All the estimates we've seen lie within the same order of magnitude and generally outline a plausible method of computation. This stands in contrast to the conspiracist estimates which generally have no quantitative support.

Computing the precise exposure for Apollo astronauts is very difficult. That's why the astronauts wore dosimeters to measure the actual exposure. The factors involved in computing expected exposure analytically include:

Exact trajectory. The Van Allen belts are not uniformly shaped. They have thick and thin spots. And the level of radiation is not constant at all points. Toward the center of the belt cross sections there is more radiation than at the edges. Most Apollo enthusiasts do not know the exact trajectory or how it relates to the location of the Van Allen belts. But they know that they don't know this, and so they frequently do their computations assuming the astronauts passed through the densest parts, and therefore err on the side of overestimating the exposure.

Exact velocity. Exposure time is very important to a correct computation of radiation dosage. Because the velocity of the spacecraft is constantly changing, the same ambiguity which governs the geometry of the trajectory also governs the rate at which it is followed. And most enthusiasts (and all conspiracists) lack the information and skill to precisely determine the velocity of the spacecraft during the Van Allen belt traversal, and therefore the exposure time.

Exact energy and flux. In any given cubic meter of the Van Allen belts there will be a soup of particles at various energy levels and fluences. Energy describes the velocity of the particle, how far it will penetrate, and how much damage it will do if it hits something. Flux is the density of particles, how many of them pass through a given area in a second. Generally, the higher the energy the lower the flux. Low-energy particles (i.e., protons 30 MeV and below) can be ignored because they do not penetrate the spacecraft outer hull. But at each point along the trajectory through the Van Allen belts there is a different continuum of flux and energy. It requires a lot of mathematics to fully solve this system. And since some of the variables are hard to determine, they're typically approximated.

Probabilistic factors. Even should a high-energy particle penetrate the spacecraft hull to the interior, it will only cause problems in the human organism if it is absorbed in tissue. It is possible for the particles to pass through the body without colliding, in which case they are harmless. The human body varies in density. Particles are more likely to collide with dense tissue like bone. The amount of absorbed radiation is a statistical probability based on how much radiation is detected by dosimeters.

To summarize then, a fully accurate analytical solution must first determine the exact trajectory of the spacecraft through the Van Allen belts. This will give a continuous function describing particle flux and energy at each point along the trajectory.

At each point in the trajectory we will have a function giving flux per given energy level. So a 100 MeV proton will have, say, a flux of 20,000 particles per square centimeter per second at that point in space. But for other energy levels the flux will be different at the same point. The total irradiation inside a spacecraft will be the sum of all the fluences at energies capable of penetrating the hull and shielding.

And at each point along the trajectory the velocity of the spacecraft must be determined so it can be known how much time the spacecraft spends at that point. This is multiplied by the conglomeration of fluences to arrive at a dose.

This dose is simply the amount of radiation present. It must be converted to a meaningful value that describes its likely effect on human tissue. Again, energy and fluence come into play, because low-energy particles (but still high enough to penetrate the shield) are likely to accumulated in the outer layers of the skin and cause damage which is sloughed off harmlessly. High-energy particles are absorbed in the bones and internal organs, causing much greater injury.

The procedure for analytically computing a radiation dose is simple enough in principle as outlined above, but of course is very difficult to actually carry out. This is why engineers generally don't try to compute the dosage to any great degree of accuracy ahead of time. They are happy simply to arrive at an order of magnitude which provides adequate design criteria. The actual radiation exposure is always measured, not computed.

So then was it measured on Apollo?

Yes. Each astronaut wore a personal dosimeter. The accumulated dose for each astronaut was regularly reported to Mission Control over the radio.

New evidence has shown that the Van Allen belts are indeed stronger and more dangerous than NASA says. [Bart Sibrel]

Sibrel misinterprets the source article published by CNN. It was reported only that the Van Allen belts were slightly larger in places and slightly denser than previously understood. This is not a new reality, merely a refinement of existing figures. We are still studying the Van Allen belts and must occasionally revise our numerical models. The new findings have implications for the astronauts in the Alpha space station. Since these astronauts will be exposed to the fringes of the Van Allen belts for an extended period, it is prudent now to provide a bit of extra polyethylene shielding to the sleeping quarters. For transitory exposure such as in Apollo missions, the new findings add only a negligible hazard.

Sibrel and others argue that NASA has under-reported the intensity of the Van Allen belts for many years as part of a cover-up. They argue that the real magnitude of the radiation is now being made known, and that it's strong enough to have precluded a successful Apollo mission.

