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/ GRAVITATIONAL. POTENTIAL GRAVITATIONAL *So we choose Lynn os mass gom el tb that POTENTIAL ENERGY ve ference point measure point Gravitetionol potential page is the energy — Stored in an object due exact amount Oy BE. yeu °PE at 7=90 /s zero. * This choice vesults —Ve’ 4 its positron above the earl surface. AP.E = mgh —+i RE because as we move — closey to earth, P-E | decreases. «his formula 1s valid ABSOLUTE GRAVITATIONAL only “when ‘gq’ i's constont POTENTIAL ENERGY (U) Amount of work done in FF i.e@ neav earth surpace. *P.E is measured wrt some reference point: ° For eu we moving a booty from earth's surface bo point at inginity dieters where evolve 0 ligible 1s Colled be potential ere nergy _____—§ it, ABSOLUTE GRAVITATIONAL POTENTIAL (V) : Gravitotionol potential V_is wor! ev unit mass in bringing @ smoll DERIVATION : ° G.P.E = Work from (0- ) * During this work foyee i's not constant So, we have to divide the path milo smolf parts in which Gorce_ss constant: Woe =WitW,tW,+---+Wh * W=FdCosO —5* W, = f.AY = £, AY Cos120 Wi = BvAY(-4) =— fv AY W, =- Mn (¥44-Re) —>x % = Ret (AYJ42Redy at is Very Small fa 20 Yo = Re + ReAY Voy = Re + Re(n— Re) he = Re + Rey - RE Yay = Rey, —>* S% we -GMm (4- Re) ey WwW Re WW, »—GMm ike VRe Wie GM = 1 = —GMm (y,-¥,) he “i -GMm[ eos) Wa - GM hs 3 epee ee oh wae ~ 6M 5, we ~ 6th) OEE) ma Jah ~ 6Mm(L. — 2) Sate) a % % Yu a onn $k =-G, eres $* — W sniff aS VAR ; . “* oil, W=-GMm st +h me W=-GMms 1 He meine W=-GMm5 i a U =~ Gata —a kk “Ve u Us wi ee ee y--GM —+k* vf 
