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Significant constraints are built into, or inherent in the Apollo system, that all conspire together to prevent a LOI burn which satisfies all the mission objectives.
Obvious among these objectives is that the orbital plane must go over the landing site, but as well as that, the approach azimuth to the target site (the angle of the approach path, relative to north) must also be acceptable. All landing approaches were made generally from the east, with the Sun behind the crew to provide adequate lighting. Additionally, as a compromise between delivering the spacecraft as close to the Moon as possible and not wishing to actually hit it, the LOI burn should not occur below 110 kilometres, which will be the initial pericynthion of the orbit. Apocynthion can be in the order of 300 km, to be lowered to a 17 km pericynthion after a safe orbit has been established.
The design of the Apollo system is a trade off of necessary and widely contradictory requirements, and many factors constrain the LOI burn and the trajectory which leads to it. Payload weight is the most critical parameter that must be managed. During premission planning, the nominal mission profile is developed together with a variety of abort scenarios. The Service Module is then fueled with only enough propellants to satisfy these parameters, as fuel not loaded is exchanged for additional payload in the form of fuel and experiments for the Lunar Module. In addition, the LM is also subject to tradeoffs between fuel and payload. In the end, the propellant margins are very tight on both the CSM and LM. Therefore, with an eye on the overall spacecraft weight, LOI must be optimized for the least burn time to conserve fuel for possible contingencies.
Limitations of the onboard computer, combined with the requirement to maintain a fixed attitude during the burn, make it difficult to efficiently enter the desired orbital plane. The necessity to maintain a fixed attitude during LOI is for operational simplicity as it is far easier for the crew to monitor the burn, and to notice any deviation from the norm when the vehicle is held in a steady attitude. Spacecraft position and velocity must be very close to the preplanned values at LOI, a necessary requirement but very difficult to achieve in practice. Errors that appear to be small can easily have large effects upon LOI.
One of the more familiar mandates in LOI planning is a free-return trajectory to the Moon to return the crew towards Earth if the spacecraft's big SPS engine should fail, an absolute essential for crew safety. Such a trajectory is a rather high energy path, which necessitates a very large (~1,000 m/s or 3,000 fps) maneuver to achieve orbit insertion, consuming a large percentage of the available fuel for the SPS. A poorly planned LOI might result in uncomfortably tight fuel margins.
Unfortunately, there are several cases where trying to solve for LOI objectives is theoretically impossible, mostly because of allowable fuel limits and guidance restrictions. Trajectory uncertainties are always a problem, and more so than one would suspect, as it will introduce errors to the final orbit.
Since mission "rules" ("requirements", actually) can never be satisfied, FIDO (Flight Dynamics Officer) has 10 different solutions computed, each which tries to violate only one of the premission requirements. It is then up to FIDO to decide which solution violates the requirements the least. It is this final compromise solution that is sent up to the spacecraft, and is referred to as the "target" or "targeting solution". These ten solutions are organized into three groups of three maneuvers, plus a single maneuver.
The single maneuver achieves an orbit with the smallest fuel expenditure, in exchange for the likely situation that none of the orbital objectives will be achieved. This solution would never be used except in the case where a landing would not be attempted and an alternate mission plan is in effect. This minimal Delta-V case does have the essential quality, however, of defining the lower bound for the remaining LOI solutions. FIDO will compare the nine remaining solutions against this value in determining the optimal maneuver.
The remaining three groups are called the basic, lunar orbit shape, and lunar landing site solutions. Maneuvers within each group will satisfy at least one, and perhaps two targeting objectives at the possible expense of violating one objective.
From the basic set of solutions, FIDO could target the spacecraft over the landing site at any one of three acceptable azimuths. While the requirement for ensuring that the orbit's plane passes over the landing site is readily apparent, the ground track, or azimuth, to the landing site is also important. Selecting an acceptable azimuth was vital, as Apollo's 15, 16 and 17 were all targeted between two mountain ranges at key points of their descent. None of these solutions came without a cost, as the basic solutions defined the most fuel intensive maneuvers.
Subsequent out-of-plane maneuvering would be very expensive in terms of propellant usage, and the LM simply cannot afford its margins cut. While the obvious concern is that the LM not hit the mountains during its descent, of equal importance is that the approach path match the terrain model stored in the computer. If the terrain the LM is flying over doesn't match the model that is stored, misleading information is used by the guidance computer, which would then be presented to the crew.
A second set, the lunar orbit shape solutions, ensure that the apocynthion and pericynthion constraints are met, at the possible expense of the other constraints. A consequence of limiting the problem to a specified maximum Delta-V is that some solutions may not exist, or if they do exist, may not pass over the landing site. Finally, the lunar landing site solutions ensure that the spacecraft will pass over the landing site at an acceptable azimuth. Much like the basic set in its objectives, it also introduced fuel constraints to the problem. As a trade-off, a lower pericynthion would be exchanged for a lower fuel requirement. Unfortunately, this constraint could result in a situation where a solution could not be found.
Planning and executing the Lunar Orbit Insertion maneuver is an example of the teamwork between the flight controllers and the crew. As one could expect, the magnitude of this computing problem is such that it could never be performed using the limited resources aboard the spacecraft. Additionally, a team of trajectory analysts are necessary to develop a consensus solution that is impossible to program into a computer. The crew, which takes this information and loads it into the computer, must perform and monitor the burn on the far side of the Moon, without assistance from the ground.
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