Astrodynamics 102 - DerAstrodynamics.com

2-Body Lambert Algorithm
Lambert's Equation for multi-revolutions (Sun)
F ( x) = (x ) y) N 0
Iterative Equation (Laguerre)
Multi-revolution Lambert Algorithm
n F (x i )
i+1 i
for i 1,
2,..
F (x i ) 2 2
F (x i ) (n 1) F (x i ) n (n 1)
F (x i )F (x i )
F (x i )
x x
References:
Sun, F.T., “On The Minimum Time Traj . . ”, AAS 79-164
Der, G. J., “The Superior Lambert Algorithm”, AMOS,2011
v (t )
Lambert Problem
Given: r (t ) , r (t ) , t , t , inc_to
Find: v (t ) , v (t )
object at t 2
2
Transfer
Orbit 2
1
r (t )
2
1
v (t )
2
2
2
Transfer
Orbit 1
Sphere
1 2
Transfer orbit 1: inc_to = 1, i < 90 o
Transfer orbit 2: inc_to = 1, i > 90 o
Multi- revolutions (N)
may have ( 2N + 1 ) solutions
for each inc_to and a given
v (t )
1
r (t )
1
object at t 1
v (t )
1