deletions | additions       diff --git a/and_showed_that_the_population__.tex b/and_showed_that_the_population__.tex  index 99d0c25..c9d975d 100644  --- a/and_showed_that_the_population__.tex  +++ b/and_showed_that_the_population__.tex 
...
and showed that the population between different Absolute Magnitudes is $N=\Sigma(H)\times\Delta H$, where the normalization magnitudes $H_K$ and $H_0$ are 5.61 and 7.36 respectively, $D$ is the planetesimal diameter (km), the albedo $p$ is 0.16, the power-law slopes $\alpha_1$ and $\alpha_2$ are 1.5 and 0.38 respectively, and the break magnitude $H_B$ which breaks the power-law into 2 parts is 6.9  With this relation, the population of the simulation can be separated into 128 logarithmically sized mass bins. It should be noted that to ensure each mass bin is filled with at least 1 integer object (ie no massless bins) bins), the maximum radius reduces from 500km until the bin containing the highest radius is filled with 1 integer object.  With the initial conditions selected, the 128 mass bins range from a minimum radius of $5m$ to a maximum of $130km$. This maximum is above the typical observed radius, making it suitable for the simulation.