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Unformatted text preview: ar toRasra rcll dV dM M =V ( # )( # )( + --l-! # + --l-! # ) # + --l-! + --l-! + --l-! rel (All doLtid .x6 dtrrc to thtuth tt .mtd hf th. oN's dr do 'tN.) v v= a= dt dt 2 v a= R uniform circular motion: C9.6 Now we arein a pGition to answertheq is th€total kinetic eneBy of an obiecttha as t r t i o n I l r a n s l a t i o nn d R oa aclling obiect)?t tu.ns out tlEt the o i dv v2 ˆ ˆ a= Now we arein a pGition to answertv −questionraisedin s€ctionC9.li w he r dt R ntonuniforminetic eneBy of an obiectthat is both moving ard rctating (s circular motion: is h€total k asa rclling obiect)?t tu.ns out tlEt the obicrt's total kineticenergyis ius I 1 v x (t ) = ax t + v0 x x (t ) = ax t 2 + v0 x t + x0 2 Ffriction = µ Fnormal 1 Fdrag = C ρ Av 2 2 v!(t ) = v (t ) − β (t ) Galilean velocity transformation a!(t ) = a (t ) − A(t ) Galilean acceleration transformation ma! = −mA + F1 + F2 + … Fictitious forces dA L Kepler’s second law: dt = 2m = constant 4π 2 GM 2 TP roblems a 3 also V = = Nepler’s tS olvino rbit 13.4 O K hird law: GM R 233 TsbleN 13.1 T ableo i u seful uations for solvin orbit Item Definitions of E and L 2E -:Dm Calculation o f e ccentricity e2:,+#GlG) Item Elliptical ase C Hvperbolicc ase 2E GM 2E GM m a m a Connection b etween a a nd E Location o f e xtremes 2GM , and L : r asin| m rr:a(l-e) rg llJ :?J) rr:a(e-\) E: L: Gt?t: M: r: ?: d: a: /c: rl:a(l+e) r/: Other useful relations ,':Hot (Kepler'st hird l aw) tang: J V- :*,(il,r T: 0: t otal s ysteme nergy system angular momentum gravitational constant satellitemass p rimary m ass distancefrom primary satellitespeedat that point angle between i and6 semimaioraxis for ellipse, analogousfor hyperbola f d istance rom p rimary t o closestpoint on the orbit distancefrom primary to farthest point on the orbit o rbital p eriod angle of asymptotes N13.4 Solving rbit Problems O The point of the last sectionis that knowing the values of 2E/m andL/m for a system involving a satellite orbiting a massiveprimary allows us to calculate a and e, which in turn completely specify the shapeof the satellite'sorbit. Table N13.1 summari...
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