Unfortunately that's a very naive argument. The United States has never been the only spacefaring nation, nor the only nation ever to study the Van Allen belts. Canada provide valuable data to the Apollo project, and the USSR duplicated all the U.S. research, and may even have conducted more. For thirty years the same body of engineering data used to produce the Apollo spacecraft has been used by all nations in designing communication satellites, probes, and other devices intended to operate in and beyond the Van Allen belts. If this data had seriously under-reported the actual radiation present, the spacecraft engineered to those standards would all have failed prematurely due to radiation damage.

This is a very important point since it involves the financial interests (to the tune of billions of dollars!) of countries with no special desire to protect the reputation of the United States. Had this data been seriously wrong, someone surely would have complained by now. Satellites are insured against premature loss, and the insurers want to make sure the spacecraft are engineered to the best possible standards. There is immense worldwide economic incentive to having the best available data on the Van Allen belts, so it's highly improbable the the U.S. has been intentionally providing erroneous data to the entire world for thirty years.

An orbital nuclear detonation in 1962 code-named Starfish Prime created a third Van Allen belt composed of high-energy electrons. This belt was a hundred times more intense than the existing Van Allen belts and was computed to have a half-life of 20 years. [Bennett and Percy, Dark Moon, p. 309]

Fig. 1 - The aurora produced by the Starfish Prime high-altitude nuclear detonation.

The authors give no reference for the claim that this artificial radiation belt was "a hundred times" more "intense" than the naturally-occurring belts. Nor do they define what is meant by "intense". The Starfish Prime test did in fact produce a temporary artificial radiation belt, and it's true that this belt persisted longer than anticipated. But it was not an impediment to the Apollo missions because it had dissipated to a safe level by then, and was very small (and easily avoided) to start with.

Radioactive half-life applies to radioisotopes only. It does not apply to clouds of magnetically-retained charged particles. The authors imply that their theory is confirmed by expert authors, but in fact the author they cite discusses only the general concept of radioactive half-life. Bennett and Percy are responsible for having misapplied it to this problem. Radioactive half-life and particle belts have nothing at all to do with each other. The dispersal of this belt doesn't have anything to do with radioactive decay, and a great deal to do with solar weather and shifting magnetic fields.

The authors argue that such a radiation belt would still be highly intense to this day. However they have shown no evidence that any of the radiation from Starfish Prime is still there. Instead they refer to irrelevant scientific principles and claim it "must" still be there.

A secret study done by the Soviet Union and obtained by the CIA determined that a meter of lead would be required to shield against deep space radiation.

Many conspiracists allude to this alleged report, but none of them can attest to actually having seen it. Since they can argue the alleged report is closely held by the CIA and therefore still top secret, the conspiracists are protected from refutation. No one can prove the non-existence of any document, much less one that is allegedly classified by an intelligence agency. Unfortunately it's more straightforward to note that the conspiracists cannot expect the world to accept an argument based on evidence which they cannot produce. If it's so top secret, how do they know about it?

It's fairly easy to show that such a document likely does not exist. We know that great thicknesses of lead are not required to shield against particle radiation. We know that Soviet science and engineering were excellent. We note with no small amusement and no small suspicion that the conclusion of the alleged report contradicts the commonly accepted principles of physics, and that it instead bears a striking resemblance to the naive assertions of inexpert conspiracy theorists who claim that only thick sheets of lead are suitable for radiation shielding. The alleged report is plausible to the lay reader but utterly unconvincing to the scientist.

The Soviet lunar spacecraft design demonstrates they did not believe a meter or two of lead was required to shield against radiation.

History provides the final proof. Had the Soviets actually believed that great thicknesses of material were required to shield against radiation, they would have questioned the design of the Apollo spacecraft. The spacecraft clearly did not provide a meter of lead shielding, yet NASA claims it successfully traversed the Van Allen belts. Yet the Soviets acknowledged then and continue to acknowledge today that the Apollo program was a clear success.

In recent years the Western world has been able to examine the Soviet spacecraft design which was to have carried cosmonauts to the moon. They did not provide a meter of lead for their spacecraft either.

Soviet cosmonauts have been quoted as saying radiation was a very grave concern.

And NASA officials have been quoted as saying essentially the same thing. Radiation is a very great concern, but there's a vast difference between a "concern" and an insurmountable obstacle. The conspiracist argument relies on the radiation problem being insurmountable, and nothing said by either NASA or cosmonauts conveys the notion that these problems couldn't have been solved.