Radiation Analysis for Moon and Mars Missions

This paper provides an overview of the radiation aspects of manned space flight to Moon and Mars. The expected ionising radiation dose for an astronaut is assessed along the Apollo 11 flight path to the Moon. With the two dose values, the expected and the measured total dose, the radiation shielding and the activity of the Sun are estimated. To judge the risk or safety margin the radiation effects on humans are opposed. By only changing the flight duration an assessment for the total dose of a journey to Mars is provided.


I. INTRODUCTION
Electronics which is used in space has to be specifically robust so that it sustains the radiation environment. Often it is packed in a metallic housing to achieve the necessary radiation shielding. Humans are much more susceptible to ionising radiation than electronics.
The flight path to the Moon or to Mars crosses the Van Allen radiation belt, a zone with free protons and electrons which demand a high shielding. After this belt the space craft is directly exposed to the solar radiation because there is no protection of the Earth magnetic field any more. Nevertheless the absorbed radiation dose of an Apollo 11 astronaut was only 0.18 rad or 1.8 mGy (Milli-Gray). This is the minimum dose of the Apollo flights; the maximum is 1.14 rad (Apollo 14) [1].
According to NASA [14] "Radiation was not an operational problem during the Apollo Program".

II. RADIATION DATA
The 0.18 rad of Apollo 11 correspond to 1.8 mGy or (optimistically) to 1.8 mSv (Milli-Sievert). Sievert indicates biological effects; depending on the kind of radiation and tissue there is a weighting factor of > 1 to be considered for the conversion from Gray to Sievert. If Grays are 1:1 converted to Sievert then in general there results a too low dose value in Sievert. Here I use the 1:1 conversion.
As a comparison the annual terrestrial dose level is according to [3] for the year 1999 4.5 mSv, other sources show 2.5 -4.5 mSv/year. This means, the 1.8 mSv are a small additional exposure.
Another example would be an astronaut in a space craft orbiting the Earth 1'000 km above the equator. If the space craft were protected with 4 mm aluminium shielding then he would be exposed to a dose rate of 2.7 mSv/h [4]. This would be about one natural annual dose per hour. The explanation for this high level is the Van Allen radiation belt which encircles the Earth: at a few hundred kilometres altitude the radiation rapidly grows. At 1'000 km above the equator it isas shown beforequite high and it increases further. At 3'000 km above the equator the dose rate is 465 mSv/h (always with 4 mm aluminium shielding), and only after 40'000 km the dose rate falls below the value of 1'000 km altitude.
To fly to the Moon and back or to Mars one does not have to cross the Van Allen radiation belt through its centre, but it generally takes more than one hour to cross it. The following two figures show the situation in the Van Allen radiation belt more in detail: first a diagram with level curves, which indicate the number of high energy particles, then the total annual dose as a function of the altitude above the equator: Re means Radius of the Earth (6370km); from [5] The scaling on the left is linear, on the right logarithmic. The data is identical.  The dose levels of Fig. 3 refer to equatorial orbits. The equatorial plane is inclined with respect to the symmetry plane of the Van Allen radiation belt (i.e. the plane perpendicular to the magnetic axis, see Fig. 1 or Fig. 4), so that equatorial orbits are not always in the area of the maximum radiation. This means that in the centre of the Van Allen radiation belt there are even higher dose rates than shown in the above Fig. 3.
With the annual doses one can determine the total dose of a mission only then exactly if the radiation over the year is constant. In the Van Allen radiation belt there is a constant (base) radiation of the free electrons and protons which are always there. Outside of the belt there is variable proton radiation from the Sun. Further radiation is neglected here.
On the way to the Moon, which is investigated first, the ionising radiation depends mainly on the activity of the Sun. If the Sun is not active the radiation is almost zero. At an eruption or flare, according to [12] up to 10 Sv can occur per event, what "in fact should be deadly".
Since the radiation beyond the Van Allen radiation belt (VAB) up to the Moon remains constant, an astronaut flying to the Moon is exposed to this radiation over a long time.
Averaged over the year 1969 the total radiation dose beyond the Van Allen radiation belt was significant, as the following table shows 1 : 1 Determined from the solar parts of Fig. 3   The values from TABLE I. exceed the dose of the Apollo 11 mission (1.8 mGy) by fareven for a high shielding. They show the serious risk, i.e. what could happen if the Sun were active as usual. By the way, even today a solar eruption cannot be predicted, not even one day in advance.
But these average values may yield wrong values for short missions. According to SPENVIS [4] the radiation dose from the Sun originated in the year 1969 mainly from a short active phase: "Cycle 20 had one anomalously large event that accounted for most of the accumulated fluence." (Cycle 20: 1966(Cycle 20: -1972 Because of the unique event in the solar cycle of 1966-1972 one could assume that during the Apollo 11 mission only little or even no (proton) radiation was radiated from the Sun. For this reason a totally radiation-inactive Sun is assumed in the following and only the base VAB radiation, which is always present, is considered, i.e. the yellow curve in Fig. 3.

