1. ; where mS;mE;mMare mass of Sun, Earth and Moon,k;kE;kMare the position vectors of kth spacecraft with respect toSun,EarthandMoon,and Gis theuniversalgravitationalconstant.
2. radialdistancefromorbitpoint small enoughsothat theoccultation of Sun isatreasonable(10-20 %) levels. • Keeptheformationalignedparallel toSun-Earthline,with adistanceof 125minbetween twospacecraft. Now,wedescribethedynamicsofbothspacecraftinaformthatwillbeusedincontrol design
3. ˙ξr=rξ+ru+rw; where ξr=(xr;xI),andletting C=[I 0]
4. r= ~ Ar0 C 0 ! ;r= ~ Br 0 ! ;r= ~ Er 0 !
5. Pr+TrP−PrTrP+Q=0; (7) where Q = QT>0 is a positive definite matrix of appropriate dimensions, and P is the matrix variable solved for. Notethat, whenthepair (Ar;Br)isstabilizable,andthefollowingrankconditionholds