▁function : ▁▁▁▁ ▁This ▁can ▁be ▁done ▁iter atively ▁via ▁Newton ' s ▁method : ▁▁▁▁ ▁Note ▁that ▁E ▁and ▁M ▁are ▁in ▁units ▁of ▁rad ians ▁in ▁this ▁computation . ▁ ▁This ▁iteration ▁is ▁repeated ▁until ▁desired ▁accuracy ▁is ▁obtained ▁( e . g . ▁when ▁f ( E ) ▁< ▁desired ▁accuracy ). ▁For ▁most ▁elli pt ical ▁or bits ▁an ▁initial ▁value ▁of ▁E 0 ▁= ▁M ( t ) ▁is ▁sufficient . ▁For ▁or bits ▁with ▁e ▁> ▁ 0 . 8 , ▁an ▁initial ▁value ▁of ▁E 0 ▁= ▁ π ▁should ▁be ▁used . ▁If ▁e ▁is ▁ident ically ▁ 1 , ▁then ▁the ▁derivative ▁of ▁f , ▁which ▁is ▁in ▁the ▁denomin ator ▁of ▁Newton ' s ▁method , ▁can ▁get ▁close ▁to ▁zero , ▁making ▁derivative - based ▁methods ▁such ▁as ▁Newton - R aph son , ▁sec ant , ▁or ▁reg ula ▁fal si ▁numer ically ▁un stable . ▁In ▁that ▁case , ▁the ▁b ise ction ▁method ▁will ▁provide ▁guaranteed ▁convergence , ▁particularly ▁since ▁the ▁solution ▁can ▁be ▁bounded ▁in ▁a ▁small ▁initial ▁interval . ▁On ▁modern ▁computers , ▁it ▁is ▁possible ▁to ▁achieve ▁ 4 ▁or ▁ 5 ▁digits ▁of ▁accuracy ▁in ▁ 1 7 ▁to ▁ 1 8 ▁iterations . ▁A ▁similar ▁approach ▁can ▁be ▁used ▁for ▁the ▁hyper bol ic ▁form ▁of ▁Ke pler ' s ▁equation . ▁In ▁the ▁case ▁of ▁a ▁par abol ic ▁traject ory , ▁B ark er ' s ▁equation ▁is ▁used . ▁ ▁F