Transearth Injection

The NASA-ese term for the manoeuvre that brought the spacecraft out of lunar orbit and homeward to Earth was trans-Earth injection (TEI). In simple terms, it was very similar to the TLI manoeuvre that sent the crew moonward in the first place in that its task was to add more speed to the spacecraft in order to raise the high point of its orbit sufficiently to take it from one world to another. To achieve this, their orbital velocity had to be raised by nearly 1 kilometre per second. With only meagre thrust available from the RCS thrusters, the big engine on the service module was the only means of gaining so much speed.

As with the TLI burn, TEI was based on a Hohmann-type transfer. In the context of the Earth-Moon system, this meant that to reach Earth, the burn had to be carried out on the side opposite Earth. In other words, the TEI manoeuvre had to be carried out over the Moon's far side. The duration of the burn raised their near-side apolune towards Earth until a point was reached when their trajectory became open ended, or hyperbolic. It was then no longer an elliptical orbit but had become an S-shaped path that would allow them to fall to Earth.

As usual, timing was everything. Mission planners needed to arrange a welcoming committee, which included an aircraft carrier, to recover the spacecraft and crew. Although the command module was designed to land on water, it was not a boat. It wallowed sickeningly in even mild swells, and the nature of its precious cargo of crew, rocks and film, along with the interest of the world, ensured that the US government made every effort to organise an appropriate reception, courtesy of the US Navy, for when the spacecraft returned. However, as aircraft carriers and their convoys could not be moved around the Earth's oceans very quickly, a prime landing area was designated in the middle of the Pacific Ocean where the largest recovery force would be stationed. Smaller forces were kept on standby at other designated sites on the other major oceans.

When deciding on a trajectory for the coast home, the Retro flight controller had to weigh a number of constraining factors. If re-entry was to be successfully negotiated, then whichever trajectory from the Moon to the Earth was used, the CM had to arrive at the top of the atmosphere at a shallow angle of 6.5 + 0.5 degrees - a condition that occurred more or less on the opposite side of the Earth from the Moon's position when the TEI burn occurred. The latitude of the splashdown site would be within Earth's tropical region for the majority of possible trajectories - i.e. between the tropics of Cancer and Capricorn - because it would be opposite the Moon at TEI and the Moon's orbit hardly strayed from the ecliptic, to which Earth's axis is inclined at 23.5 degrees. Other solutions were possible, but would have required too much propellant to achieve. The Apollo system worked on a propellant shoestring and planners could not be profligate with the stuff, which constrained the possible trajectories further.

An even narrower set of trajectories was selected by the 24-hour rotation of the Earth. Retro knew that the command module would fly about 2,000 kilometres from its point of atmospheric entry to its point of splashdown, and there was only one moment in each day when the revolving Earth brought the landing site and its ships to coincide with that point 2,000 kilometres downrange of the start of entry. He therefore had to decide whether he wanted the crew to make a faster return or to keep it leisurely - a decision made in view of the state of the consumables on board. The faster return used slightly more propellant but caught Earth one rotation early in case other consumables were low. Otherwise, a slower trajectory would allow extra time for more science if all other considerations allowed.

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