▁for ▁all ▁dimensions ▁of ▁the ▁system ▁to ▁determine ▁the ▁complete ▁center ▁of ▁mass . ▁The ▁utility ▁of ▁the ▁algorithm ▁is ▁that ▁it ▁allows ▁the ▁mathematics ▁to ▁determine ▁where ▁the ▁" best " ▁center ▁of ▁mass ▁is , ▁instead ▁of ▁guessing ▁or ▁using ▁cluster ▁analysis ▁to ▁" un fold " ▁a ▁cluster ▁str add ling ▁the ▁periodic ▁boundaries . ▁If ▁both ▁average ▁values ▁are ▁zero , ▁, ▁then ▁ ▁is ▁undefined . ▁This ▁is ▁a ▁correct ▁result , ▁because ▁it ▁only ▁occurs ▁when ▁all ▁particles ▁are ▁exactly ▁even ly ▁spac ed . ▁In ▁that ▁condition , ▁their ▁x ▁coordinates ▁are ▁mathemat ically ▁identical ▁in ▁a ▁periodic ▁system . ▁ ▁Center ▁of ▁gravity ▁ ▁A ▁body ' s ▁center ▁of ▁gravity ▁is ▁the ▁point ▁around ▁which ▁the ▁result ant ▁tor que ▁due ▁to ▁gravity ▁forces ▁van ishes . ▁Where ▁a ▁gravity ▁field ▁can ▁be ▁considered ▁to ▁be ▁uniform , ▁the ▁mass - center ▁and ▁the ▁center - of - gravity ▁will ▁be ▁the ▁same . ▁ ▁However , ▁for ▁sat ell ites ▁in ▁orbit ▁around ▁a ▁planet , ▁in ▁the ▁absence ▁of ▁other ▁tor ques ▁being ▁applied ▁to ▁a ▁satellite , ▁the ▁slight ▁variation ▁( gradient ) ▁in ▁gravit ational ▁field ▁between ▁closer - to ▁( strong er ) ▁and ▁further - from ▁( we aker ) ▁the ▁planet ▁can ▁lead ▁to ▁a ▁tor que ▁that ▁will ▁tend ▁to ▁align ▁the ▁satellite ▁such ▁that ▁its ▁long ▁axis ▁is ▁vertical . ▁ ▁In ▁such ▁a ▁case , ▁it ▁is ▁important ▁to ▁make ▁the ▁distinction ▁between ▁the