Sunday, February 27, 2022

More on Orion

Based on an initial simulation it seems that the Apollo 16 Lunar Module Orion, abandoned in lunar orbit in 1972, smashed into the surface of the Moon about 5 weeks later. Would it be possible to locate the impact crater? Let’s get the best estimate we can for the initial orbit, run a randomized series of simulations, to try to narrow the search.

In previous investigations I have relied on the Mission Reports to provide the initial orbit state. For Apollo 16, the record is much richer. In particular, there are orbital state vectors (i.e., position and velocity information) for each of the hundreds of photographs taken by the “Metric Camera” experiment, which was in the science bay of the Command Module. In particular, this file has all the state information for every photo taken during the mission. 

A subset of these is of special interest…those from the “Rev 60” and “Rev 63” mapping passes. This refers to the fact that the photos were all taken during the 60th or 63rd revolution of the Apollo 16 CSM around the Moon. By this time John Young and Charlie Duke had returned from the lunar surface, and rendezvous and docking took place during Rev 53.  The LM was jettisoned during Rev 62, so the Rev 60 and 63 mapping passes bracket the last known position of Orion.

I grabbed a set of the Rev 60 data points and adjusted a simulation so that I fit them as closely as I could. Though trial and error I found that I could match them to within +/- 20 meters of altitude. Based on the documentation, this original state vector data was fitted in 1972 to a solution for the orbit that was generated using the best gravity model and ephemeris available at that time. I’m using a better gravity model and a modern ephemeris, so I’m not surprised that I don’t match up exactly. A residual error of +/- 20 meters seems pretty good.

Then I did the same thing for Rev 63 data points to get another estimate of the CSM orbit after the LM was jettisoned. With these estimates for the orbit, I can propagate to the moment of jettison and compare to the values published in the Mission report. (The simulator can run “backwards”, so it can reverse propagate from Rev 63 just as easily as it propagates forward from Rev 60.) The results are shown in Figure 1.

Figure 1: Comparing Orion's initial state, from 3 different sources.

Not bad! The positions are all within 0.5 km of each other, and the velocities match up well. The velocity difference when working backwards from Rev 63 is slower than the others, which is expected…it accounts for the ~2 ft/sec separation maneuver performed after Orion was jettisoned. 

The next step is to compensate the horizontal flight path angle, i.e., the HFPA. Orion was jettisoned “upwards”, away from the Moon, at about 2 f.p.s. and so this slightly increases the angle that it is moving relative to the local horizontal direction. It works out to be about 0.021 degrees, so adding this to the HFPA gives 0.42 degrees.

Now we can generate random sets of initial conditions that are similar to these and see where the impacts occur. I adopted the "Rev 60" state as the “nominal” case, and then varied randomly around those values. I generated a total of 350 randomized parameter sets and ran them all. Each run takes about 8 minutes to simulate, and I have a python script that automatically runs then one after another, so the whole batch completes in about 2 days. Each run produces a ground track file, and I post-process all of these as a batch to extract the impact locations.

What are the results? All 350 simulated impacts occurred between May 28th, and June 2nd of 1972. That's a fairly tight cluster. Looking deeper, there are some things that were expected, and other things I found surprising. Figure 2 is a plot of the impact date versus impact longitude for all 350 trials. The first thing to notice is the overall trend. Impacts that occur earlier are farther to the East, and the later ones are progressively farther West. This is to be expected, because the Moon is rotating Westward under the orbit as it destabilizes. (The impacts are also focused in a narrow band of latitudes, from 8.5 to 10 °N, which is under the plane of the orbit.)

Figure 2: Impact Longitude versus Date. Later impacts occur farther West.

Then notice the next trend…the impact longitudes occur in bands. For instance, notice that near the end of May 29th, the impacts are mostly around 104 °E, and then during May 30th they shift and are clustered around 99 °E. This clustering also isn’t surprising…it’s a consequence of the lunar terrain. The impacts always occur on the highest nearby terrain as the orbit drops lower and lower, so these impact clusters correspond to tall features of the Moon’s surface. Figure 3 below shows the latitude and longitude of the impacts (as red dots) superimposed on a map of the Moon, and it’s obvious that the dots are clustered around craters and mountainous areas. (At this scale it's hard to see that there are a lot of overlapping dots.)

Figure 3: Impact locations superimposed on a map of the Moon.

One thing I did find surprising is that the impact times are also quantized…they tend to be concentrated into buckets separated by about two hours. A lot of the individual impacts are overlapping on the plot in Figure 1 above, so it’s easier to see this time quantization if we zoom in on a few impacts like in Figure 4 below. Now you can see that there are 6 trials that resulted in impacts around 20:00 hours (10 PM) on May 29th, then 3 others around 22:00, then another 4 around Midnight, and so forth. On the one hand, the two-hour separation makes sense. If the spacecraft barely misses a mountain on one pass, it is likely to be lower, and therefore to impact that mountain on the next pass, which will come two hours later. (The time to complete one revolution is about two hours.) But all the trials have slightly different orbits and slightly different periods, so after 5 weeks orbiting the Moon all those virtual spacecraft in all those trials should have spread out, like race cars around an oval track in a long race.  

Figure 4: Details of impacts occurring around midnight on May 29th, showing how the impacts are occurring in clusters separated by about 2 hours.

It turns out that they do spread out, but the ones that are in similar orbits, with similar orbital periods, tend to impact around the same time. So, the impact times are sorted by orbital period. I would not have guessed this, but in hindsight it also makes sense. It turns out that the impact times depend on the energy of the initial orbit. Lower energy results in earlier impact, and vice versa. The energy of the orbit also determines the orbital period. Therefore, impacts that occur around the same time, which started with similar energy, also have the same period, resulting in the clustering of the impact times. Figure 5 below shows a plot of initial orbit altitude versus impact time, and there is a clear relationship. (The altitude plotted is the average of the initial apolune and perilune altitudes, which directly ties to the orbital energy.)

Figure 5: The time of impact correlates to the initial energy of the orbit, which also relates to the orbital period. This explains the clustering of the impact times.

What have we learned so far about Orion? It seems clear that Orion must have impacted the Moon sometime around the end of May of 1972, about 5 weeks after it was jettisoned. Longitude of the impact is probably between 70 and 120 °E. The impact location is likely to be on a mountain or crater wall, along a narrow track between 8 and 11 °N Latitude, and there seem to be just a handful of locations where the impacts are concentrated. Could we actually locate the impact crater? Although we have narrowed down the search considerably, we are still talking about huge areas of the Moon. (One degree of longitude along the Moon's equator is about 20 miles.) In my next post we'll dig into some other sources of data to see if there are any clues that could be helpful to narrow the search even more.

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