Chapter 1
Simply stated, the "Newtonia n TV-bod y problem" i s the mathematical stud y
of how heavil y bodie s mov e i n setting s wher e th e dynamic s ar e dictate d b y
Newton's la w o f motion . I n practica l terms , thi s are a no w include s jus t
about an y dynamica l syste m tha t eve n remotel y resemble s Newton' s law .
Beyond th e insigh t th e subjec t provide s fo r understandin g astronomica l
issues, th e Newtonia n iV-bod y proble m ha s historicall y serve d a s a sourc e
of mathematica l discover y an d ne w problems . Th e purpos e o f thi s boo k i s
to introduce th e reade r t o a selective portion o f issues about th e Newtonia n
TV-body problem whil e outlinin g an d describin g som e ope n problems.
1.1 Mar s
How do the heavenly bodies move? A quick introduction ca n be provided b y
using elementary comple x variable s t o describ e som e simple orbits . Th e ul -
timate purpose of this exercise is to show how surprising levels of complexity
can aris e eve n i n particularl y "nice " an d "wel l behaved" settings . Late r i n
this chapter, these orbits are used to describe and motivate an open researc h
Start wit h a myster y tha t mos t surel y bothere d generation s o f schoo l
kids: i t mos t certainl y trouble d m e whe n I wa s i n th e fourt h grade . I t
involves th e stor y o f Galile o bein g force d t o recan t hi s view s tha t th e Sun ,
rather tha n Earth , i s th e cente r o f th e sola r system . Eve n a chil d ca n
appreciate th e fac t tha t i f th e churc h fel t i t wa s necessar y t o forc e Galile o
to recant , the n th e stake s i n th e issu e mus t hav e bee n high . But , wha t
A companio n boo k [90 ] i s bein g prepare d tha t addresse s issue s othe r tha n thos e de -
scribed here .
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