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class21-22 - F r =-k r 2(20 review the derivation of the...

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REFERENCE: Arya, Sections 7.5 to 7.7 EXAMPLES: Arya 7.1 and 7.2 Review the derivation of the following important equations: 1. The angle as a function of radial distance θ ( r )= ± ( L/μr 2 ) dr ² 2 μ ³ E - V ( r ) - L 2 2 μr 2 ´ (18) 2. The path equation d 2 u 2 + u = - μ L 2 u 2 F µ 1 u (19) 1.1 Inverse-square forces For the case of orbits in an attractive inverse-square force ±eld
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Unformatted text preview: F ( r ) =-k r 2 (20) review the derivation of the orbit equation r ( θ ) = α 1 + ± cos θ (21) where the constants are α = L 2 kμ and ± = · 1 + 2 EL 2 μk 2 . (22) This is an equation for a “conic section” with its focus at the origin, discussed in Arya, page 270: 3...
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