Apollo Investigation

Trajectory of Apollo 11 through the Van Allen belts

by Xavier Pascal and Aulis Editors

“Essentially it knows where it is going because it knows where it came from and how it got there. It does not give out any signal so it cannot be detected by radar or be jammed.”

July 1969 NASA press release referencing the
‘inertial [flight] guidance system’ for its Apollo spacecraft

The Earth is surrounded by belts of radiation which were discovered by both the Russians and the Americans in the late 1950s. Although the then Soviet Union was equally involved with the exploration of this region, it was eventually named after the American scientist Dr. James Van Allen.1

Fig. 1
Fig 1. Basic cross section of the radiation belts around Earth (not drawn to scale). The outer belt is composed of electrons, the inner belt comprises both electrons and protons.

The radiation aspects of the Van Allen belts is not the principal reason for this article. Here we are concerned with the trajectory claimed to have been taken through the belts by the Apollo spacecraft. However, all the Apollo missions would have to travel through these belts to reach the Moon, so a brief summary of the state of knowledge concerning these belts, both then and now, is required.

In the late 1950s it was ascertained that most of the particles that form the belts emanated from the Sun via the solar wind while other particles trapped in the belts were thought to come from galactic radiation. These trapped energetic particles produced extremely high radiation levels, dangerous to unprotected living tissue.

Fig. 2

Fig 2. Van Allen’s original diagram from 1958 featured a plain disk representing the Earth. These magnetic belts surround the planet leaving only the polar regions open to cosmic radiation.

The depth of the two principle Van Allen belts are estimated differently, depending on the source, but thanks to Van Allen’s original statement that from some 40,000 miles the belts were less intense, and that an Earth-orbiting space station must orbit either below 400 miles or beyond 30,000 miles from Earth, it was generally considered that the two belts started at an altitude of about 400 miles and extended to 36,040 miles above the Earth’s surface. At least until recently.

Note: While altitudes are expressed from the surface of the Earth, the Van Allen belts are measured in radii from the innermost core of the planetary body. Van Allen illustrated the belts' energy levels extending to a distance of 6.5/7Re (Earth radii) and noted that the inner belt was most dangerous at a distance of 1.5Re the outer belt at some 3.5-4Re was a conservative limit. In 1958 Van Allen considered that the radiation associated with the Earth’s belts extended to some 66,695 miles (16.82Re).2

Over time, better technology has enabled progressively improved studies of these belts and their environment. In 1998 Professor Clive Dyer, an expert in such matters, is on the record for stating:

The worst part of the belts is at the heart of the lower radiation belt, measured from the Earth’s surface that is about 1.5 radii out. The upper belt peaks at about 3.5 to 4 radii out. [emphasis added]

This mix-and-match description turns out to be confusing for the public. Dyer is quoting the same measurements as Van Allen, but stating measurements from the surface of the planet. Whereas Van Allen’s diagram measures the radii from the core of the planet, as is usual for this evaluation of the Earth’s magnetic region.3- 3.3

Conditions in the belts
For the longest time after the Apollo missions, the general consensus was that there were two scenarios for the belts. They were either normally ‘quiet’ during solar minimum or ‘active’ during the solar maximum. So much so that in 1976, Sawyer and Vette released a model plotting the fluxes of Van Allen protons and electrons as functions of magnetic shells and magnetic field strength. Based on averages of satellite data from the late 1960s and early 1970s, the AP-8 Max and AP-8 Min considers proton fluxes during the solar max and solar min respectively while the AE-8 Max and AE-8 Min considers electron fluxes during solar max and solar min respectively. Together this model was known as the AX-8 and became the industry standard model for the Van Allen fluxes.3.4

CRRES satelliteThe scientific community’s complete trust in the AX-8 was shattered in 1991, when the Combined Release and Radiation Effects Satellite (CRRES) detected an enormous influx of electrons with energies between 15MeV and 50MeV. These electrons flooded the gap between the two belts and elevated the normal fluxes in the other two belts by several orders of magnitude. This influx was attributed to a massive solar flare that occurred on March 24, 1991, and it took until 1994 for the belts to decay back to ‘normal’ conditions.

This was a surprise to both astrophysicists and anybody reliant on GPS and communication satellites at the time (who no doubt got a rude awakening when they tried to use their phones and navigators). J.B. Blake et al. (1992) summarised the situation and put into context the cause of this surprise:

The event has engineering implications as well; a heavily-shielded satellite in the region of the injection would suffer a radiation dose much higher than expected. It is fortunate that present-day space missions do not spend much time in this region of the Earth's magnetosphere.
The injection event of 24 March was truly amazing, and the observation is unique for its location, magnitude, and energy during the 35 years of space research. However, this region has not been well patrolled since the 1960s, and it required good luck for CRRES to be on the right part of its orbit at the right time. Thus, it is difficult to conclude that the event itself was truly unique.3.5 [emphasis added]

Indeed, in the years that followed the CRRES event, it became apparent that injection events were a regular occurrence, and by 1998, it was found that the shape and energy within the belts was changing much faster than originally thought. As for being ‘well patrolled’, given that 35 years of research takes us back to 1957, and given the official assertion that any Apollo mission went very fast through the belts, one might better state that the Van Allen belts have never been well patrolled, until very recently.

At the beginning of the 21st century, in 2012, two eponymous probes were launched into the Van Allen belts, which soon revealed that the belts were essentially particle accelerators, transforming particles of relatively low energy into those of extremely high energy. Within days of their installation, these two probes fortuitously recorded a third region spontaneously forming within the belts due to large solar flares over replenishing the radiation.4

Fig. 3

Fig 3. Side view of the new belt. The side cut of the belts to 30º north and south of the core centre line (not on our mapped equator) at 1.5 radii, and from just below 3 radii through to just beyond 5 radii). These peak intensity regions do not automatically infer that the rest of the belts are totally harmless territory for the space traveller. Nor does this sampling of the electron flux mean that the dangers of the Van Allens are confined within the 30° boundaries illustrated here. Image: Daniel Baker in American Scientist.

