Question about Apollo 13 explosion

[Messierhunter]

I'm trying to come up with an educated guess as to the direction and speed that Apollo 13's missing service module panel left the spacecraft. I guess this could be said to fall under the category of "space physics," so does anyone know where I could find the exact attitude and orientation of the Apollo 13 CS/LM stack at the moment of the explosion, as well as the amount of acceleration recorded by the X,Y,Z accelerometers during the explosion?

 

[SpaceNut]

My guess would be no, the explosion wasn't a planned event, and I'm pretty sure they were into the 'BBQ roll', so it's most likely an unknown as to the exact orientation at the time of the explosion. Makes one wonder though the fate of that panel, doesn't it.

 

[Ghostrider]

The delta-V imparted by the explosion itself is another unknown variable, because we don't know how much energy was imparted on the panel, not enough to alter its trajectory however.

 

[Saturn V]

The direction was "OUT" and the speed was "FAST."

 

[garyw]

which means the panel would have gone around the moon and as Apollo 13 wasn't in a free return trajectory it would have gone.... somewhere.

 

[Messierhunter]

The delta-V imparted by the explosion itself is another unknown variable, because we don't know how much energy was imparted on the panel, not enough to alter its trajectory however.

The exact value may be unknown, but I already know there are some upper and lower limits we can assume based on what we do know; the bay 4 panel that blew off required at least 24 psi to be blown off, and if the amount of acceleration the rest of the spacecraft experienced were known, we could reasonably assume that the force applied to the panel in the opposite direction could not be much greater than the force applied to the CSM/LM. That would give us an upper and lower bound, and simulations of the panel's orbit could be run with a variety of delta-V's within those bounds. I just found this document, in which NASA simulated the panel separation event with models, and found a non-uniform pressure of 40 psi most closely resembled the actual flight event.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710003551_1971003551.pdf

 

[Ark]

A hundred years from now, someone's gonna be drifting along on their interplanetary trajectory and get *****slapped by a scorched chunk of aluminum with the Stars and Stripes on it.

 

[Andy44]

which means the panel would have gone around the moon and as Apollo 13 wasn't in a free return trajectory it would have gone.... somewhere.

Apollo 13 was in the hybrid orbit at the time of the accident, which takes you around behind the moon at a low altitude but is not a true free return. The panel likely went into a high orbit around Earth. May still be there.

 

[Messierhunter]

Apollo 13 was in the hybrid orbit at the time of the accident, which takes you around behind the moon at a low altitude but is not a true free return. The panel likely went into a high orbit around Earth. May still be there.

I agree, and in fact I hope it is. Had it followed the Apollo 13 trajectory according to AMSO and a relatively recent news story, it would slam into the earth's atmosphere over the atlantic almost perpendicularly on the third orbit (the article and the orbiter simulation agreed pretty well considering that AMSO's scenario didn't account for any delta-V due to the explosion as far as I'm aware). Just for fun I tested to see what would happen if you added some delta-V with a short burn in the direction the bay 4 panel is facing at the start of the AMSO A13 scenario just before the explosion. The result was that the new trajectory continually orbited the earth with regular perturbtions by the moon. It didn't seem to result in any collisions until at least 1971, but I didn't run the simulation any longer than that. What it showed me was that if propelled in certain directions, it's entirely possible that the Apollo 13 panel could indeed still be out there in high earth orbit. Since it's quite small it would be hard to spot just about anywhere along the orbit until it gets near periapsis (my quick and dirty test resulted in a periapsis that varied between 40,000km and about 100,000km), so it could easily remain undiscovered for 40 years. Even if it did re-enter the atmosphere a long time ago it would still be nice to know that that was its most likely fate based on knowing the rough trajectory it took.

---------- Post added at 10:03 PM ---------- Previous post was at 09:39 PM ----------

Quick update, something struck me and it wasn't the missing panel. In the movie Apollo 13 I remember them instructing Swigert to assume a certain attitude and "null your rates" which I believe would mean that they were NOT in the barbecue roll at the moment of the explosion. That's just the movie though and we all know it's far from reliable when it comes to those technical details. Looking through the actual mission transcript online I see that on page 166 of the pdf they do tell Swigert to "roll right to 060 and null your rates for photography of Comet Bennett."
http://www.jsc.nasa.gov/history/mission_trans/AS13_TEC.PDF
At 02 07 50 12 Swigert states he's "going to maneuver to 060, 090, and 0." This looks like the key to me, 060 must be the roll angle, so is 090 pitch and 0 yaw or the other way around? The explosion occurs only 5 minutes later as they're taking care of the other house keeping measures, so I think it's safe to assume they have not resumed the barbeque roll by then. If that's true, it should be easy to figure out at least what direction the bay 4 panel was facing at the moment of the explosion. Does anyone know what the standard protocol was for reporting those attitude numbers? If I can find that out I can at least come up with some reasonable numbers for delta-V using the previously posted report as a guide. I figure I'll sim a range of possible delta-Vs out to the present, translate them all to TLE's, and fish around in those areas one by one to see if I can find anything. I can easily knock out a couple dozen possible TLE's and their surrounding areas each night with clear weather when the missing panel should be close to earth. Even if the TLE is off by several minutes I can follow each possible track forwards and backwards by that amount to see if anything is there.