III. ESTIMATION OF THE RADIATION DOSE ACCORDING TO AN IDEALISED STRAIGHT FLIGHT PATH
In this chapter I describe a heuristic approach to estimate the dose level assuming a straight trajectory with an average speed. The trajectory is in the ecliptic, i.e. in the plane of the Earth orbit around the Sun. I will refine this approach in the next chapter.
To determine the radiation dose of the Apollo 11 mission, I always take the smallest value for the total dose per investigated area. So at the end the result is a lower limit of the total dose. A reason for this is the total dose value of 1.8 mGy which looks small. Therefore I check whether under favourable circumstances such a low level can be obtained.
The approach is as follows: 1. The Van Allen radiation belt shall be crossed at its border. I assume a maximum crossing angle of 35°: • The Earth axis is 23.5° inclined relative to the ecliptic.
• The magnetic pole was in 1969 11.5° displaced relative to the geographical North Pole ( [9], see also Fig. 1) Therefore the Van Allen radiation belt may have had a maximum inclination of 35° with respect to the ecliptic.
2. In the radiation determination program [4] all switches are now set to "Minimum" to achieve as small as possible total dose levels. In particular I tuned the program so that there is no contribution from the Sun at all. For this I selected the solar minimum year 1996 instead of 1969! "No contribution from the Sun" can be correct for a certain period of time and in a year of a solar minimum this is the normal case. But for the solar maximum year 1969 [4] this assumption is very optimistic, even if in that year the solar activity was smaller compared to earlier solar maximum years and if the main part of the total dose in that cycle came from one single eventwhat, by the way, was not known in 1969.
Summarised only the part of the radiation in the Van Allen radiation belt is considered which is always present, i.e. the radiation of the "trapped" free protons and electrons.
3. The total dose of Fig. 3 is calculated for equatorial orbits, it therefore corresponds to a mean value in a cone of 35° (in Fig. 5). In the centre of the Van Allen radiation belt the total dose value is higher. All the same I take the too low mean value for the central value and remain on the conservative side.

The radiation dose is initially calculated in rad or
Gray. I make a 1:1 conversion from Gray to Sievert, i.e. there results a too low dose value in Sievert. For the comparison with the mission value this has no impact, because the mission value is given in rad (1 rad = 10mGy). Sievert is used for biological effects. Fig. 4 shows the constellation of the magnetic axis with the maximum inclination of the Van Allen radiation belt with respect to the ecliptic. The ecliptic is shown in red. The green ellipse shows the short path through the VAB.
The angle between the blue line, which is perpendicular to the magnetic axis, and the red line, the ecliptic, is 35° as described above. The lunar orbit is inclined 5° with respect to the ecliptic, but the Moon was at the arrival of the Apollo 11 quite exactly in the ecliptic [10] so that the flight path is also about in the ecliptic. These 5° may therefore not be added to further shorten the flight path through the VAB in the case of Apollo 11. Apollo 11 could have penetrated the Van Allen radiation belt in the best case under an angle of about 35° to get a minimum radiation dose. The following figures show the situation for protons and electrons separately. The path length in the zone with more than 1E+05 high energy electrons (yellow marked) is 3.1Re  20'000km.
40% of the yellow part are in the zone with more than 1E+06 high energy electrons/(cm 2 s).
The flight path is tangential to the proton belt and avoids the zone with the maximum radiation. In the electron belt it still avoids the centre, but it crosses a zone with rather high energy electrons. Fig. 6 shows that the exit path in the electron belt is in an area where already small changes (upwards or downwards) have a large effect.
If therefore the Apollo 11 flight path were located slightly above the shown line then the dose calculation along the red path would yield a too high dose. For this reason I present in the next chapter a total dose calculation with the flight path as it is described in the Mission Report [11]. The integration of the dose rate over the flight path is made there (and not here).

