Help with Radiation

[Vincent McConnell]

Just the other day, I was talking to Jarrah White. We all know his stance on Apollo. Now I'm no expert in radiation by any means of the word, and it was just last week that I even got the idea what MeV and REM was.
Well Jarrah offered the following theories on why the Apollo shielding should have been about 10cm thick. I'm sure there are plenty of people here who know a lot more about radiation than me, so I'd like to tell you guys what the calculations were and I want you to debunk the holy living hell out of me.

Jarrah says the outer belts had an average of 10-100MeV. I told him we could work on the principle that they were 50MeV.
Now, here is what he told me. To find the "aerial density?", we must multiply 50 by .545cm^2.
We have 27.25cm^2.

Now he said we have to divide that by the density of the material itself. Aluminum has a density of 2.7cm^3.
We get about 10.09cm^3 worth of shielding. The LM had paper thin shielding.
Jarrah says this is also without all the "secondary" radiation you'd get from particles bouncing off each other and fragmenting. According to him, with these numbers, the Apollo astronauts should have absorbed 1200REM, when the official log says they absorbed 2REM.

Like I said, I'm no expert, so of course the data means little until I can get a better understanding from the Pro-Apollo side (like me).
By no means, I hope everyone realizes, does this mean I have doubts about Apollo.
Well anyway, I was hoping some of you radiation guys could come and tell me why you don't need 10cm. Thank you!

[PhantomWolf]

Well the most common mistake made by HBs is that he was using the LM's hull as a measure of shielding for passage through the VA Belts. During which flight was the crew in the LM for either passage of the VA belts?


The rest of it is pretty much bunk. I loved the '"secondary" radiation you'd get from particles bouncing off each other and fragmenting' part, that was a real hoot. VA Belt particles are protons and electrons, if they fragment you get quarks. I suppect that he was meaning Bremsstrahlung or 'Braking radiation', however this is more intense the denser and thicker the metal (to a point, after a certain thickness the secondary radiation is shielded against as well.) Thus Aluminium is perfect for avoiding high levels of Bremsstrahlung.

[vq]

Several other board members can probably go into a lot more detail on the problems with the calculation, but basically every step in the formulation you outline is incorrect.

Consider the following:

• What does "an average of 10-100MeV" mean? An average should be a single number, and is only useful if the shape of the distribution is known.
  
• Where does exposure time come in to the calculation? The belts do not have a single line where they suddenly stop; they are a gradient with more dense and energetic particles at the center (which the astronauts did not pass through at all) and less dense particles further out.
  

A successful model of the radiation exposure will need to mathematically integrate both the density and energy of the particles encountered, along the specific path that a given Apollo mission traveled and then consider the mitigating effect of the CM pressure vessel, insulation, etc. There are probably other important factors I am leaving out; this is just a first glance at the method you outlined.

[Vincent McConnell]

Jan 30, 2012 22:36:36 GMT -4 vq said:

Several other board members can probably go into a lot more detail on the problems with the calculation, but basically every step in the formulation you outline is incorrect.

Consider the following:

• What does "an average of 10-100MeV" mean? An average should be a single number, and is only useful if the shape of the distribution is known.
  
• Where does exposure time come in to the calculation? The belts do not have a single line where they suddenly stop; they are a gradient with more dense and energetic particles at the center (which the astronauts did not pass through at all) and less dense particles further out.
  

A successful model of the radiation exposure will need to mathematically integrate both the density and energy of the particles encountered, along the specific path that a given Apollo mission traveled and then consider the mitigating effect of the CM pressure vessel, insulation, etc. There are probably other important factors I am leaving out; this is just a first glance at the method you outlined.

Sorry. Total screw up.. I meant 10-100MeV RANGE

[Bob B.]

I don’t have time to consider the math right now, but here are a few points to ponder:

• There are far more particles at the low end of the energy range than at the high end. The average energy is going to be well below the middle of the range. Furthermore, many of the particles have energies below 1 MeV. Why does Jarrah say 10 MeV is the lower limit?
  
  
• Why does Jarrah believe the shielding of the LM is pertinent to a discussion about the Van Allen Radiation Belts? The astronauts were inside the CM during the passage past the VARB.
  
  
• The spacecraft flew around the density parts of the VARB. The following article illustrates the trajectories:
  
  www.braeunig.us/apollo/apollo11-TLI.htm
  
  
• The CM had a shielding rating of about 7 to 8 g/cm².
  

[vq]

Jan 30, 2012 23:40:12 GMT -4 Vincent McConnell said:

Sorry. Total screw up.. I meant 10-100MeV RANGE

No need to apologize. The vast majority of the particles in the inner belts are actually much less energetic than even the low end of that range. Remember that the distribution of particles across the range of energies is linear, either.

imagine.gsfc.nasa.gov/docs/ask_astro/answers/970228a.html

The link above mentions that a satellite in an orbit that passes through the belts would get 2500 rem of exposure per year. The astronauts passed through the belts in a matter of hours. Remember that satellites designed by parties independent of NASA use these numbers to design their satellite shielding, so the satellite's electronics would fail if NASA were lying about the intensity of the radiation in the belts.

[Vincent McConnell]

Jan 31, 2012 0:42:15 GMT -4 Bob B. said:

I don’t have time to consider the math right now, but here are a few points to ponder:

• There are far more particles at the low end of the energy range than at the high end. The average energy is going to be well below the middle of the range. Furthermore, many of the particles have energies below 1 MeV. Why does Jarrah say 10 MeV is the lower limit?
  
  
• Why does Jarrah believe the shielding of the LM is pertinent to a discussion about the Van Allen Radiation Belts? The astronauts were inside the CM during the passage past the VARB.
  
