Abstract: Itisessentialtosavefuelinorbitcontrolformicro/nanocompanionsatelliteduetothelackofresources.TheminimumfuelcontrolstrategyoftherelativeellipsephaseininplanecompanionflyingwasstudiedbasedontheHillequationandtheextremevaluetheoryofdualfunction. Whenthephaseneededtochangeisacuteangle , andthevelocityincrementislessthantheresultthatmultiplieshalfoforbit′smeanangularbytherelativeellipsesemiminoraxis(ΔV<05nb),thetheoreticalanalysisresultsshowthatthemostefficientcontrolmethodoftherelativeellipsephaseisimpulsivecontrolparalleltothelateraldirection, thevelocityincrementistheresultthatmultiplieshalfoforbit′smeanangular,therelativeellipsesemiminoraxisbytheabsoluteofphase′scosine(ΔV=05nb|cosΘ|,andthephasewillbetheleft（thephaseisπ/2）orright（thephaseis-π/2）pointofrelativeellipseaftercontrol.Therelativeellipsesemiminoraxiscanbereducedatthesametime. Whenthephaseneededtochangeisnotacuteangle, itisneededtobedividedintoseveralacuteanglesforsavingfuel. Furthermore,theorbitcontrolstrategyofacompanyingsatellite′sphasecontrolwasgainedbyapplyingthetheory.

Key words: Hillequation, Changeofphase, Controlquantity, Controltime, Controldirection, Inplanecompanionflying, Companionsatellite