▁Ke pler ' s ▁equation ▁is ▁ ▁where ▁ ▁is ▁the ▁mean ▁anom aly , ▁ ▁is ▁the ▁ecc ent ric ▁anom aly , ▁and ▁ ▁is ▁the ▁ecc ent ric ity . ▁ ▁The ▁' e cc ent ric ▁anom aly ' ▁ ▁is ▁useful ▁to ▁compute ▁the ▁position ▁of ▁a ▁point ▁moving ▁in ▁a ▁Ke pler ian ▁orbit . ▁As ▁for ▁instance , ▁if ▁the ▁body ▁passes ▁the ▁per ias tr on ▁at ▁coordinates ▁, ▁, ▁at ▁time ▁, ▁then ▁to ▁find ▁out ▁the ▁position ▁of ▁the ▁body ▁at ▁any ▁time , ▁you ▁first ▁calculate ▁the ▁mean ▁anom aly ▁ ▁from ▁the ▁time ▁and ▁the ▁mean ▁motion ▁ ▁by ▁the ▁formula ▁, ▁then ▁solve ▁the ▁Ke pler ▁equation ▁above ▁to ▁get ▁, ▁then ▁get ▁the ▁coordinates ▁from : ▁ ▁where ▁ ▁is ▁the ▁semi - major ▁axis , ▁▁ ▁the ▁semi - min or ▁axis . ▁ ▁Ke pler ' s ▁equation ▁is ▁a ▁trans c endent al ▁equation ▁because ▁s ine ▁is ▁a ▁trans c endent al ▁function , ▁meaning ▁it ▁cannot ▁be ▁solved ▁for ▁ ▁algebra ically . ▁N umer ical ▁analysis ▁and ▁series ▁exp ans ions ▁are ▁generally ▁required ▁to ▁evaluate ▁. ▁ ▁Altern ate ▁forms ▁▁ ▁There ▁are ▁several ▁forms ▁of ▁Ke pler ' s ▁equation . ▁Each ▁form ▁is ▁associated ▁with ▁a ▁specific ▁type ▁of ▁orbit . ▁The ▁standard ▁Ke pler ▁equation ▁is ▁used ▁for ▁elli ptic ▁or bits ▁( 0 ▁ ≤ ▁e ▁< ▁ 1 ). ▁The ▁hyper bol ic ▁Ke pler ▁equation ▁is