guidance, flight mechanics and trajectory optimization

The total velocity error in this case is
and the out of plane thrust angle is
Figure 2.7
Out of Plane Steering Angle
If an elliptic target orbit is considered, each successive calculation
of the desired velocity from Equation (2.l-l) can be viewed as a problem in-
volving a new set of initial conditions and a new circular orbit with a
period slightly different than at the last calculation. Since the limits as
t - -5/B of Equations (2.12) and (2.13) remains, the same, even if n
is a function of time, the implication is that a rendezvous will occur for an
elliptic orbit. Shapiro [Reference (2.ll)] has shown that a rendezvous
will not occur for elliptic target orbits by the use of a single application
of Equation (2.11) as in the method discussed in Section (2.2.2.1).
The general idea of this method can be used with other schemes by
changing the time to rendezvous at each correction point so as to gradually
reduce the.range rate. If a range range-rate schedule is used, the time to
rendezvous can be calculated from the present position and desired range-rate.
For example, a fixed range range-rate schedule being considered for an Apollo
rendezvous is given in Table 2.1 (Reference 2.9)
45
‘Y