graph, the blue points represent the average mass in grams of a fetus at a given week of gestation, while the red line is the mass predicted by a simple model treating the fetus as a sphere of uniform density with a linearly increasing radius.

The “model” was set up by taking the 40-week length reported at BabyCenter, and dividing by two to get an approximate radius for the spherical baby. Then I assumed that the actual radius increased linearly from zero to the final value, calculated the volume of the sphere, and multiplied by a constant density to get reasonable agreement between the model and the data.

If you take the numbers I put into this, and use them to estimate the mass of a cell in this model baby, you find that a cell with a volume of one cubic micron (10^{-18} m^{3}) would have a mass of about 50 femtograms, which is kind of low, but remarkably good for such a silly model.

Oh, the things I will do to amuse myself…