From Space Vehicle Design, Second Edition
4.3 Non-Keplerian Motion
We have, to this point, reviewed the essential aspects of two-body orbital mechanics, alluding only briefly to the existence of perturbing influences that can invalidate Keplerian results. Such influences are always present and can often be ignored in preliminary design. However, this is not always the case, nor is it indeed always desirable; mission design often involves deliberate use of non- Keplerian effects. Examples include the use of atmospheric braking to effect orbital maneuvers and the use of the Earth's oblateness to specify desired (often sun-synchronous) rates of orbital precession. These and other aspects of non- Keplerian orbital dynamics are discussed in the following sections.
4.3.1 Sphere of Influence
Of the various possible perturbations to basic two-body motion, the most obvious are those due to the presence of additional bodies. Such bodies are always present and cannot be easily included in an analysis, particularly at elementary levels. It is then necessary to determine criteria for the validity of Keplerian approximations to real orbits when more than two bodies are present.
If we consider a spacecraft in transit between two planets, it is clear that when close to the departure planet, its orbit is primarily subject to the influence of that planet. Far away from any planet, the trajectory is essentially a heliocentric orbit, whereas near the arrival planet, the new body will dominate the motion. There will clearly be transition regions where two bodies will both have significant influence on the spacecraft motion. The location of these...
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