ARO309 - Astronautics and Spacecraft Design
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ARO309 - Astronautics and Spacecraft Design Winter 2014 Try Lam CalPoly Pomona Aerospace Engineering
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ARO309 - Astronautics and Spacecraft Design . Winter 2014 Try Lam CalPoly Pomona Aerospace Engineering. Lambert’s Solution. Chapter 5. Introductions. This chapter only covers the basic concept of determining an orbit from some observation - PowerPoint PPT Presentation
Transcript of ARO309 - Astronautics and Spacecraft Design
ARO309 - Astronautics and Spacecraft Design
Winter 2014
Try LamCalPoly Pomona Aerospace Engineering
Lambert’s Solution
Chapter 5
Introductions
• This chapter only covers the basic concept of determining an orbit from some observation
• In practice, this is not referred to as orbit determination
• Space OD is actually a statistical estimation or filtering method (example: Kalman Filter)
• We will only cover Lambert’s problem (Section 5.3) from this Chapter
Lambert’s Problem
• Given 2 positions on an orbit r1 and r2 and Δt, what are the velocities at those two points, v1 and v2.
Lambert Fit• Steps to find v1 and v2:
1. Find the magnitude of r1 and r2
2. Decide if the orbit is prograde or retrograde
3. Compute the following
4. Compute Δθ
for prograde for retrograde
Lambert Fit5. Compute the function
6. Find z by iterating using Newton’s method until convergence
you can start with z0 = 0 (or positive z0 if an elliptical orbit), where
Lambert Fitwhere
7. Note: the sign of the converged z tells you the orbit type:
z < 0 Hyperbolic Orbitz = 0 Parabolic Orbitz > 0 Elliptical Orbit
Lambert Fit8. Compute the function y(z) using the converged z
9. Compute f, g, fdot, gdot
10. Compute
Example 5.2 (Text Book)
Example 5.2 (Text Book)
Example 5.2 (Text Book)
