guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
1.0 STATEMENT OF THE PROBLEM<br />
SATELLITE RENDEZVOUS<br />
This monograph is directed to that portion of the rendezvous problem in<br />
which the relative distance <strong>and</strong> velocity between an active spacecraft <strong>and</strong> a<br />
passive target satellite must be reduced from moderate values (say 50 km <strong>and</strong><br />
5 km/set) to small values (say less than 5.0 meters <strong>and</strong> 1.5 meters/set).<br />
&-board relative position <strong>and</strong> velocity sensing are assumed for the purpose of<br />
allowing precise manual or automatic steering. These observed quantities are<br />
to be utilized to drive the state of the system to zero in a reasonable time<br />
with as little fuel as possible. Neither the gross orbital changes which have<br />
been brought about previous to this closing (rendezvous) maneuver, nor the<br />
final phase, known as docking, will be considered. The target satellite will<br />
be assumed to be in a closed orbit; <strong>and</strong> since perturbative influences (such as<br />
a non central gravity field) will be nearly the same on both vehicles with the<br />
result that their effect will be very small, the orbit will be assumed to be a<br />
two-body orbit, Since this monograph represents an attempt to survey the known<br />
information regarding the rendezvous problem, it will be analytical in nature<br />
<strong>and</strong> will not refer to any particular spacecraft or its capabilities.<br />
The problem of station keeping is similar to that of rendezvous in that<br />
it is assumed that a satellite is to be maintained in a specified orbit with a<br />
specified phase within tolerances similar to those mentioned for rendezvous.<br />
Thus, in a sense, the target is a point which moves along a desired path (this<br />
path may not correspond to the motion in the actual gravitational field). On<br />
the other h<strong>and</strong>, the chase vehicle moves along a path relative to this desired<br />
path which is defined by the perturbative influences acting on the vehicle <strong>and</strong><br />
the differences in the positions <strong>and</strong> velocities. Accordingly, the position<br />
coordinates of the chase vehicle may consequently deviate from those of the<br />
target. After such a deviation has accumulated for a period of time the prob-<br />
lem of returning the active craft to the nominal path in a substantially<br />
shorter time is the rendezvous problem as presented. Of course, it is assumed<br />
that the active craft possesses a mechanism by which the deviations from its<br />
nominal <strong>trajectory</strong> are determined as they may be needed.<br />
The discussions begin with the presentation of the field free case; i.e.,<br />
the case in which the same gravity acts on both satellites. This problem is<br />
of little physical importance; however, it serves to provide valuable insight<br />
into a more rigorously formulated system. It might be surmised, at first<br />
thought, that in this case no <strong>guidance</strong> technique would be necessary since an<br />
astronaut could effect the rendezvous by line-of-sight thrusting. This would<br />
approach would, however, cause the motion of the active craft to be one of<br />
constant angular momentum about the target. That is, if an angular momentum<br />
caused by an initial small velocity (v ) perpendicular to the line of sight<br />
exists at the distance ro, then, if thg'distance is reduced to 10B3 r. <strong>and</strong><br />
1<br />
-