From 01426f1080e7bfaf222583d171ccf3c645250a00 Mon Sep 17 00:00:00 2001
From: Will King <kin12017@byui.edu>
Date: Sat, 6 Mar 2021 16:50:50 -0800
Subject: [PATCH] Kessler region depends on loss functions

---
 CurrentWriting/sections/06_KesslerRegion.tex | 15 +++++++++++++++
 1 file changed, 15 insertions(+)
 create mode 100644 CurrentWriting/sections/06_KesslerRegion.tex

diff --git a/CurrentWriting/sections/06_KesslerRegion.tex b/CurrentWriting/sections/06_KesslerRegion.tex
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+++ b/CurrentWriting/sections/06_KesslerRegion.tex
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+\documentclass[../Main.tex]{subfiles}
+\graphicspath{{\subfix{Assets/img/}}}
+
+\begin{document}
+Given the definition of kessler syndrome and the law of debris above, we can now 
+explicitly describe the proto-kessler region.
+\begin{align}
+ \epsilon < -\delta D_t + g(D_t) + \gamma \sum^n_{j=1} l^i(\{s^j_t\},D_t) + \Gamma \sum^n_{j=1} \{x^j_t\}
+\end{align}
+As being in the proto-kessler region is a prerequesit to being in the kessler region, we see that
+the kessler region depends on the collision rates of the constellation operators.
+
+Although this is a straightforward result, I have not found it in any of the models I've examined so far.
+I suspect it will impact optimal pigouvian taxation, but of course, I need to verify this.
+\end{document}