These two probes revolutionised scientist’s understanding of the Van Allen belts and although there is still no consensus on the actual depth of these belts, nevertheless the extent of the region has been revised such that the AX-8 has had to be replaced by the AX-9. Still there are unanswered questions. Due to their penetrability, high energy electrons pass clean through most detectors light enough to be carried to space, thus exact fluxes of >15MeV electrons are unknown. Such that both the AE-8 and AE-9 only measure the proportions of electrons with energies up to 7MeV.

In 2013 Nature published a statement that considers the belts to be a continuous zone from the so-called ‘edge of space’ (the Kármán line) through to some 37,282 miles out, (that is 9.4 radii from the core of Earth, and 2.4 radii further out than Van Allen’s original drawing):

The outer ring orbits at a distance of some 10,000-60,000 kilometres above Earth, (6,213-37,282 statute miles) and encircles an inner band of even more energetic particles, roughly 100-10,000 kilometres above Earth (62-6,213 statute miles).5

Others go further and state that spacecraft must travel some 6.72Re (26,634m) before the inner belt is cleared (the new third belt region has been added to the inner belt region) and to 12Re (47,583m) before the outer belt is cleared. In either case, if 9.4 through to 12Re is considered to be the end of the Earth’s radiation belts, it is not the end of the radiation environment for the space traveller.

Fig. 4

Fig 4. Illustration with distances measured from the surface of the planet relating to the safety of small satellites traversing the belts. Albeit taking 5.9 days to reach the Moon instead of the 3 allocated to Apollo 11, it is a useful comparison and emphasises the problems for hardware caused by the radiation within the belts. (1km x 0.621 = 1 statute mile.)

Today, space agencies do not want to expose astronauts to the radiation within the Van Allen belts. Additionally, the sheer energetic variability and unpredictable behaviour of the belts is a further difficulty to overcome in planning for the safe passage of crewed space flights beyond low-Earth orbit (LEO).

So what about Apollo?
While better technology has led to a revised view of the belts, this region was behaving in the exact same way back in the 1960s, we just did not have the technology to know the detail. The ‘normal’ radiation flux data from which the AX-8 averages were derived may have been valid at the time the satellites recorded it. But the records show that the Apollo missions would likely have coincided with an injection event.

The March 24, 1991 solar flare responsible for the CRRSE injection event delivered so much radiation to the vicinity of the Earth that it caused the Northern Lights to be seen in Alabama and Kansas. Likewise, the Apollo missions were preceded by big solar flares that produced similar visual effects. The solar flares of August 1972 which occurred between the Apollo 16 and 17 scheduled missions, caused the lights to be seen in Colorado and even Florida! These are just the most famous examples, but there were of course others. And remembering that the third belt produced by the CRRSE injection event took three years to decay to normal conditions, it is remarkable that Apollo 10 was allowed to launch just days after a big solar flare on May 13, 1969, which caused the Northern Lights to be seen in New York, Illinois and Connecticut.

Table A
Table A. Solar Proton Events during the Apollo program with the potential of triggering injection events in the Van Allen belts. The CRRES injection event and the legendary flares of 1959 and 1960 are also listed for comparison. Table courtesy Jarrah White.

Whatever the true state of knowledge within the US space agency back in the 1960s, after making matters considerably worse by attempting to force a way through the belts by exploding nuclear bombs (instigated by Dr. Van Allen himself), when it came to Apollo, it was asserted that the Apollo missions would avoid the worst of the belts through careful planning and – by going very fast.

That assertion often comes up in defence of the official Apollo record. But is there any validity to this excuse? Again, we need to lay some ground rules. The following statement is from James Van Allen’s 1962 Space World article:

The outer zone is much more difficult to avoid [than the inner zone]. There do appear to be 'cones of escape' over the North and South geomagnetic poles. The half angle of these outward-opening cones is about 20°.5.1

Due to the tilt of the Earth’s geographic axis and its geographic poles being off-centre to the geomagnetic poles by 11.5°, this places the minimum latitudes for Van Allen’s cones of escape between 58.5° and 81.5° north or south of the equator (depending on which side of the of the Earth you are ‘escaping’ from).

Van Allen’s sentiments appear verbatim in the 2005 textbook, The Physics of Space Security by David Wright et al: "…like the proton flux, the electron flux is highest near the equator and becomes negligible at a latitude of 60° north or south."

So for the Apollo astronauts to be able to ‘avoid’ the most dangerous parts of the belt, their outbound trajectory at the bare minimum must take them to a latitude >60° above or below the equator. This is why Van Allen had proposed back in 1959 that “manned space rockets can best take off through the radiation free zone over the poles”. Which brings us to the nub of the trajectory problem.

The Problem
Rocket and Space Technology In an article published in 2009 titled Apollo 11’s Translunar Trajectory posted at Rocket and Space Technology, Robert A. Braeunig produced charts, tables and diagrams to support his claim that the trajectory of the Apollo 11 command and service module (CSM) would have allowed the spacecraft to avoid the dangerous parts of the Van Allen belts.

Braeunig asserts that he is not depicting the course of an actual Apollo trajectory orbit, merely illustrating how all the Apollo CSMs avoided the dangerous zones of the belts. Yet at the same time, the title of his piece shows that he is particularly concerned with the Apollo 11 mission.

