This is the long-delayed second post in my discussion of the departure and return orbits of the Apollo missions. If you haven’t read the first post, you can find it here—it’ll give some useful background to what follows.

The diagram at the head of this post shows a plot of Apollo 11’s departure trajectory, superimposed on a chart of the inner Van Allen Radiation Belt—the one that presents the greatest radiation hazard to astronauts on their way to the Moon. It’s a graph of distance against geomagnetic latitude, and it’s orientated so that the geomagnetic equator is horizontal. The white dots mark intervals of one hour after Translunar Injection. You can see how Apollo 11’s orbital tilt lofted it over the northern fringes of the inner VAB, thereby avoiding the densest area of radiation near the geomagnetic equator. And its return orbit did the same in reverse:

The white dots now mark hourly intervals before the “entry interface” at 400,000 feet altitude—the point at which the Apollo capsule began to significantly interact with Earth’s atmosphere.

It’s often said that all the Apollo lunar missions followed this same sort of trajectory, to avoid passing through the central part of the Van Allen Belts—I’ve even made that claim myself, previously. And certainly some of them did. Here are the departure trajectories of the three other missions that swept north of the VAB, with Apollo 11 for comparison:

As my graph title indicates, all these missions had Translunar Injections over the North Pacific. As I explained in more detail in my post How Apollo Got To The Moon, a TLI in the northern hemisphere was used when the Moon was situated south of the celestial equator. The more southerly the Moon, the more northerly the TLI, and you can see that reflected in the trajectories above—Apollo 15 had the most northerly TLI, and its trajectory is the one that begins to head south most rapidly.

Here’s a map of all the Apollo Translunar Injections:

The green grid lines show the orientation of the Earth’s geomagnetic field, which contains the Van Allen Belts, and the yellow tint indicates the region between forty degrees north and south geomagnetic latitude—the approximate limits of the dangerous inner VAB. The labelled coloured dots mark the position at which each mission’s S-IVB stage engine was ignited, and the tip of each coloured arrow is the position at which, ten seconds after engine shut-down, Translunar Injection was deemed to take place. You can see how Apollos 8, 11, 12 and 15 all have TLIs in the northern hemisphere. (Apollo 11 actually fired up the S-IVB while it was still in the southern hemisphere, but TLI was achieved north of the equator.) But there’s another cluster, containing Apollos 10, 13, 14 and 16, with TLIs south of the equator. As you can see from my map, while the “North Pacific” group were heading towards the fringes of the VAB as their trajectories rose away from Earth, the “South Pacific” group were on trajectories that were heading towards the middle of the VAB. Apollo 17 constitutes a “North Atlantic” group all on its own, but has the same problem as the South Pacific TLIs—it has the densest part of the VAB ahead of it, rather than behind it.

I’ll show you the departure trajectories of these missions in a minute, but there’s something else worth noting before I leave the TLI map. The dotted black line marks the ground track of the typical Earth Parking Orbit from which the Apollo missions departed—their second pass over the Pacific, leading into the third pass over the Atlantic. This is the track followed if the mission took off on schedule, right at the start of the launch window. Under those circumstances, the Saturn V would launch somewhat towards the northeast, on an azimuth of approximately 72° east of north. If there were launch delays, the launch azimuth would shift progressively towards the east, and eventually towards the southeast, reaching a maximum of 108° just before the launch window closed. Here’s an aerial view of the Apollo launch pads at Cape Kennedy, with that range of azimuths marked:

This shift in the launch azimuth resulted in Earth Parking Orbits with progressively more westerly ground tracks, allowing TLI to always take place on the opposite side of the Earth from the Moon, despite the launch delay and associated eastward rotation of the Earth. (To be more accurate, TLI was orientated with reference to the Moon’s position at the time Apollo would arrive there, three days after TLI. For more on that, see How Apollo Got To The Moon.)

You can see that most Apollo missions launched along the “standard” ground track. Apollo 14 had a short launch delay, so ended up a little to the west of standard. Apollo 17 had a very long delay, and its TLI shifted all the way across the Atlantic from the planned position. The westerly shift for Apollo 15 has another explanation, however—it was the first of the heavier “J” mission launches, and its launch window was made deliberately narrower. It launched on time, but in a more easterly direction—an azimuth of 80°. This ensured that the Saturn V got more of a boost from the west-to-east rotation of the Earth, making it easier to propel the heavier load into orbit. (Subsequent “J” missions went back to the standard launch window.)

So here’s a plot of the South Pacific (and North Atlantic) TLIs:

You see the problem—all of these missions were obliged to track through denser regions of the inner Van Allen Belt. Apollo 14, with the most southerly TLI, actually speared right through the most concentrated radiation. It was the speed of transit that protected these astronauts from an excessive radiation dose, rather than the orientation of their trajectory.

Now, if we look at the return trajectories, we can see that the Apollo missions all reentered the atmosphere on a west-to-east trend, but otherwise came in from all sorts of directions:

The dotted lines connect the atmospheric interface (coloured and labelled dot) with splashdown (black cross).

The variety of return trajectories is even clearer when we look at a geomagnetic plot:

All the South Pacific / North Atlantic TLIs, which took an increased radiation exposure on the way out, come back through only the fringes of the inner VAB. (Apollo 16, in particular, hooked “under” the Earth at high southern latitudes, accounting for that mysterious kink in the geomagnetic plot of its return trajectory.) Of the North Pacific TLIs, which departed through the fringes of the VAB, Apollo 11 and Apollo 15 returned in the same manner. Apollo 8 penetrated more deeply on the return than on departure, and Apollo 12 speared through the higher radiation region.

While there are on-line tools, like SPENVIS, which will calculate spacecraft radiation exposure from a model of the Van Allen Belts and a set of orbital elements, it’s pretty futile to attempt this for the Apollo missions, since we can’t accurately model the radiation shielding effect of the complicated structure of the Command/ Service Module, let alone the additional partial shielding provided by the S-IVB stage and Spacecraft Lunar Module Adapter, to which the CSM was still attached during its outward passage through the VAB. And, given the variability of the VAB radiation environment, we’d also need to make some educated guesses about the real proton and electron flux to which the spacecraft would have been exposed.

But we know that most of the astronauts’ radiation exposure came during the small number of minutes during which they passed through the VAB, with a lesser contribution mounting up throughout the rest of the mission, from exposure to cosmic rays and secondary radiation from the lunar surface.

So we would anticipate that the longer-duration missions (15, 16, and 17) would have more cumulative exposure to radiation; and that the North Pacific TLIs (8, 11, 12, 15) would have lower VAB exposure on departure than the other missions. Apollo 14, with its very southerly TLI, would receive a significant VAB dose on departure, and Apollo 12, with a return trajectory close to the geomagnetic equator, would sustain the highest VAB dose on return.

All the astronauts wore film badges to record their overall mission radiation dose. The readings, averaged over all three astronauts, were published in a NASA publication, Biomedical Results of Apollo, in 1975. I’ve graphed them below:

So it all hangs together. You can see how Apollo 14 received the highest mission dose, because of its departure trajectory. And Apollo 12 had the highest dose of the North Pacific TLIs, because of its return trajectory. Of all the South Pacific TLIs, Apollo 13’s was closest to the equator, and so sustained the least VAB exposure; it was also a shorter mission overall (the explosion on board meant that the mission simply looped around the Moon and came straight back to Earth), and so has the lowest dose of all the South Pacific TLIs.

Being able to plot the near-Earth trajectories of the missions makes sense of what is otherwise a rather random-seeming scatter of radiation doses.