The existence of the power law has been witnessed in various networks created by humans in various forms as discussed in class. As previously discussed it shows in various social constructs such as social networks and even actor collaborations, however the power law also makes itself apparent within nature and in our planet. What is even more interesting however, is that the power law exists to even a scale as large as celestial bodies, from Pluto, to our moon and even the sun itself, the power law is everywhere.
One study looks into the the craters in Pluto, upon the recent high resolution pictures of Pluto, scientists were able to look at the actual craters in the planet. It investigated 87 craters in Pluto, ranging from sizes of 0.87km to 37.77km. It was found that there was a scaling coefficient of “α = −2.4926 ± 0.3309”, with a “Dmin = 3.75 ± 1.14 km” (or xmin if we use the formula we discussed in class). Upon values of distance D within the range “[3.75 ± 1.14 km, 37.77 km]” there was a log likelihood (L) = 104.5688. It is incredibly interesting that these scientists are using the same formulas we are to calculate the scale and witness power law on a celestial scale!
Below indicates a segment of craters within Pluto that were analyzed for their crater size
The study then continued to look at how these craters were very comparable to power-laws in other celestial bodies such as our Moon, Mar’s satellites Phobos and Deimos, and even the Earth! As an interesting tangent, the study also referenced how the power law existed in the relationship between the frequency of solar flares and total flare energy. Going on to provide other examples such as the distribution of initial masses for star populations, Kepler’s third law, and even to the scale of the distribution of galaxies in the universe! It is incredible to think of how this law shows itself throughout the universe. From human social constructs, things we made, to the scale of galaxies in the Universe!