Shortly after astrophysicist Jarrah White published in 2016 his own calculations for Apollo, Braeunig took down both his articles of 2009 and 2014 without explanation or notice.6 In fact, he also removed any mention of the Apollo Moon landing hoax topic from his entire website. Despite this, his images and trajectory have become the ‘go-to’ reference for all those wishing to reiterate the mantra “How Apollo ran the belts”. Which is most unfortunate, because the timing and the trajectory Braeunig adopted are incompatible with the data produced by NASA for that mission.7

Note: Reader beware! The same data appearing in different NASA documents can be expressed in using different measuring systems: kilometers (km), nautical miles (nm), statute miles (m), are all used by NASA. Braeunig has added to the confusion by collating data from various sources and then adopting the letter ‘m’ to signify meters, instead of the customary statute mile. In order to avoid Braeunig’s very convenient confusion, this article will avoid the SI system and adopt the statue mile (mile or m) for the remainder of this article. Thus the radius of the Earth, 1Re is 3,963 statute miles.8

Fig. 5

Fig 5. Apollo trajectory plotted by Braeunig ostensibly curving around the belts. The red dots are ten-minute markers, proving to Braeunig’s satisfaction that Apollo traversed the belts in only 1 hour 40 minutes. The beige outline is a cheat, leading the uninformed observer to imagine that there is no more radiation extant beyond the coloured cone, where red, orange denotes the most energetic regions, and purple the least energized.

Fig. 6

Fig 6. Data derived from the Van Allen probes. Upper image, combined outer and inner belts, and lower, detail of the inner belt. Both are configured from a top view of the globe, these diagrams do not reflect the closeness of the outer belt to the globe as seen in Van Allen’s original side view diagram (Figure 2), but they do convey the amount of energy extant within the belts surrounding the planet. Illustration: Daniel Baker in American Scientist.

Braeunig included another version of his Van Allen belt trajectory In figure 7 below, the location of the continents on the geographic globe encourages the observer to imagine that the Apollo 11 spacecraft was leaving for the Moon from an altitude located above a longitude some 31 degrees east of Greenwich and above a latitude north of Earth’s equator.

NASA documentation does not support that translunar injection location.

Fig. 7
Fig 7. Braeunig’s Illustration of the Van Allen belts. Note that this two-dimensional side cut now includes a three-dimensional globe viewed from the side. So that the radius from the Earth’s core, which is generating the Van Allen belts, is now seen to be above the globe’s mapped equator.

The published location of the translunar injection listed by NASA occurs north east of Australia just above the equator at the geographic coordinates 9.98°N, 164.84°E. And that will take the spacecraft from an altitude of 207.8 miles to 4,730.7 miles into the belts.

Table B

enlarge Table B, Trajectory parameters from Ignition (in LEO) for TLI through to mid course correction. Note that NASA is using nautical miles in this table. The conversion is nm x1.15078 = one statute mile.

The above table is in several sections. As stated the reference body is Earth, for the most part, since the three space flight columns are referenced specifically to the inertial guidance system and CSM/Earth (mission control) computations. Time is calculated from the moment of launch. Latitude and longitude are referenced to Earth. Altitude is in nautical miles, (not miles as is written) and relates to the distance of the spacecraft directly above the coordinates supplied. From which it can be seen that the spacecraft is travelling counterclockwise but away from the planet while continually descending, not rising above the mapped equator as Braeunig would have it.

Worst still, a quick look at that latitude column reveals that Apollo 11 never exceeded 60° North or South of the equator – the bare minimum Van Allen put for reaching his ‘cones of escape’ over the poles where the radiation becomes negligible. However, this plot also replicates the segment of LEO from launch though to crossing the Atlantic.

Fig. 8
Fig 8. Three Earth obits of an Apollo CSM. Marked in red and gold – the coordinates for the Apollo 11 from ignition for TLI NE of Australia through to mid course correction. The manoeuvres undertaken over the Cape and the Caribbean were apparently so effective that Apollo 11 didn’t need carry out this mid course correction.

Braeunig’s misleading trajectory with its implication that the Apollo 11 mission left Earth on a trajectory north of both the magnetic and the geographic equator has had unintended consequences, since it has entrapped many Apollo supporters who use his illustrations to defend the Apollo record, believing that the Apollo 11 CSM actually took this trajectory.

Notwithstanding the dubious radiation dose calculations offered by the space agency for the Apollo missions, the key problem here is that Braeunig’s timing and trajectory for the Apollo CSMs in general and the Apollo 11 mission in particular is an example of the considerable muddle that has been created by those taking the principles NASA uses for flight profile illustrations and technical diagrams as the actual event, and then applying these theoretical diagrams to a real time mission trajectory.

A NASA document by Robin Wheeler from 2009 totally contradicts Braeunig’s claims. Titled Apollo lunar landing launch window: the controlling factors and constraints, it is available on the NASA history website, and although technical, this Apollo lunar landing launch window document is worth reading as it describes the trajectories that would have to be taken by any Apollo crew, should they wish to reach the Moon.9

Fig. 9

Fig 9. Note that the title logo depicts the Moon orbiting off to the top right of the Earth.

After launch, we learn that a maximum of three orbits in LEO were designed into the Apollo flight plan to check out the spacecraft systems before it was to be boosted into a translunar trajectory (TLI). That event could occur on either the 2nd or 3rd of these so-called ‘parking orbits’. A misnomer if ever there was one.

Fig. 10
Fig 10. Apollo 11 chart for the first orbit of the spacecraft around Earth after launch from Florida. In the event we are informed that Apollo 11 went for TLI after only 1.5 Earth orbits.

Note: After TLI had taken place the crew were obliged to rearrange the combination of CSM and LM and jettison the S-IVB section of the rocket, which would itself travel to the Moon. Thanks to the NASA media information packs which had earlier informed the world that the Apollo 9 mission was the dress rehearsal concerning these manoeuvres, and the fact that Apollo 9 performed its dress rehearsal in LEO, most people apparently have concluded as Clive Dyer did when in conversation with Aulis in 1998:
“What they did was park in LEO and when they had rearranged their space craft they travelled through the VABs at a great rate so they didn’t pick up too much radiation.”10

And that explains the reason for initially calling the Apollo Earth orbits ‘parking orbits’. Nothing could be further from the truth. Despite the mental image of three crewmen sorting out their hardware in the parking lot of a LEO supermarket, for a theoretical lunar trajectory the rearranging of the space craft is required to take place after the TLI has boosted the CSM to well above the altitude of the ISS (and the Hubble telescope). And it is initiated while the craft was orbiting just north of NASA’s KSC above a latitude of 30.18ºN, 81.71ºW).

