guidance, flight mechanics and trajectory optimization

The velocity correction, SVtO) represent the corrections which must be
added to the "first order" require: velocity so that the miss distance at
rendezvous will be reduced to zero.
Figures 2.9 and 2.10 (taken from Reference 2.12) illustrate a comparison
of the first and second order scheme described above.
KcyfaFlg5to9
lo = 50 NM
A: With fint-whr AV1
m mldsouna correctIon.
5: WI”, fint-dar AV,
ona mld-cms comestIm.
0
1 I
m
I I
40
I I
M)
I I1
80
R.n&zrun Tlfw, 1, Mln
Figure 2.9
Figure 2.10
As can be seen in these figures, the effectiveness of the improvement depend
upon the initial separation distance and rendezvous time r . As a consequence
of reducing the number of midcourse corrections, the second order
technique requires a smaller total A V to perform the rendezvous maneuver.
This difference
times.
becomes more significant for large initial separations and
2.2.4.6 Direct Calculation using Two-Body Orbits
Perhaps the most straightforward method of determining the impulsive
velocity required for rendezvous is obtained by using the equations of
absolute motion of the two vehicles. The relative notion can then be de-
termined as the difference of the respective absolute motions. However, since
the relative positions and velocities will be several orders of magnitude
smaller than their absolute counterparts, it is seen that great computational
precision is required. Furthermore, the errors in the knowledge of the orbits
of the two vehicles must be small in order to maintain acceptably small errors
in the relative motion. The method has the advantage, however, of providing
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