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lecture26 - Perturbations Until now weve dealt almost...

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Perturbations Until now, we’ve dealt almost exclusively with two-body motion, a pure Keplerian orbit. It is now time to consider other forces that act on a satellite. Perturbations are small forces that are not included in the point-mass (= spherically symmetric mass distribution) attraction of the Kepler problem. Implied: solution qualitatively similar to un- perturbed problem is obtained, but not ex- actly the same answer. L. Healy – ENAE404 – Spring 2007 – Lecture 26 (May 1) 1
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What is a perturbation? Example: geopotential perturbation (which we’ll learn about) causes the orbit to be not-quite-a-conic, but it’s very close. Not a perturbation: Third body forces near Lagrange points qualitatively affect the or- bit but are not a slight change - Figure 1– 18, is not a perturbation from Kepler, when the third body influence is significant. May be random or have random compo- nent (e.g. drag) or may be predictable (e.g. geopotential). Small in magnitude vs. small in effect (long- term). L. Healy – ENAE404 – Spring 2007 – Lecture 26 (May 1) 2
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Outline of perturbation topics Forces Effects; how orbits propagated with per- turbations: “general perturbations”: analytical for- mula give approximate and qualitative understanding of effects. “special perturbations”: numerical inte- gration for accurate and precise compu- tation of effects. Focus is on general perturbation in this class; how perturbations affect orbit design. L. Healy – ENAE404 – Spring 2007 – Lecture 26 (May 1) 3
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Forces included Ref.: Montenbruck & Gill, Satellite Orbits Sec. 3.1, Vallado Section 8.6. Beyond the central force of the earth (or what- ever body the satellite is orbiting), perturba- tions can include the “big four”, in roughly descending order of magnitude, geopotential perturbations (non-sphericity of earth’s mass distribution). drag luni-solar, planetary (third body) solar radiation pressure The actual relative importance of these de- pends on the type of orbit. For a given orbit or ephemeris need, we may choose to ignore some (or all!) of these perturbations. L. Healy – ENAE404 – Spring 2007 – Lecture 26 (May 1) 4
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Relative magnitudes of perturbing forces Relative magnitudes depend on orbit – alti- tude is the primary parameter that governs the perturbation force, could vary quite a bit in a highly elliptical orbit. From Montenbruck & Gill, Fig. 3.1: L. Healy – ENAE404 – Spring 2007 – Lecture 26 (May 1) 5
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Potential and force Newton’s laws of gravitation and motion for a point mass ¨ r + μ r 2 ˆ r = 0 .
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