According to NASA documentation, the docking of the CSM and the LM took place at an altitude of 6,119 miles, that’s 1.54 radii into the belts, when measured from the surface (2.54 radii measured from the core). As by that time they were also 51 minutes from the initial TLI it is already clear that Braeunig’s one hour forty minutes to get beyond the 6.5 radii he has illustrated, is not going to work out, not least because from TLI onwards, the space craft is continually slowing down during its trajectory.11

Braeunig’s red dotted time line of 1 hour 40 minutes is also ten minutes short of the time NASA has allocated from TLI to the moment of distancing the CSM from the S-IVB component, which would then be on its own lunar trajectory. By then the CSM was at 19,126.8 miles altitude, and that is only 4.82 radii (5.82 radii from the core) into the belts. And it has taken 1 hour and 50 minutes to so do. There was plenty more belt left, and apropos those 64,000 miles that James Van Allen considered part of Earth’s radiation environment back in 1969, NASA seemingly marks that particular boundary of 17.12 radii some eleven hours into the flight plan: it is at that point that ‘Barbecue Mode’ (the thermal passive control achieved by slowly rotating of the spacecraft around its axis) was initiated.

Already flawed relative to NASA’s own narrative when it comes to distance travelled, Braeunig has also chosen to illustrate his article with another view of the energetic Van Allen belts to which the degrees of arc are inscribed on the hemisphere representing Earth.

Fig. 11a
Fig 11a. Braeunig’s trajectory avoiding the heart of the inner belt. This early AP8 diagram of the proton belt at solar minimum shows how the heart of the inner belt encircles the planet to a height of 45° above and below the planet’s centreline.

Remember: even under 'normal' circumstances, since Apollo is not above the minimum safe latitudes, the crew would already be subjected to more than 70rem from the 8-400 MeV protons that they would have encountered along the trajectory and also would be subjected to substantial fluxes of >15 MeV electrons at 4-5 radii out.

Fig. 11b
Fig 11b. Braeunig’s inclusion of his trajectory onto a mapping of the energy flux here the outer belt rising to over 60° of latitude around the planet.

Interestingly, scaling his three separate images to the exact same radius, reveals discrepancies between his ten minute time markers where there should be none, and different arcs are present, one lower than the other.

Fig. 12
Fig 12. Braeunig’s three trajectory diagrams scaled to the radius on the disk representing the globe. The red lines drop the time markers to the radii. Note the mismatch of the time markers on the two arcs.

Braeunig’s trajectory might well inform the viewer that the spacecraft sensibly avoids the heart of the inner belt, but his effort is all in vain, because as already stated, the only ‘belt-free zones’ are above 66.67° of geographic latitude and even these north and south pole regions are subjected to radiation. Furthermore ‘trajectory’ is a literal misdirection.

Theory and Practice
What is really of interest is the trajectory that the CSM would have taken if it had actually left LEO. Wheeler’s launch window document clearly states that this trajectory depended on the position of the Moon on its orbit. Regarding transfer energy considerations this document states: "…In order to arrive in the vicinity of the Moon the spacecraft was 'aimed' (targeted) at a position where the Moon would be at the time of its arrival as illustrated in figure 5".

Fig. 13

Fig 13. This is Wheeler’s figure 5. A centre-to-centre view of the Earth on its own orbital path and the Moon is again illustrated orbiting the Earth off to the upper right. This plot of a theoretical free return trajectory for translunar spacecraft (not to scale) is in fact the illustration of a trajectory used for the Apollo missions from Apollo 12 onwards.

The lunar position in space is not constant, nothing is constant. Everything, the Earth, Moon and Sun is rotating on its own axis while orbiting some other body. (Even the CSM was scheduled to rotate on its longitudinal axis for most of the voyage). During the time the CSM travels towards its destination, the Moon also travels along its own orbital path around the Earth, and the Earth is orbiting the Sun.

Therefore, in order to optimise the trajectory of the craft and to minimise fuel-consuming craft maneuvers, rather than directing the CSM towards the position of the Moon at launch, the CSM trajectory is calculated on the position of the Moon when the spacecraft arrives within its vicinity, some three days later.

Free Returns
Chemical rocket-propelled spacecraft essentially perform a huge elliptical slingshot trajectory which assures that the craft will return to Earth without expenditure of propellant. These free return trajectories come in several varieties: cis-lunar, circumlunar and hybrid.

The highly-elliptical Earth orbit illustrated in figure 13 above offers a free return to the atmospheric entry corridor trajectory and is a hybrid free return. As it falls short of attaining lunar orbit, a mid-course manoeuvre was required to change the CSM onto a translunar trajectory. This hybrid was adopted for Apollo 12 through to 17.

The earlier missions, Apollo 8, 10 and 11 were designed with circumlunar free return trajectories. but the Apollo records state that these three Apollo missions were so well executed that there was no need to use the free return. Instead, upon arrival at the Moon, a manoeuvre was undertaken in order to acquire lunar orbital insertion (LOI).

Fig. 13aFig 13a: This circumlunar trajectory illustration from the NASA Apollo 8 Mission Report also illustrates the route of the S-IVB. NASA

Apollo 13, the 'Rescue Mission' had it all: it was planned as a hybrid trajectory but this was changed to a circumlunar trajectory when ‘all did not go well’. This mission was then able to adopt the free return, albeit with some trajectory adjustment burns along the way.

In the specific case of Apollo 11 circumlunar trajectory, its translunar injection occurred on July 16 and the direction of travel was to the location of the Moon on July 19, when LOI should be acquired. And it is here that Braeunig once again has deviated from the given data.

