Notes_F%20BP

Notes_F%20BP - F1 Conic Sections Ellipse 0 e 1 a>0 E...

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Conic Sections Ellipse 1c o s p r e θ = + periapsis () 01 1 p p ra e e == = + apoapsis 180 1 1 a p e e = + D 1 2 pa ar r =+ also known as mean distance Circle (special case; e = 0) 2 22 v ar p = μ − = − E 2 c v rr v r μμ =⇒ = ⇒= F1 ωθ −= true anomaly Lines of apsides 0 ascending < 0 descending γ >
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positive by definition () ( 2 21 IP ab h aa e p π μ = = General Ellipse: 2 22 v ra −= 2 2 c vv a μμ =− = 2 c < 2 2 dA h dt dA h =→ = area of ellipse 3 a IP = 2 π μ F2
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Parabola Orbit NOT closed; particle leaves vicinity of attracting body 2 02 2 c vv r v μ =→ = “escape speed” at distance r 2 00 2 v v r = F3 Can just barely escape gravitational influence
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Hyperbola
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Notes_F%20BP - F1 Conic Sections Ellipse 0 e 1 a&gt;0 E...

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