From 751f4fe9c25572eb2632e20b14464275e4067410 Mon Sep 17 00:00:00 2001 From: Will King Date: Fri, 5 Mar 2021 13:15:22 -0800 Subject: [PATCH] Wrote most of Kessler Syndrome Section --- CurrentWriting/Main.pdf | Bin 161721 -> 166060 bytes .../sections/02_KesslerSyndrome.pdf | Bin 94251 -> 96570 bytes .../sections/02_KesslerSyndrome.tex | 36 +++++++++++++++--- 3 files changed, 31 insertions(+), 5 deletions(-) diff --git a/CurrentWriting/Main.pdf b/CurrentWriting/Main.pdf index 6dd9c83ab4f2887fdf25dfe9e2e2157319710dd7..cb0888fbd5157edc1f62bd8b913d92e35ccd00b2 100644 GIT binary patch delta 44856 zcmZs=Q*5A*7p+~}nqq3(wr$&-x}Cax%c*TnZQC}cwr$(z_x+Ra;v{EZJvaMeubq{w zWVKzxR>s4{&4AX#&;A7GWBFBgqYDSd&YpOSNd;WuuG{YqKW-Z4JxNRC!yd~x2l+~^ zK}o?wSS^9VncWLTHV!g~x05x+yg%}%;zT43Ycrm0f`}VdrVk9HyY$R%Z|V6yX4lbD zi`!S}Y;IH)E|L6R9bZ+WveV=|JUebeJM$tfsy`RhZ1LsS`*yxxuIZl8XdBITe$lC4 z8wKP}=#GEztx5dqIx=k7Qny?DVXDsZ@}y&aF6sC1wbuT7c6oEQ$7S1n8PB7;>Q5eS zw^?QTCdbH~PQS@>gmkUFL=YPZXAF!qn&PM~d7`Y16M2Az$ZH;UtnVyatWQ&qhxf%U 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z-7f;1Bv|?}e8i8>Y%HHEKxmb*T6=f)OkPB5M91!SG!rD9e=Go-u8>&TpZ-mE65R0{IN?{jshGS6M5(J zjYZ1>0A2x-uu@ZzyZ{g09${)APrI 0 \right\} +\end{align} +It may be, under certain situations, the case that optimal launch rates cycle along with +debris and stock levels, leading to a cycle in and out of the proto-kesslerian regions. +This is an issue because, assumning a stable cycle, Rao's definition +of the kessler region would capture this behavior, but the $\epsilon$-kessler definition +would not. +I believe, but have not verified, that some choices of $\epsilon$, although permitting cycles, +would relegate them to levels with minimal economic impact. +%Maybe can be studies by phase or flow diagrams? + + +%Area of research: What makes a good \epsilon? +This leads to the important question of ``What makes a good value of $\epsilon$?'' +One method, in the spirit of \cite{Adilov2018}, is to choose a change in debris, $D_{t+1} - D_t$, such that +the loss of satellites in periods $t+1$ to $t+k$ is increased by or to a certain percentage, say 50\%. +I've put very little thought into addressing this general question so far, +and need to analyze the implications of different choice rules. + + \end{document}