Note: Xavier Pascal has pointed out something important concerning Braeunig’s trajectory. However, both Braeunig and Wheeler stop short of where exactly the Moon would be found on July 19, 1969. And to know the answer to that we have to move from the theoretical to the practical and get into time-related data and astronomy.

When it came to plotting the Apollo spacecraft trajectory, as already stated, the Apollo mission events were timed from the moment of launch from Florida, called Ground Elapsed Time or GET 00.00.00. This was independent of GMT/UT, all local times, and any artificially engineered summer times extant at the time of the mission.12

In order to confirm the accuracy of their trajectory relative to the computed data, the Apollo astronauts were scheduled to take readings of specific stars. The computer was loaded with 37 star positions, and the CSM navigator (Mike Collins on Apollo 11) was charged with overseeing the data concerning the inertial guidance system. This required ascertaining the position of the stars, along with the spacecraft’s known speed, distance from Earth and GET. The angle between two star positions was then computed relative to a position on Earth ‘which only the computer knows’.

We are reminded of that NASA statement ‘Essentially it knows where it is going because it knows where it came from and how it got there’. Since the onboard computer was puny, the accounts of this flight have the astronauts asking Mission Control where they were, Mission Control was unfazed by their failure to complete star sightings, and the accuracy of their trajectory was not impacted by the lack of these seemingly vital navigational references. That ‘knowing computer’ was most likely based on Earth, bringing the image of IBM aka HAL to mind.13 And remembering that Jodrell Bank in the UK had stated that ‘they did not have the pointing data’ to track Apollo 11, recalls NASA's statement: ‘It does not give out any signal so it cannot be detected by radar or be jammed.’

Even if many of these star sightings were apparently unobtainable, and only those who have read into the data would really know the whereabouts of the Apollo spacecraft, the plan reveals that for the precise timing of events concerning the CSM and the natural motion of the Moon, GET was the timing adhered to and adopted by the mission planners wherever they were based in the world. It is thus the equivalent of sidereal time, which is the moment at which an object in space is identified relative to the background stars.

The Moon moves along its orbit at a rate of some 12.85° a day, and consulting an ephemeris, in July 1969 the Moon was to be found moving through the constellations of: Cancer on July 13th (Apogee) and 14th (New Moon); Leo on the 15th, 16th and 17th; Virgo on the 18th (arrival at the equigravisphere) and 19th (LOI) Libra on the 20th (landing and EVA) the 21st and 22nd. Scorpio on the 23rd.

For an observer on Earth, in the summer of July 1969, Virgo and Libra were to be found below the celestial horizon, in the southern hemisphere. Although it was deemed necessary to co-opt the Australian tracking stations during the Earth orbits of the Apollo craft, it is also the case that the Apollo record cites the eastern tracking station of Honeysuckle Creek as a specific requirement for transmitting the initial EVA data for Apollo 11.

Fig. 14
Fig 14. Azimuthal mapping of the planet and the constellations. The celestial ecliptic and equator are part of the astronomical map. And a disclaimer to any Flat Earthers: this azimuthal projection of the Earth that you pretend is a map of your fantasy world is in fact a map of the globe with everything below the north pole flattened into a disc. That’s right, the ‘flat earth map’ is a map of the globe!

Notice that the astronomy maps of time-based events mark the track of the Earth against the background stars, clockwise. The Sun and the Moon’s ecliptic tracks around the Earth are also seen to move clockwise against the background stars, as we perceive their orbits from Earth. The theoretical maps and plans used by NASA to illustrate the procedures of a lunar expedition use instead the geocentric model of the counter-clockwise Moon’s orbit around the Earth, and always illustrate the Moon in the top right corner. This is independent of the Moon’s actual location against the background stars. The following four illustrations from 1962, the 1968 Apollo 8 schema, and two of the Apollo 11 schema make the point.

Fig. 15a
Fig 15a. The Apollo plan for lunar orbit rendezvous was finally established by James Webb at NASA on November 7, 1962. Here the Sun is shining from the left side of frame. NASA

Fig. 15b

Fig 15b. Another Apollo 8 flight event profile: Note the confusing arrow for the Sun indicates the location, not that the Sun is shining towards the east. On December 24 and 25 the Moon was to be seen moving through the constellation of Pisces, and Apollo 8 was intended to be there and back, hence no intervening Moon images between LOI and TEI. Also note that here we do not see the S-IVB trajectory but we do see the equigravisphere data.

Compare the above illustration with the same map drawn for Apollo 11, when the Moon at the time of LOI was in the constellation of Virgo.

Fig. 15c
Fig 15c. This ‘road map’ to the first lunar landing as Aldrin dubbed it, is annotated with days of the month, and one Moon for each day. The Sun is accurately represented and the Earth globe at the centre shows the continents of North and South America. NASA

Fig. 15d

Fig 15d. Closer view of the two moons between LOI and TEI which indicate the two days spent between landing and departure. The Moon was tracking through the constellations of Virgo and Libra respectively.NASA

Now compare the above map with another Apollo 11 profile from NASA:

Fig. 15e
Fig 15e. Here each Moon denotes an event rather than a specific day. The Sun is illustrated coming from below. And the outbound trajectory looks to be virtually horizontal. NASA

These examples, along with Wheeler’s earlier trajectory illustrations, demonstrate that when it comes to diagrams of flight profiling, the natural inclination of right-handed draftsmen and the mathematically inclined, has led to a preference for the Moon to be positioned at right and top right of frame. The reality is somewhat different. The flight profiling is illustrating the motion of objects through space. Whereas the Moon was in different constellations at the times ascribed to the various missions.

This brings us back to the direction the Apollo spacecraft is taking in Braeunig’s illustrations. Although he is careful to state that his trajectories do not necessarily represent the actual path taken by the CSM and/or the S-IVB, even when he focuses on the Apollo 11 trajectory and all his diagrams say the contrary, in fact, as Xavier Pascal has noticed, Braeunig has copied the theoretical while ignoring the practical.

