Showing posts with label Apollo Passive Seismic Experiment. Show all posts
Showing posts with label Apollo Passive Seismic Experiment. Show all posts

Tuesday, May 24, 2022

Impact Phase

 As I mentioned in my previous post, I have generated over 350 parameter sets that strike the Moon within one hour of the May 29th seismic event that seems to record the final impact of the ascent stage of the Apollo 16 Lunar Module Orion. Are all of these useful? What time difference should disqualify a simulation? If the simulation misses by 5 minutes, is that OK? If it misses by a full hour, is it meaningless? To answer this question, we need to dig deeper into the data, to try to understand what’s behind the time shifts. 

Let’s start with Figure 1, which is showing the distribution of impact times. Each vertical bar represents one 4-minute period, and the height of the bar shows how many of the simulations strike the Moon within that period. The red bar near the middle of the graph is the target time, around 21:14 on May 29th, 1972. The height of that bar is 30, meaning that 30 of the simulations impact within that 4-minute window. Overall, this set is centered about 6 minutes later on 21:20, and the impacts cover a total time span of 90 minutes. 

Figure1: Distribution of impact times from my simulation set. The red bar is at the time of the recorded impact event, and 30 of the simulations strike the Moon within that 4-minute window.

If you read my earlier post about “nudging” the orbits closer to a target impact time, you might be wondering…why not continue nudging until all the impacts occur at exactly the right time? The reason is that nudging stops working once you get the impact within one orbital period of the target. Huh? Let’s say the period is exactly 2 hours. (It’s close to that.) And let’s say we have a case where the impact is early by 2 hours and 20 minutes. We nudge the VMAG parameter a bit higher and re-run the simulation. Sure enough, this time Orion skims over the impact point, and zooms around for an extra revolution…then slams into the Moon two hours later on its next pass. Now, instead of being 2:20 early, it’s just 20 minutes early. Unfortunately, further nudging barely affects the 20-minute miss. In fact, another nudge might push the impact out by another 2 hours, making things worse.

We need to work with the impact times we have. Maybe we can understand what’s driving those offsets in the impact times? Let's call it impact phase. Once again (as has happened over and over during this investigation) the answer becomes obvious once the data is viewed in the right way. Take a look at Figure 2, which compares the “miss” time, in minutes, versus the initial orbit period in seconds. Aha! Notice that a one second increase in the orbit period shifts the impact time by about 7.2 minutes…or about 430 seconds. If Orion struck the Moon on May 29th, it would have been on about the 435th revolution around the Moon since jettison. So, a one second increase in the period means that 435 revolutions later, it has fallen behind by 435 seconds. And that is exactly what we see in Figure 2. Slower orbits mean later impacts, and vice versa. Impact phase is controlled by the orbit period.

Figure 2: Time offsets from the target vary linearly with the orbital period. It makes perfect sense!

(Another very interesting thing about Figure 2 is that it gives us a great way to validate that the May 29th seismic event was actually Orion. If we knew exactly the orbital period of Orion, we could confirm that it lines up with the observed impact time. I have looked for sources that could confirm Orion’s orbital period without success. Do you have any references? Please leave a comment.)

But now let’s get back to the original question. If a given simulation misses the impact time, can it still be useful to predict the impact location? One way to answer this is to take a given parameter set, and tweak it so as to vary its period, shifting the impact time, and then take a look at how the impact location moves around. Dramatic position shifts would mean we should ignore those simulations that aren’t close to the right time. Modest shifts would indicate that the exact time of impact is not so critical.

Figure 3: A sweep of one parameter set, to vary the impact time. Although the impacts are spread over a range of 2-plus hours, the impact locations are all within 1.4 km of each other. 

One way to change the orbital period is to raise the orbit, so that is what I’ve done in a set of simulations shown in Figure 3. You see that the RMAG parameter (the distance from the center of the Moon) is gradually raised to 1849.2 km. The VMAG parameter has been “nudged” to bring the impacts within one orbit of the target time, while all other parameters are held constant. Notice the impact locations. They remain in a tight pattern centered around 104.3 °E, near 10 °N. These locations are all within 1.4 km of each other, despite the fact that the impact times go from 84 minutes before the target to 53 minutes after. 

