Mathematics 4362 Astrodynamics

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Mathematics 4362Astrodynamics
Aero / Astro 4262 Astrodynamics
Week 2, Vallado Section 1.3
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Youve seen it before ..
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Orbital Energy Review
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Gravitational Physics

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Gravitational Potential Energy

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Kinetic Energy

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Total Specific Energy

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Total

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Total

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How about for a parabolic trajectory?
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How about for a hyperbolic trajectory?
Conservation of Energy and Angular Momentum
still hold . So .
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Hyperbolic Energy
Recall, from the First Law derivation
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Hyperbolic Energy (continued)
At Perigee, n0
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Hyperbolic Energy (continued)
Substituting into energy equation
And for a hyperbola
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Hyperbolic Energy (continued)
Substituting into energy equation
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Hyperbolic Energy (continued)
But from the General Form for the Conic section
hyp
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Hyperbolic Energy (continued)
Evaluating at perigee
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Hyperbolic Energy (continued)
Substituting into the Energy equation
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Hyperbolic Energy (concluded)
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Vis-Viva Equation for All the Conic-Sections
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Problem Hints
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