Destination Moon
A planisphere displaying the position of the stars relative to the geographic north pole and the ecliptic centre, allied with an ephemeris giving the position of the Sun, Moon and the planets reveals that in July 1969, an observer on Earth would see that the Sun was traversing the constellation of Cancer, until July 23rd, when it moved into Leo – the constellation, not the orbit! Earth was therefore located opposite the Sun, in the constellation of Capricorn, and the angle formed with the line to the Moon at LOI is of some 31°. Overlaying this data onto the constellations produces this:

Fig. 16
Fig 16. Geometry of the trajectory in 2D: E = Earth at TLI, M = Moon at LOI, S = Sun at launch. Some of the most famous two-burn nearly-ballistic lunar transfers were those used in the Apollo program. The mission implemented a low-Earth parking orbit with an inclination of approximately 31.38°.14

All of the above, taken together with Wheeler’s information on the principles involved in crewed space flight to the Moon, along with that comment on the virtually ballistic nature of the Apollo trajectories from another NASA document make it clear that that Braeunig has created enormous confusion, albeit adjusting the evidence to fit his viewpoint is not convincing. But in both these aspects he has been supported by others such as The Wire.

Fig. 17

Fig 17. Emulating Braeunig in The Wire, the red ellipse is supposed to illustrate the trajectory taken by the CSM along the ecliptic.

The June 2019 article in The Wire “How NASA Worked Around Earth’s Radiation Belts to Land Apollo 11 on the Moon” illustrates the planet with its magnetic and geographic axis inverted (in 1969 the northern magnetic pole was to the west of the geographic pole, not as illustrated) and here the northern geographic pole is inclined towards the ecliptic which only occurs in the northern winter. Nor does it take into account the actual location of the Sun and Moon, having apparently confused the ecliptic plane with the quasi-ballistic nature of the trajectory from Earth to the Moon. As seen in the astronomy, the Moon was actually lying below the ecliptic at the time of the Apollo 11 LOI.

Accountability and Responsibility
The confusion between the Apollo record accounts, the various measuring systems of both time and distance – and when it comes to crewed space flights beyond LEO, the sheer avoidance of this region by all the space agencies to date, is proof enough that crewed Apollo missions were not sent through these belts. For had they done so, the agencies would be quite happy to send astronauts through them now.

The excuse that modern technology requires more stringent measures might have some relevance when it comes to hardware, but it does not stand up to scrutiny when it comes to human crews. Bio-organisms are as vulnerable today as they were in the 1960s. And to repeat, the radiation belts are as difficult to negotiate today as they were in the 1960s. Ignorance is not bliss in this particular instance, a fact with which Lockheed Martin would concur.

Lockheed Martin has ostensibly set out three levels of consideration when it comes to protecting human crews from space radiation.15 On Earth and in LEO where the ISS orbits, the protection is required to produce as low a risk as is reasonably achievable. And then deep space is referred to separately from the intended crewed visits to Mars and the Moon (cislunar space is the distance from LEO to the Moon’s orbit) and once again, the time factor used to differentiate these two expeditions and environments.

Fig. 18
Fig 18. Lockheed Martin’s banner associated with its research into radiation protection for astronauts. The acronym ALARA could just as well be ALARM – since even LEO is not entirely safe for the ISS when it travels through the South Atlantic Anomaly, image: Lockheed Martin.

If there is no level of exposure to radiation considered safe now, as the conditions of space remain the same, there certainly wasn’t any additional safety for astronauts during the Apollo period. Nor would it be necessary to differentiate between similar environments using the length of voyage as the excuse. The length of voyage certainly increases the risks for the bio organism but those risks are extant from the start of any voyage beyond LEO. And If as many would assert, it was simply a matter of ‘going very fast through the Van Allen belts avoiding the dangerous bits’, crewed exploration of space would be much further along today, and none of Braeunig’s data mix-ups, and other inaccurate and deliberately confusing statements concerning the Apollo record would be necessary.

Former NASA administrator Sean O’Keefe, attempted to retain Apollo mythology while making statements about Elon Musk’s Starship ‘enterprise’ when he noted:

I remain cautious about Starship’s deeper-space capabilities for humans, despite its size and innovation, given that it relies on the same chemical propulsion systems used in spaceflight since Yuri Gagarin took the first trip and Alan Shepard was right behind him in 1961.
Mars is 65m miles away… Cutting the distance can only be achieved if you add space propulsion and right now we have none of that. We have no means to achieve it. No one on this rock knows how to do that.
The second thing we don’t have is the means to provide shielding sufficient to preserve human life. As it stands, the radioactivity is so extraordinary you wouldn’t make it, much less get back. Those are the two fundamental limitations I see to anyone being able to achieve anything much beyond the lunar objective at this stage.16

O’Keefe surely knows that ‘deeper space’ is a misleading description. Deep space is everywhere beyond LEO and that includes Earth’s protective region of the Van Allen belts with their unpredictable accelerated particle activity – and the totally unprotected surface of the Moon. As Lockheed Martin clearly states:

“There is currently no level of exposure considered safe.”

Xavier Pascal and Aulis Editors
Additional input from Jarrah White

Aulis Online, January 2022


Astrophysicist Jarrah White has provided more detail on the radiation in the Van Allen belts along with a report on Braeunig’s Apollo radiation data:

Bennett and Percy noted in their 1999 book Dark Moon that the size of the belts varied from reference-to-reference and this had nothing to do with the discovery of any third belt activity. Today we understand the belts to be a far more dynamic system than was thought, and that their geometry is dramatically influenced by enrichments of solar and cosmic radiation. Bearing in mind that this region was equally dynamic back in the 1950s and 60s, it is important to lay some groundwork for conditions considered ‘normal’ in the belts and conditions considered during ‘injection events’ and what astronauts venturing into these regions would be up against in both circumstances.

