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Unformatted text preview: Perturbations Until now, weve dealt almost exclusively with twobody 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 pointmass (= 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 What is a perturbation? Example: geopotential perturbation (which well learn about) causes the orbit to be notquiteaconic, but its 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 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 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 (nonsphericity of earths mass distribution). drag lunisolar, 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 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 Potential and force Newtons laws of gravitation and motion for a point mass r + r 2 r = 0 ....
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This document was uploaded on 04/27/2011.
 Spring '11

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