Binney tremaine 1987 fig 6 10 4182013 uw astr

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Unformatted text preview: ©2013 2 Jz +2 2R 8 Epicyclic mo8on •  Energy is _______, so effec8ve poten8al determines amplitude of oscilla8ons 2 1 " dR % E = $ ' + Φeff (R, z = 0; Jz ) = constant !! 2 # dt & ρ !! = R − Rm € ∂ 2 Φeff d2ρ ≈ −ρ 2 dt ∂R2 !! =− Rm ρ ρ Rm = !! −4BΩ 4/18/2013 UW, ASTR 323, SP13, Eric Agol ©2013 9 Epicycles φ 2ΩAR/κ AR ρ R !! = Rm + ρ(t) = Rm + AR sinκt Ω(Rm) φ(t) = φ 0 + Ω !! 2Ω + AR cosκt κRm € 4/18/2013 UW, ASTR 323, SP13, Eric Agol ©2013 10 Closed radial orbit Iner8al frame:...
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