Professor Dyer’s 1998 statements were reiterated by Herbert Funsten et al in their 2013 paper:

In situ measurement of this region of the Earth’s space environment presents an extraordinary challenge due to the large fluxes of penetrating radiation. In particular, substantial electron fluxes are typically observed at energies that can exceed 15 MeV in both the inner radiation belt (typically centered near 1.5Re) and outer radiation belt (typically most intense near 4-5Re at the Earth’s magnetic equator), as well as inner belt proton energies that can exceed 100MeV.3.1

15MeV electrons represent the primary electron hazard in the outer belt, because such electrons will penetrate 8g/cm2 of shielding. Furthermore, when electrons are stopped in material, they lose their energy in the form of secondary X-ray photons, bremsstrahlung radiation. Thus, satellites expected to operate within these regions require several cm of aluminium to stop the electrons and an inner layer of high-Z material such as lead to attenuate secondary X-rays.3.2

In his 1958 papers, James Van Allen put the end of the outer belt at 66,695 miles but also suggested an outermost ‘safe’ altitude of about 30,000 miles. This altitude ultimately become the orbit of geosynchronous and geostationary satellites, and has caused some NASA followers to downplay the radiation hazard. Basically their argument is: ‘If the radiation is strong enough to harm humans, why are there hundreds of satellites happily living in the outer Van Allen belt?’

This is a false argument. Although the belts continue out beyond 60,000 miles, for all intents and purposes at geostationary orbit there are almost no electrons with energies >1MeV. Such electrons are relatively easier to shield, requiring only 0.545g/cm2 of aluminium to stop them.3.3 In addition, geostationary orbit is still within the magnetosphere of Earth, which provides some protection from solar and cosmic radiation.

As regards Braeunig and the Apollo radiation data: Braeunig has also claimed that the CSM would have adequately protected the Apollo astronauts while traversing these belts. He published a follow up article in 2014 titled Apollo and the Van Allen Belts: an estimate of the radiation dose received. Braeunig cross-referenced the coordinates he attributed to Apollo 11’s alleged trajectory with the corresponding proton and electron fluxes recorded in the AX-8 Max models for the Van Allen belts and concluded that the astronauts should have only received a total dose of 32 millirem.

The conclusions that Braeunig attempted to draw, however, were based on outdated underestimates for the penetrability of ionized particles and deliberately deceptive downplaying of the amount of radiation the astronauts would have received. This 2014 article became the subject matter of a video critique titled MoonFaker: Radiation Reloaded by Jarrah White.5.2

Table C

Table C. Proton attenuation in material plotted as a function of proton energy and areal density of materials. Note that the Apollo CSM hull was made of aluminum, stainless steel and ablative resin rated at 8g/cm2, as annotated by Jarrah White. It is clear to see that the walls on the CSM will only block out protons with energies up to ~8MeV (Million Electron Volts), not 100MeV as Braeunig claimed, image: J.W. Keller et al. 1963.

Citing a table based on outdated and primitive estimates from 1937, Braeunig claimed that the CSM walls would block out all protons with energies up to 100MeV. White argued that NASA’s own data from 1963 indicated that a hull of steel and aluminum rated at 7-8g/cm2 would at best stop protons with energies up to 8MeV, leaving the astronauts exposed to any >8MeV protons. Braeunig also claimed that any protons with enough energy pass through the spacecraft walls will also pass clean through the astronauts and do little damage, when in fact that the >100MeV protons in the inner belt are in the same energy range as those used in proton therapy and proton tomography – which are stopped by tens of centimeters of human flesh.

Table D
Table D. A comparison of the AP-8 predictions with actual measurements made by the TIROS/NOAA satellite. These curves consider protons encountered along a 690km circular orbit with an inclination of 29°, this inclination is comparable to that used by Apollo and manned US spacecraft in general. A quick look reveals that the AP-8 under predicted the proton fluxes by a factor of 3. NASA’s Christian Poivey recommended using this as a correction factor when using the AP-8. Braeunig made no attempt to apply correction factors his use of the AP-8 or as he liked to call it, ‘the bible of Van Allen fluxes’, image: C. Poivey

In addition, Braeunig was overconfident about the particle fluxes the AX-8 models gave for his coordinates. He even denied the existence of >15MeV electrons in the outer belt because none are listed in the AE-8. His mindset was essentially: ‘If the AX-8 says it, it must be true! If it’s not in the AX-8, it doesn’t exist!’ In fact, modern astrophysicists now take the AX-8 with a grain of salt because of its tendency to underestimate the particle fluxes by several factors. And when converting his calculated absorbed dose to the equivalent dose, Braeunig used a Radiation Weight factor of 2 for the protons when in fact a factor of 5 is demonstrably more appropriate for solar and VAB protons.

After accounting for all the deliberate errors that Braeunig made, White calculated that the actual doses that the Apollo 11 crew should have received would have been in the order of ~100rem (71.2rem for the outbound trip, and 28.5rem for the return trip), not 0.032rem. White did not dispute the purported trajectory that Braeunig attributed to Apollo 11. In fact, he generously used Braeunig’s coordinates in his own calculations. It is these coordinates that are Pascal's own point of contention as it seems Braeunig has made yet another deceptive attempt to downplay the issue.


