TABLE OF CONTENTS The results of the previous sections are sufficient for the analysis of all basic orbital transfers, including those for interplanetary missions. However, trajectory design for such missions is sufficiently complex to justify separate discussion.
Although trajectory design for advanced mission analysis or actual mission execution will invariably be accomplished using direct numerical integration of the equations of motion, such procedures are inappropriate for preliminary assessments. Not only are the methods time-consuming and highly specialized, but also, without a preliminary analytical solution, they offer no way to eliminate the many cases that are not at all close to the actual solution of interest.
For initial mission design and feasibility assessments, the so-called method of patched conics is universally employed. We consider the application of the method in some detail.
As the name implies, this approach uses a series of Keplerian orbits to define the trajectory. Each separate conic section is assumed to be solely due to the influence of the dominant body for that portion of the mission. The different segments are "patched" at the sphere of influence boundaries between different bodies given by Eq. (4.93). Thus, a spacecraft trajectory between Earth and Mars will be modeled for departures as a geocentric escape hyperbola, which at great distances from Earth becomes a heliocentric elliptic orbit, followed again by a hyperbolic approach to Mars under the influence of that planet's gravitational field.
Patched-conic trajectory designs are accomplished in three well-defined steps:
The heliocentric orbit...
