Sugar Content

This one’s sketchy, but fun. I will assume that Luna has the same density as the average girl. Using the average female’s mass and volume, density can be calculated as \(\rho = \frac{51.7\ kg}{4.99*10^{-2}\ m^3} = 1040\ \frac{kg}{m^3}\). Recall from “Volume” that Luna’s volume is given by \(V=1.52*10^{23}\ m^3\). Using density and volume, calculating Luna’s mass is easy.


\(M=\rho V = 1.57*10^{26}\ kg\)


Now a brief non-sequitur. One serving of gummy bears contains 18 grams of sugar. The “World’s Largest Gummy Bear!™” is claimed to contain 51 servings of gummy bears. The seller claims that it weighs “approximately 5 pounds,” but Amazon gives a more exact shipping weight of 4.8 pounds (about 2.2 kilograms). Some dimensional analysis gives an interesting result:


\(\frac{18\ grams\ sugar}{1\ serving} * \frac{51\ servings}{1\ giant\ bear} * \frac{1\ giant\ bear}{2.2\ kg} * \frac{M\ kg}{1\ Luna}\)

\( = 6.6*10^{28}\ grams\ of\ sugar \)


Luna’s sugar content if she were made of gummy bears.

Let’s put this into perspective. The annual world production of sugar in 2015 was 172 million metric tons of sugar, or 1.72*1014 grams. At that rate, it would take \(\frac{6.6*10^{28}\ grams}{1.72*10^{14}\ grams} = 3.85*10^{14}\) years for the Earth to produce the amount of sugar needed to make a gummy bear the size of Luna.

A number so big is hard to conceptualize, so consider this. At a liberal estimate, the universe is 13.820 billion years old. With some more dimensional analysis, we find:


\(\frac{1\ universe}{1.3820*10^{10}\ years} * \frac{3.85*10^{14}\ years}{1\ Luna} = 28000\ universes\)


Which is the number of universes it would take working in parallel from the beginning of time to create enough sugar to make one Luna by the present day.

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