  
• The spacecraft flew around the density parts of the VARB. The following article illustrates the trajectories:
  
  www.braeunig.us/apollo/apollo11-TLI.htm
  
  
• The CM had a shielding rating of about 7 to 8 g/cm².
  

I noticed on your page that you said the Apollo 11 orbital altitude was 180KM. Do you know what their Perigee and Apogee was? I play a game in which I get to build, launch and maneuver rockets and I'd like to replicate the Apollo 11 orbit. Thanks.

[Count Zero]

Vincent - Here is the Earth orbital parameters for all of the Apollo missions.

It comes from a wonderful resource called Apollo by Numbers

Enjoy!

P.S. What's the game?

[Vincent McConnell]

Jan 31, 2012 1:37:44 GMT -4 Count Zero said:

Vincent - Here is the Earth orbital parameters for all of the Apollo missions.

It comes from a wonderful resource called Apollo by Numbers

Enjoy!

P.S. What's the game?

Well that was a great load of help! Thank you!
It's called "Kerbal Space Program" and it's a load of fun. It has taught me a lot about Orbital Mechanics.

[ka9q]

The Apollo parking orbits were all quite low to maximize efficiency. It would have been even more efficient to launch directly into a lunar trajectory, but the launch windows would have been extremely limited. So much so that they wouldn't have made it to the moon by the end of the decade. So early on in the planning for Apollo a parking orbit was chosen that would let them choose the time and place of the TLI burn somewhat separately from the launch time. This in turn was a major driver in the design of the Saturn V's S-IVB stage that had to burn once for earth orbit injection and then restart a few hours later for TLI. Making a large rocket engine restartable when it burns non-hypergolic fuels and uses a turbopump to get them into the engine is decidedly non-trivial.

The J-class Apollo missions (15-17) used even lower parking orbits - less than 100 nautical miles - to increase the Saturn V's throw weight to the moon. These would have been very short lived orbits had they stayed in them more than 1-2 orbits before TLI.

[ka9q]

Jan 31, 2012 1:37:44 GMT -4 Count Zero said:

Vincent - Here is the Earth orbital parameters for all of the Apollo missions.

Yes, note how all the lunar missions before Apollo 15 used 100 nautical mile parking orbits, while Apollos 15-17 used 90 nautical mile orbits.

BTW, I've never particularly liked the practice of describing orbits by their apogees and perigees because of the ambiguities associated with the earth not being quite spherical. Are the altitudes given with respect to an elliptical earth or a spherical one? And if it's elliptical, do the figures actually reflect the closest and furthest distances to the earth's surface, or are they the distances to the surface when the satellite reaches geometric perigee and apogee, i.e., closest and furthest approach to the center of the earth?

It's much more precise to describe an orbit by either its classical Keplerian orbital elements (with eccentricity plus either mean motion or semi-major axis describing the size and shape of the orbit in space) or by its state vector, a 3-dimensional position vector plus a 3-dimensional velocity vector.

[Glom]

180km? Didn't Freedom 7 get high than that?

You have got to love Jarrah's calculations here. It's not even dimensionally correct.

[Daggerstab]

Jan 31, 2012 1:39:40 GMT -4 Vincent McConnell said:

Jan 31, 2012 1:37:44 GMT -4 Count Zero said:

P.S. What's the game?

Well that was a great load of help! Thank you!
It's called "Kerbal Space Program" and it's a load of fun. It has taught me a lot about Orbital Mechanics.

Ah, another KSP fan.

An early version of the game is available for free download as a demo version. It looks like a sillier, more user-friendly version of Orbiter (Orbiter doesn't have green-skinned bug-eyed astronauts). I recommend at least trying the demo.
kerbalspaceprogram.com/

Here's a video demonstrating a flight to the Mun:
www.youtube.com/watch?v=bGd_BFu9e10

And yes, it works as a nice introduction/demonstration of orbital mechanics. I laughed the first time I thought "Now I'm going to reach apogee and execute a circularization burn" and it worked.

[Bob B.]

Jan 31, 2012 2:15:13 GMT -4 ka9q said:

Are the altitudes given with respect to an elliptical earth or a spherical one? And if it's elliptical, do the figures actually reflect the closest and furthest distances to the earth's surface, or are they the distances to the surface when the satellite reaches geometric perigee and apogee, i.e., closest and furthest approach to the center of the earth?

That's a question that took me quite a bit of digging to come up with an answer. I eventually got a response from a NASA flight controller who went and talked to the flight dynamics guys for me. He tells me that the altitudes are measured from a spherical datum. In the case of NASA, the datum is 3443.9307 nautical miles, i.e. Earth's equatorial radius. So if a spacecraft's radius vector at perigee is 3567.2859 nautical miles, they report the altitude as 3567.2859 - 3443.9307 = 123.3552 n.mi. regardless of how high it really is above the ground.

I also know another guy who is an expert on the Russian space program, and I seem to recall him telling me that the Russians do the same thing, but they use Earth's mean radius as their datum rather than the equatorial radius. That was from a conversation on another forum; I doubt I could ever find it again to verify.

[Bob B.]

Jan 31, 2012 3:12:27 GMT -4 Glom said:

180km? Didn't Freedom 7 get high than that?

Yes, Mercury-Redstone 3 reached an apogee of 187.5 km.

You have got to love Jarrah's calculations here. It's not even dimensionally correct.

It was hard not to notice that. Bit of advice Vincent... always check units. If the units aren't dimensionally correct then you know there is a screw up somewhere. First off, density is g/cm³. Second, if we divide cm² by g/cm³, we get

cm² / (g/cm³)

= cm² X cm³/g

= cm⁵/g

Also, what does "10.09 cm³ worth of shielding" mean? Isn't Jarrah trying to calculate a thickness? The units in the problem are so screwed up that I really can't comment further on his math because I don't understand what he is trying to do.

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