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