ixed - point ▁iteration ▁▁ ▁A ▁related ▁method ▁starts ▁by ▁not ing ▁that ▁. ▁Re pe ated ly ▁subst itut ing ▁the ▁expression ▁on ▁the ▁right ▁for ▁the ▁ ▁on ▁the ▁right ▁yields ▁a ▁simple ▁fixed - point ▁iteration ▁algorithm ▁for ▁evalu ating ▁. ▁This ▁method ▁is ▁identical ▁to ▁Ke pler ' s ▁ 1 6 2 1 ▁solution . ▁ ▁function ▁E ( e , ▁M , ▁n ) ▁▁▁▁ ▁E ▁= ▁M ▁▁▁▁ ▁for ▁k ▁= ▁ 1 ▁to ▁n ▁▁▁▁▁▁▁▁ ▁E ▁= ▁M ▁+ ▁e * sin ▁E ▁▁▁▁ ▁next ▁k ▁▁▁▁ ▁return ▁E ▁ ▁The ▁number ▁of ▁iterations , ▁, ▁depends ▁on ▁the ▁value ▁of ▁. ▁The ▁hyper bol ic ▁form ▁similarly ▁has ▁. ▁ ▁This ▁method ▁is ▁related ▁to ▁the ▁Newton ' s ▁method ▁solution ▁above ▁in ▁that ▁▁▁▁ ▁To ▁first ▁order ▁in ▁the ▁small ▁quantities ▁ ▁and ▁, ▁ ▁. ▁ ▁See ▁also ▁ ▁Ke pler ' s ▁laws ▁of ▁planet ary ▁motion ▁Ke pler ▁problem ▁Ke pler ▁problem ▁in ▁general ▁relativ ity ▁Rad ial ▁traject ory ▁ ▁References ▁ ▁External ▁links ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁Ke pler ' s ▁Equ ation ▁at ▁Wol fram ▁Math world ▁ ▁Category : J oh annes ▁Ke pler ▁Category : Or bits <0x0A> </s> ▁Has b ial aye ▁is ▁a ▁village ▁in ▁the ▁Bal av é ▁Department ▁of ▁Ban wa ▁Province ▁in ▁western ▁Bur k ina ▁F aso . ▁As ▁of ▁ 2 0 0 5 ▁it ▁had ▁a ▁population ▁of ▁ 8 4 5 . ▁ ▁References ▁ ▁Category : Pop