One more update, according to Apollo 11's transcript, it looks like the standard attitude for the barbecue roll would be pitch 090, yaw 0, so I suspect Swigert was saying he was rolling to 60 degrees with a pitch of 090 and a yaw of 0. I'll have to do some more research to find out how to match those angles in orbiter, something I should probably already know how to do .

 

[Andy44]

Just a thought, I don't think TLEs are very good for describing orbits like the Apollo hybrid. I would look for a plain old state vector.

 

[Messierhunter]

Just a thought, I don't think TLEs are very good for describing orbits like the Apollo hybrid. I would look for a plain old state vector.

That's why I would use orbiter to simulate it out to present day in state vectors before translating to tle which is what my telescope requires to track a satellite. I'd only translate from state vectors at the last moment and use the tle's to track it while it's close to earth and the orbit mimics a regular earth orbit. Does that make sense or am I missing a huge obstacle?

 

[tblaxland]

I suspect Swigert was saying he was rolling to 60 degrees with a pitch of 090 and a yaw of 0. I'll have to do some more research to find out how to match those angles in orbiter, something I should probably already know how to do .

I agree. From my readings of the Apollo Flight Journals, roll, pitch then yaw, was the standard convention for communicating attitudes (except to note that the angles were actually Tait-Bryan rotations composed in the order pitch-yaw-roll, or Euler angles composed roll-yaw-pitch, as evidenced by the scales on the FDAI).

As for converting that into Orbiter, you first need to know what the REFSMMAT orientation was at the time.

 

[Andy44]

Well, for one thing, Orbiter's propagator, while mathematically very good, is missing many perturbations. Earth oblateness, for example, is not modeled. Nor are the lunar mascons, which would affact the panel as it swings by the moon.

Worst of all, you really have no idea, with any accuracy, what the panel's velocity was at the time of the explosion. You have only a WAG. And that large error will have grown up over nearly 4 decades such that finding it with a telescope would be a nearly miraculous event.

 

[tblaxland]

As for converting that into Orbiter, you first need to know what the REFSMMAT orientation was at the time.

On reflection, it was most likely the PTC REFSMMAT, described here: http://history.nasa.gov/ap15fj/04troubleshoot_ptc.htm#ptcref

Earth oblateness, for example, is not modeled.

Au contraire - that is what the "non-spherical gravity" option is all about. Oblateness is modelled quite well, with non-spherical components as a function of latitude modelled down to the J6 co-efficient. Gravity field non-uniformity as a function of longitude is not modelled however, but its effects are much smaller than the latitudinal variations.

Nor are the lunar mascons, which would affact the panel as it swings by the moon.

That would be a bigger effect. EDIT: Apollo 13's trajectory would have had an ascending node that took it away from the largest mascons (those associated with the major mare). IIRC, the mascons had much less effect on the lunar parking orbit of Apollo 14 than on 15 & 17. Also, because the panel would have been on a hyperbolic trajectory, the only time that it would have been close enough for the mascons to have had a major effect would have been over the farside, where the mascons are significantly smaller:

Worst of all, you really have no idea, with any accuracy, what the panel's velocity was at the time of the explosion. You have only a WAG. And that large error will have grown up over nearly 4 decades such that finding it with a telescope would be a nearly miraculous event.

To be fair, TN-D6087 makes it a little better than a WAG, if only marginally. In any case, I wish him the best of luck.

 

[Andy44]

Au contraire - that is what the "non-spherical gravity" option is all about. Oblateness is modelled quite well, with non-spherical components as a function of latitude modelled down to the J6 co-efficient. Gravity field non-uniformity as a function of longitude is not modelled however, but its effects are much smaller than the latitudinal variations.

In my textbooks "oblateness" is all about longitudinal variations, and they are indeed very important. If not for them, satellites in GEO would never have to burn any prop.