IV. ESTIMATION OF THE RADIATION DOSE ACCORDING TO THE APOLLO 11 FLIGHT PATH
The basic assumptions for the total dose calculation are unchanged with respect to the previous chapter. Also here a value is calculated which could have been achieved under the most favourable radiation conditions. The small blue circles are points which have been used to draw the trajectory in Fig. 7 and Fig. 8. These circles are often entry or exit points of radiation zones (see TABLE II. below). Comparing these two figures with the ones in the previous chapter one recognises that the flight path obviously crosses the Van Allen radiation belt quite exactly at its maximum inclination. The trajectory is slightly above the ecliptic and circumvents the central region even better.
Also the return path is more favourable. Here the fact helps that the Moon was at the time of the departure from the Moon already 2° below the ecliptic.
With this data and the knowledge of the exact time between the different points of the trajectory the total radiation dose can be determined.
The total dose is calculated analogously to the level curves of the high energy protons and electrons, i.e. the maximum dose in the centre of the two belts is reduced according to the level curves. This procedure is justified on the one hand that the total dose is proportional to the number of the (high energy) particles, on the other hand in Fig. 3 (annual dose) the total dose decreases along the x-axis in the same extent as the level curves in Fig. 2, e.g. about a factor of 3 from 5Re to 6Re.
The calculation of the total dose is demonstrated for a shielding of 4 mm aluminium. The maximum intensities are according to Fig. 3: for the proton belt this is 4.110 5 rad/year or 465 mSv/h and for the electron belt 3.110 5 rad/year or 355 mSv/h. TABLE II. shows the determination of the total radiation dose. I counted only the permanent available radiation in the Van Allen radiation belt, i.e. no solar radiation.
For the intensity the lowest value of the respective zone is used. From the maximum of all zones (310 5 for protons and 310 6 for electrons) to the next lower zone (the lower end is a power of 10) the maximum value is reduced by a factor of 3, then for every lower zone by another factor of 10.  The total dose depends on the shielding thickness (and material). From the total dose calculation [4] there result also dose values for further shield thickness'. Quantitative information about the radiation shielding of the Command Module CM is not known to me. Such shielding is not necessary for flights in Low Earth Orbits up to 500 km, but for flights higher than 1'000 km altitude it is crucial.
Assessment of the radiation shielding of the CM: The inner structure of the CM consists of an aluminium honeycomb sandwich bonded between sheet aluminium alloy. The outer structure, the heat shield, is made of steel honeycombs. [16] & [17] With this construction technique one can get a high stability with little material.
Areas with low radiation shielding excessively reduce the total shielding. In summary the above required 7 mm shielding may look about realistic. The above data show the span of the possible radiation. Solar flares can produce even stronger radiation rates than the above values which are based on one year average. Further radiation sources as galactic or cosmic heavy ions have not been considered. All this makes a manned flight above the Van Allen radiation belt to a not calculable risk.
Electronics has generally a design margin of 2, i.e. it is tested to twice the expected radiation dose. I would expect a margin greater than 2 for manned space flight.
The above radiation levels are small for electronics. Even commercial electronics starts to degrade only after 1..10 krad. Humans are more susceptible, as shown in the next chapter.
The risk for electronics components is no principal problem. A 90% probability for a success is OK for a robotic mission with a pioneer character. But I doubt whether this would be OK for a manned mission as well.
As soon as a space craft is on the way to Moon or Mars there is no possibility to return. On the surface of the Moon the astronauts can plan extravehicular activities depending on the space weather. But if a strong solar flare event occurs in the direction of the space craft then the crew is lost. 2 This value is based on the default model for solar protons (ESP). Another model, the King model, predicts 95 mSv.

