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a> ite) G.P due to point mass ot a dist” "5 Us - G@Mme V= -@M % S 1 GP. dhe to combination of point mass *- GS, (ms) Vp = ~ Gm - Gm - Gm - Gime %, Ss %s Be % Cs) r G.P. clue to aed ar Unifoam thin b> Unifosm Shel. Solid Sphere: Vet « - GM Vout « - GM as rol Veur = —- GM Vex = - GM R R Vin -_ - iv Vi e- GM. 3 2 Ve R a? [2s #] : hig Veentse » —3. GM | 2 R- i Va / _— , as se yx JR - 360k | a 37) ly ey 194 GPR die to Unifosm Ring :- Vp =» —-GM Hat Ring (x20) Va Ve -G&M R G. P Tneagy te Us - GMm Total no.of = n-1) eg tesms 2 G.P.E. of Eosth - mass System We Foom Susface to height “his Au = Q@Mmb = An) (+R) RLS] { Escape Velocity te Ve = / 44 Ve= /2gR Ves /Sagme B= const” Ve «& R Ms Const” Veo Ax \e7 Velocity of object at co when Prgjecteol with Vg > Ve. Vio * [Vgr-Ne* 23) # BE. ofa particle ploced on Caath »- BE = -GMm R # (pel, vg on > BDsatite Susface = Time Pesiod of Satellite :- Gar trax Te oN = ot mane es? tevex? Vo GMe Cmax + Spin Keplea’s law %- ¥ > inax min “Smin All-e A = Venin Cmax +¥imin =1q —_ I * dA = const” *% L 2 const® dt Qm * SV = const” * Smedn = Cmax +Bmin z 3 * TE. —GMm % Te to [Ma | (Smax + Emin) , 2 gavi S ae Surface ony ¥ M = Congt” \ °~ Se ~ Tres a, ee NI Se conse FR b> Above Surface. a s doR*™ hace a CReh) dns a] "2 x o> Below Surface es da" al] a> Vasiation of ‘9 Ave to Shape of Easth- Re. Rp +4. Km dp > J NOTE :- ¥ Mass = Paop. of mattes. * wt as We move fsom C quater to Pole. e> Voslation of “gy” dlule to rotation of Carth About its own Axis :- lus ps ace!” due" te gravity 0.34 a a Sere * 4 Ree Ye Kam hof @Q= measused from oo ™ | Newton's law of Gravitation «— | Fe Gm, mall | SS S= 6.6% x19 Kg! m s> “ty = > = "Sager OT 7 Nevtwal Point -- cpcls mm is fom Sma | eo. Charge. y q to m v3 = mM gh cere | Fret = GMin | oe L ~ 7 A(d+t) | <——__ x > due to xed | on Particle. W> G. Field intensity s- Dis® Ul to Foace. ——~>—— > T- £& = E N/ty t= oh — AOLLOW SPHERE. ‘SOLTD SPHERE. | Tet = - GM & Tot « - GM 4 | We out Tea = - Gt & Tan = - GM R | R R | Linside =O Tm = GMyr Fine G@Mme | R° e 