 

[tblaxland]

In my textbooks "oblateness" is all about longitudinal variations, and they are indeed very important. If not for them, satellites in GEO would never have to burn any prop.

Oblateness as I understand it: http://en.wikipedia.org/wiki/Oblate_spheroid

I agree that longitudinal variations are significant for a GEO sat and if they didn't correct for it we would have all our comms sats sitting over the Pacific and Indian oceans. Over the course of a typical Apollo mission they would be still be insignificant but I guess they wouldn't be if you wanted to propagate forward 40 years.

What about solar radiation pressure? Exospheric drag could also be important, depending on the movement of the perigee.

 

[Ghostrider]

The exact value may be unknown, but I already know there are some upper and lower limits we can assume based on what we do know

Silly me - I should have thought of that. The pressure minimum at least. Now that I think of it, telemetry should have recorded the CSM/LM stack shift following the explosion.

 

[Andy44]

Silly me - I should have thought of that. The pressure minimum at least. Now that I think of it, telemetry should have recorded the CSM/LM stack shift following the explosion.

Yes, if you can get a hold of the state vectors before and after the accident and propagate them forward and backwards to the time of the blast you can back out the delta-V.

But it still doesn't tell you which way the panel blew off, since most of the impulse would probably be from the expanding cloud of O2 blasting away from the SM. The panel probably ripped off on one edge first and then the others a split second later, tumbling away at an angle to the venting gas.

Too many variables. Unless the USAF has spotted it on radar since then, and were able to identify what they were seeing, it's like finding a needle in a haystack.

 

[Messierhunter]

But it still doesn't tell you which way the panel blew off, since most of the impulse would probably be from the expanding cloud of O2 blasting away from the SM. The panel probably ripped off on one edge first and then the others a split second later, tumbling away at an angle to the venting gas.

Actually we know the pressure was non-uniform centered over the O2 shelf behind the panel and we even have a good idea of what that distribution looked like. We also know from the damage to the high gain antenna (taking out the feed horn I think without ripping the whole thing off completely) a good idea of the angle it departed the spacecraft, which agrees with the above since the O2 shelf is closer to the CM than the high gain. The expanding cloud of gas would probably have less of an effect after that point I would think.

---------- Post added at 09:21 AM ---------- Previous post was at 07:37 AM ----------

What about solar radiation pressure? Exospheric drag could also be important, depending on the movement of the perigee.

That is something that has been bugging me in the back of my mind. Of course, if I discover that the trajectory isn't altered enough by the explosion and the panel still burns up in the atmosphere, solar radiation pressure doesn't matter one bit. If, however, I find that the panel should still be in orbit, I'm wondering if I could simulate the effect of radiation pressure by creating the panel as a custom spacecraft3 vessel and attaching a tiny thruster with a force equal to the expected radiation pressure (which requires making some assumptions about the sun-facing surface area given a rotating panel) with ridiculously high ISP (to prevent any significant mass loss) to simulate it. Of course that would require keeping it aligned to the sun at all times, and I don't know if there are any easy ways to do that aside from writing a custom autopilot. Perhaps it would be easier to use a proper orbit propagator (like a 30 day trial of this perhaps? https://www.stk.com/resources/help/stk613/helpSystem/stk/vehSat_orbitProp_LOP.htm) that accounts for all these things once I have the state vectors of the panel just after the explosion. The nice thing about orbiter is that it's free, but a proper program designed to do this kind of thing would probably make it easier to set up a batch of possibilities covering a range of possible delta-Vs and average cross-sectional areas (for solar radiation pressure and drag) and then just knock them out one by one as the orbits bring each possible panel location close to earth. How accurate are AMSO's in-flight scenarios with regards to the historical trajectories?

 

[tblaxland]

The nice thing about orbiter is that it's free, but a proper program designed to do this kind of thing would probably make it easier to set up a batch of possibilities covering a range of possible delta-Vs and average cross-sectional areas (for solar radiation pressure and drag) and then just knock them out one by one as the orbits bring each possible panel location close to earth. How accurate are AMSO's in-flight scenarios with regards to the historical trajectories?

You might want to consider GMAT. Its propagator objects look like they will model Earth's gravity non-uniformities better, it can model solar radiation pressure and can use the Jacchia-Roberts model for the upper atmosphere.

Regarding AMSO's accuracy, the Moon's position in Orbiter is accurate to within very small amounts so I expect that the trajectory would need to be suitably close to the real thing. This document might also be useful to check it: Apollo 13 Trajectory Reconstruction via State Transition Matrices