VI. EFFECTS OF RADIATION
The impact of radiation is shown in the following table [6]: The natural annual dose is 2.5 -4.5 mSv.
The optimistically determined mission dose of the previous chapter is according to the above table well in the save area.
The maximum operational dose limit for each of the Apollo missions was according to [14] "set at 400 rad to skin and 50 rad to the blood-forming organs… In the heavy, well shielded Command Module, even during one of the largest solar-particle event series … the crewmen would have received a dose of 360 rad to their skin and 35 rad to their bloodforming organs (bones and spleen).
This estimation of the received radiation dose fits perfectly to the maximum dose values, but it is in contradiction to the physical effect of radiation and shielding: the radiation which passes the cover of the CM is a penetrating radiation 3 . The additional shielding effect of the skin is then negligible, so that all organs receive the same dose. All reported points almost exactly correspond with the simulation. The used curves can therefore be regarded as perfect for this consideration.
For the numerical simulation the following differential equation is integrated.
r is the vector from the centre of the Earth to the space craft;  is the gravitational constant (6.67410 -11 m 3 /(kgs 2 )); M is the mass of the Earth (5.97610 24 kg) and ̈ is the 2 nd time derivative of r, i.e. the acceleration vector.
The reference system is Earth fixed (not rotating with the Earth, i.e. inertial): the origin is in the centre of the Earth, the x-axis in the direction of the vernal equinox, the z-axis = Earth axis in the direction of the North Pole and the y-axis results from the right-handed system.
The position of the Earth axis relative to the Moon and the position of the Earth on its orbit are shown in Fig. 10:   Fig. 10 shows the constellation at TLI (Translunar Injection), i.e. after the acceleration phase behind the Earth: from this point in time the flight goes "in free fall" in direction Moon. The direction of the Moon corresponds already to the one of the arrival in the lunar orbit of Apollo 11, at 174° [10] & [11] (ecliptic) longitude (from vernal equinox ).
The Sun is shown in yellow in the middle of Fig. 10. On the left there is once again the Earth on March 21, i.e. at equinox. The inclination of the equator is indicated as well.
The geomagnetic pole was 1969 at (78.5°N, 70°W) [9]. Its direction from the North Pole is indicated.
TLI was behind the Earth, seen from the Moon: (10°N,  165°W) [11]. The direction is also indicated.
For a better imagination of the trajectory one can take the logo of the Apollo Flight Journal [13]. I have complemented it with directional arrows in Fig. 9.
The main results of the trajectory calculation have already been worked into chapter III, specifically in Fig. 7 and Fig. 8.

Moon 174°
For a better understanding of the flight path I present several additional curves to you: first the flight path, as it already has been shown in Fig. 7 and Fig. 8. The points which have been used for the dose calculation in the electron belt and which are marked with blue circles in Fig. 8 are also here indicated with blue circles Now there follow two figures in the equatorial and in the ecliptic reference system. The latter corresponds probably the best with our imagination: the Moon was at the approach about in the ecliptic, at the departure it was 2° below the ecliptic.   The radiation level on a flight to the Moon or Mars can vary from moderate over significant to deadly.
Moderate radiation levels can be expected when the Sun is almost calm. Then one may overcome a flight to the Moon and back with a moderate shielding without radiation damage. The shielding is only compulsory in the Van Allen radiation belt.
The flight path of Apollo 11 avoids the centre of the Van Allen radiation belt in an elegant way. It's a pity that this skilful trajectory has not been highlighted by NASA. For an even better avoidance one would have to fly first a polar parking orbit and then to turn off in direction Moonor Mars. But this would cost much more energy.
If the Sun suddenly got active, what cannot be predicted, also not for a short time span [lectures of solar researchers] & [14], one would rapidly be covered with a health affecting dose.
This substantial risk is confirmed by the following two statements of ESA [7] "In the near-term, manned activities are limited to low altitude, and mainly low-inclination missions." and [8] "During the Apollo missions of the 1960s-70s, the astronauts were simply lucky not to have been in space during a major solar eruption that would have flooded their spacecraft with deadly radiation". With other words the radiation risk of a manned lunar mission or beyond is regarded as not controllable.
The radiation, specifically the massive rise from 500 to 1000 km altitude [ Fig. 3], is also a main reason why the International Space Station ISS remains between 300 and 400 km altitude.