From this, I conclude that I need not be too concerned about impact time shifts of less than one orbit. The full database of impact locations seems to be useful as an indicator of where Orion’s remains can be found.

Sunday, March 20, 2022

Orion's Time of Impact

In a previous post we found that the Apollo 16 Lunar Module “Orion” probably hit the Moon in late May, 1972. It would be great if there was a database that could help us to pin down the time of impact more precisely, which would help to narrow the area of the impact. It turns out there is such a database, which is the seismic data collected from the Moon by the Apollo Passive Seismic Experiment, the PSE. The PSE probably recorded the impact of Orion, but in 1972 the impact would not have been recognized as that of a Lunar Module. With our modern simulations could we pick out a seismic event from all that data? Let’s check it out.

Figure 1: One of the PSE detectors, in the foreground, as deployed on the Moon. The Apollo 11 detector overheated after a few weeks, so the later ones were insulated with a reflective blanket.

Seismometers were placed on the lunar surface by each of the Apollo missions up to and including Apollo 16. The one from the Apollo 11 mission failed after two months, but in May of 1972 all of the other stations, from Apollo 12, 14, 15, and 16 were operating and their data was being continuously recorded back on Earth. (Lots of data, which consumed thousands of the open reel magnetic tapes used to record it at the time.) Over the next decade the data was analyzed, and a catalog of lunar seismic events was published in 1981. This catalog is available online today, in its coded format, along with an explanation of the coding. The analysis showed that the events had different characteristics, and could be grouped into various categories such as deep moonquakes, shallow moonquakes, and meteoroid impacts. 

One of the most unexpected features of the Moon became apparent as soon as the first seismic data began streaming back to Earth. To the surprise of the scientists, seismic events on the Moon lasted much longer than anticipated. Unlike Earth, where water and other viscous material dissipates seismic energy, the Moon is very brittle and completely dry, so there is much less absorption of the waves as they propagate around. One of the scientists went so far as to say that the Moon “rings like a bell”. Of course, this shouldn’t be taken literally…but moonquakes definitely reverberate much longer than earthquakes.

One interesting category of seismic event are those from the intentional impacts of Apollo hardware. There are 4 known events from discarded Lunar Modules, as shown in the table below. The table shows the date, the time when the seismic signals started and ended, and the peak amplitudes at each of the 4 PSE stations. The first is the Apollo 12 Lunar Module ascent stage, which crashed near that landing site in November, 1969 right after the placement of the A12 PSE station. Of course at that time the A12 station was the only one operating. For each subsequent LM impact, another station was operating. Also notice that the amplitudes tend to be largest at the newest station. That’s because the LM’s were usually crashed near the most recent landing site. This page lists the impact locations of these Lunar Modules, along with other impact locations. No PSE station was added for Apollo 17, so that impact was more distant from the stations. Notice that in all cases the vibrations lasted for more than one hour. The A12 impact lasted 65 minutes, even though it had a shallow impact angle. The A17 LM impact waves lasted over two hours.

Figure 2: PSE event data for the 4 known Lunar Module impacts

The impact of Orion would not have been recognized as an LM event in 1972. There was no tracking of the stage once its batteries died, and the modeling and computing at the time was insufficient to predict when Orion’s orbit would destabilize. Orion’s impact would have looked like a meteoroid event. Given that we see from simulations that Orion likely struck the Moon at the end of May, 1972, are there any meteoroid impact events in the catalog that could represent the demise of Orion?

Below is a list of all the catalogued meteoroid (type ‘C’) impact events between May 23rd and June 6th of 1972. Remember that in our first set of simulations, all the impacts occurred between May 28th and June 3rd. Notice that there is only one meteoroid event in that period, on May 29th. That is a very interesting event, given that it is right in the middle of the range of the trials. Could this be the impact of Orion? It lasts 98 minutes, and generates substantial amplitudes at all the stations. There is also a cryptic comment: “DIST”.

Figure 3: All the PSE meteoroid impact events from around the end of May, 1972. The May 29 event seems particularly interesting as a possible record of Orion's impact.

