▁bodies ▁is ▁found ▁by ▁sum ming , ▁for ▁all ▁ ▁pairs ▁of ▁two ▁bodies , ▁the ▁potential ▁energy ▁of ▁the ▁system ▁of ▁those ▁two ▁bodies . ▁ ▁Consider ing ▁the ▁system ▁of ▁bodies ▁as ▁the ▁combined ▁set ▁of ▁small ▁particles ▁the ▁bodies ▁consist ▁of , ▁and ▁applying ▁the ▁previous ▁on ▁the ▁particle ▁level ▁we ▁get ▁the ▁negative ▁gravit ational ▁binding ▁energy . ▁This ▁potential ▁energy ▁is ▁more ▁strongly ▁negative ▁than ▁the ▁total ▁potential ▁energy ▁of ▁the ▁system ▁of ▁bodies ▁as ▁such ▁since ▁it ▁also ▁includes ▁the ▁negative ▁gravit ational ▁binding ▁energy ▁of ▁each ▁body . ▁The ▁potential ▁energy ▁of ▁the ▁system ▁of ▁bodies ▁as ▁such ▁is ▁the ▁negative ▁of ▁the ▁energy ▁needed ▁to ▁separate ▁the ▁bodies ▁from ▁each ▁other ▁to ▁infinity , ▁while ▁the ▁gravit ational ▁binding ▁energy ▁is ▁the ▁energy ▁needed ▁to ▁separate ▁all ▁particles ▁from ▁each ▁other ▁to ▁infinity . ▁ ▁therefore , ▁, ▁ ▁Neg ative ▁gravit ational ▁energy ▁As ▁with ▁all ▁potential ▁energ ies , ▁only ▁differences ▁in ▁gravit ational ▁potential ▁energy ▁matter ▁for ▁most ▁physical ▁purposes , ▁and ▁the ▁choice ▁of ▁zero ▁point ▁is ▁arbitrary . ▁Given ▁that ▁there ▁is ▁no ▁reasonable ▁criter ion ▁for ▁prefer ring ▁one ▁particular ▁finite ▁r ▁over ▁another , ▁there ▁seem ▁to ▁be ▁only ▁two ▁reasonable ▁choices ▁for ▁the ▁distance ▁at ▁which ▁U ▁becomes ▁zero : ▁ ▁and ▁. ▁The ▁choice ▁of ▁ ▁at ▁infinity ▁may ▁seem ▁peculiar , ▁and ▁the ▁consequence ▁that ▁gravit ational ▁energy ▁is ▁always ▁negative ▁may ▁seem ▁counter int uit ive , ▁but ▁this ▁choice ▁allows ▁gravit ational ▁potential