1. ARO309 - Astronautics and Spacecraft Design
Winter 2014
Try Lam
CalPoly Pomona Aerospace Engineering

2. Lambert’s Solution
Chapter 5

3. 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

4. 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.

5. Lambert Fit Steps to find v1 and v2: Find the magnitude of r1 and r2
Decide if the orbit is prograde or retrograde
Compute the following
Compute Δθ
for prograde
for retrograde

6. Lambert Fit Compute the function
Find z by iterating using Newton’s method until convergence
you can start with z0 = 0 (or positive z0 if an elliptical orbit), where

7. Lambert Fit
where
Note: the sign of the converged z tells you the orbit type:
z < 0  Hyperbolic Orbit
z = 0  Parabolic Orbit
z > 0  Elliptical Orbit

8. Lambert Fit Compute the function y(z) using the converged z
Compute f, g, fdot, gdot
Compute

9. Example 5.2 (Text Book)

10. Example 5.2 (Text Book)

11. Example 5.2 (Text Book)