In searching the web for PSE data, one name comes up again and again: Dr. Yosio Nakamura. He was obviously deeply involved in analyzing all the data, as his name appears on many of the publications. Even the catalog of PSE events is tied to his name. As this article explains, he was intimately involved in the PSE project from beginning to end. He helped to capture and analyze the first data from Apollo 11, and was back in Houston for Apollo 12. He also helped to preserve the data in the 1990’s, by arranging for all the raw data of over 12,000 reels (!) of the original tapes to be transferred to more modern, and more compact Exabyte cassettes. Today he is an emeritus professor at the University of Texas in Austin.

I contacted Dr. Nakamura, explaining my interest in the meteroid event of May 29, 1972, and he was kind enough to reply back. Not only that, but he was also kind enough to visit the facility where the raw data is stored, examine the event records, and perform some analysis. Here is what he was able to say: 

“Two things are clear: (1) The recorded amplitude at the Apollo 16 station is definitely larger than that at the Apollo 14 station, even considering that the Apollo 14 station tends to record amplitude slightly larger than that at the Apollo 16 station because of local site effect.  This means that the impact location is east of the seismic network.  (2) Seismic signals are detected at all four stations.  This means that the impact location is not far into the far side of the moon, because if it were, the seismic signals would be significantly reduced because of the high shear-wave attenuation in the lower mantle.”

These facts do fit with the simulation results for Orion, which showed it impacting between 70 and 125 degrees East longitude. Was there any way from the timing of the signals to triangulate the impact location? 

“Because the onsets of the seismic signals of the {May 29} event are too weak to be read precisely to compute the impact location, I have been looking at the amplitudes of their signals instead. One of the attached files shows plots of the catalogued amplitudes vs. distance of the {May 29} event with suggested impact locations compared with those of the other LM impacts. In the top figure, the catalogued amplitudes are plotted, while in the bottom figure, catalogued amplitudes are adjusted, or compensated, for the difference in detection sensitivity among stations."

Below is Professor Nakamura's "bottom" figure, with the compensated amplitudes

Figure 4: Nakamura's plot of compensated PSE amplitudes versus distance for the known LM impacts, as well as for theoretical Orion impacts at two longitudes. This is the "bottom plot" that he refers to.

"One thing that is clear from the bottom plot is that there are some differences in the amount of seismic energy radiated from LM impacts:  Similar amount of energies were radiated from 14 LM and 15 LM impacts, while 12 LM impact radiated less energy, producing about 1/2 of the first two in seismic amplitudes and 17LM impact radiated more energy, producing about 3 times more amplitudes than the first two.  This happened even with nearly equal impact energies (3.14-3.43 x 10^9 J) and impact angles (3.2°-4.9° from horizontal) (NASA TM X-58131, Table 4-111)."

"Considering this range of observed amplitudes, the amplitudes and the distance ranges of the assumed impact location of the {May29} event are consistent with those for a LM impact.  If anything, it radiated more energy than the 14 and 15 LM impacts but similar to the 17 LM impact, and/or it may have been closer to the seismic network than assumed.  One thing we cannot do with this set of amplitude data is to pinpoint the impact location within say better than ~30° or `~1000 km or so in any direction.”

He then adds a final valuable clue…

“I estimate the time of this impact to be about 7 minutes before the cataloged time 21:22 UTC, or about 21:15 UTC, with an uncertainty of ±2 min. This is based on an impact distance of 3000±1000 km from the nearest station.”  [See the comment below.]

Wow! The simulations pointed us to one of the events in the PSE catalog. This event seems to fit well with what we know so far about Orion's orbit. The event is "consistent with those for a LM impact" at the range of impact locations we simulated, and if it's right, we now know fairly precisely the time of Orion's impact. With that information, we should be able to go back and refine the simulations, focusing on those that result in impacts at the stated time. That should GREATLY narrow down the area where Orion could have impacted. Could we actually locate the impact crater? 

I want to express my gratitude to Professor Nakamura for his kind assistance. I feel very fortunate to have benefitted from his expertise. Thank you!