1. According to The Wire: How NASA Worked Around Earth’s Radiation Belts to Land Apollo 11 on the Moon, due to their ability to launch spacecraft into high polar orbits, the Soviets (now Russians) principally investigated the outer belt while the Americans, obliged to launch at lower inclinations relative to the equator, principally investigated the inner belt
2. Van Allen’s original article titled Radiation Belts around the Earth was published in March 1959 in the Scientific American volume 200 Number 3, ten months after Van Allen had made the scientific community aware of the results described in this article, during a lecture on May 8, 1958
Also see Journal Nature doi:10.1038/nature, 2013, 12529
3. Variability of belt size and interviews with Professor Clive Dyer. Bennett & Percy, Dark Moon Apollo and the Whistle-Blowers, Chapter Three, Aulis Publishers, 1999
3.1. H.O. Funsten et al. 2013, Helium, Oxygen, Proton, and Electron (HOPE) Mass Spectrometer for the Radiation Belt Storm Probes Mission, 2013
3.2. David Wright, Laura Grego, and Lisbeth Gronlund, The Physics of Space Security: A Reference Manual
3.3. J.W. Keller et al. 1963 in Astronautical Engineering and Science, from Peenemunde to Planetary Space: Honoring the Fiftieth Birthday of Wernher Von Braun, McGraw Hill
3.4. AE-8/AP-8 Radiation Belt Models and also New Twists in Earth's Radiation Belts
Jarrah White’s tables calculating Van Allen proton doses based on the fluxes recorded in AP-8 are available for download
3.5. J.B. Blake et al. 1991, Injection of electrons and protons with energies of tens of MeV into L < 3 on 24 March 1991
4. See Aulis Online News Item Van Allen Probes Revolutionize View of Radiation Belts
and also American Scientist, New Twists in Earth's Radiation Belts, Daniel Baker
5. Journal Nature doi:10.1038/nature, 2013, 12529
5.1. James Van Allen (1961) Space World, The Danger Zone: Earth is wrapped in deadly belts of radiation
5.2. Jarrah White, 2016, MoonFaker: Radiation Reloaded
6. The Internet Archive cached record of the original Robert A. Braeunig article: Apollo 11's translunar trajectory and how they avoided the radiation belts
7. Apollo 11 The NASA Mission Reports Volume Three (from the archives of the National Aeronautics and Space administration) Robert Godwin editor. (With special thanks to Steve Garber NASA HQ & Benny Cheney NASA JSC). 2002, Apogee Books, an imprint of Collector’s Guide Publishing Inc., Burlington, Ontario, Canada
8. NASA criticised for sticking to imperial units, despite losing a Mars Orbiter probe in 1994, due to a mix up of unit systems, NASA has still not fully adopted the international system of units (SI) legislated by the US in 1988. In June 2009 it was revealed that the future build of the Ares rocket (based largely on a shuttle design) was going to be built using the English units system. NASA spokesman Grey Hautaluoma said that since “The Shuttle and US segments of the ISS and much of the Ares launch vehicle and Kennedy Space Center ground systems are legacy hardware built in the English system of units…We found the cost of converting the relevant drawings, software and documentation to the SI would exceed what we can afford.”
Also, When NASA Lost a Spacecraft Due to a Metric Math Mistake
9. Robin Wheeler, Apollo lunar landing launch window: The controlling factors and constraints.
10. Interview with Professor Clive Dyer. Bennett & Percy, Dark Moon Apollo and the Whistle-Blowers, Part One, Chapter Three, Aulis Publishers, 1999
11. Any spacecraft on this trajectory only picks up speed again at the 5/6ths marker of the distance between the Earth and the Moon, known as the equigravisphere. And that distance is dependent on the position of the Moon relative to its orbital path which varies by some 30,000 miles from its apogee to perigee (farthest and nearest approach to Earth)
12. British Standard Time Act 1968 (1968 c. 45). The fact that this time act – Intended to permanently establish the time for general purposes at one hour in advance of Greenwich mean time over a period that coincided with the lunar missions of Apollo 8, 10,11,12 and 13 is somewhat suspicious. Date of Royal Assent: 26 July 1968. The experiment began on 27 October 1968 effectively continuing daylight saving into the winter. The British government, determined to get this BST bill passed, made strong representation for it in parliament and in the face of vociferous opposition, whipped it through parliament by December 1968. Establishing an intended period of five years, from March 1969 (with hindsight that would cover Apollo up to the Apollo Soyuz project. Extremely unpopular with most of the public from the very start, the issue was again debated in the Commons on 2 December 1970, this time it was left to the politicians to decide! The vote for the experiment to be discontinued won by 366 to 81. However, the effective end of the experiment became 2 am Greenwich meantime on 31 October 1971. The complete volte-face of the Government, infers that whatever was intended to be achieved by confusing the time reference points from just prior to Apollo 8, 1968 onwards had been achieved. The Odyssey of the Lost Apollo CM
And also:
13. Authors’ communication with Jodrell Bank, Bennett & Percy, Dark Moon Apollo and the Whistle-Blowers, Part Two Chapter Nine, Aulis Publishers, 1999
14. Paper discussing lunar trajectories surveyed short 3-6 day direct transfers, longer 3-4 month low energy transfers, and variants that include Earth phasing orbits and/or lunar flybys. The 3-6 day direct transfer involved ‘a large maneuver to depart the Earth, a large maneuver to insert into orbit at the Moon, and a ballistic coast’. Apollo was considered a ‘two-burn nearly-ballistic lunar transfer’ This direct transfer was also used in the Surveyor and Lunar Reconnaissance Orbiter mission, among others.
A Survey Of Ballistic Transfers To Low Lunar Orbit, Jeffrey S. Parker Member of Technical Staff, JPL, California Institute of Technology, M/S 301-121, 4800 Oak Grove Dr., Pasadena, CA 91109 Rodney L. Anderson Member of Technical Staff, JPL, California Institute of Technology, and Andrew Peterson Research Assistant, Georgia Institute of Technology, Atlanta, GA 30332.
15. Lockheed Martin’s article discussing astronaut protection from radiation, How a Wearable Vest Can Protect Astronauts from Radiation in Deep Space.
16. Quoted in an article by Richard Luscombe in The Guardian, Sean O’Keefe was NASA Administrator from December 21, 2001, overseeing the ISS budget overruns, the aftermath of the Shuttle Columbia disaster and the gearing towards the new lunar and Martian programs before resigning on December 13, 2004.

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Xavier Pascal is an aerospace engineer and a very experienced IT computer professional specialising in real-time systems. Over the years he has constructed a number of electronic interfaces with digital electronics. Xavier Pascal is sufficiently qualified to read and understand the technical documentation of the technology deployed in the Apollo space project, and his observations of the intentional flaws in the documents form much of the basis of this article.

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