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.