Monday, February 14, 2022

Impact Analysis


The simulation environment I am using, GMAT, doesn’t know anything about the Moon’s mountains or valleys. When it calculates the altitude of an orbit, that altitude is relative to the “mean radius” of the Moon, somewhat comparable to “sea level” on Earth. So far, in the simulations I have run for the Eagle and Snoopy, that hasn’t mattered, because the orbits of both objects remain high above the surface. But to estimate the location of a possible impact, as for the Apollo 16 subsatellite, we have to do a deeper analysis. In this post I’ll explain how that works. 

Let's start with the big picture. An orbit has become more eccentric…the high point of the orbit has moved higher, and the low point of the orbit has moved lower. On Earth, as the spacecraft began to skim the atmosphere, it would slow down, then burn up, and the heaviest bits might make it all the way to the surface. Since the Moon has no atmosphere, the spacecraft, at the low point of its orbit, can zip past the lunar surface at very low altitude, moving more than a mile per second, and if it misses the surface, even barely, it can continue around for another pass. 

Figure 1: The path of a spacecraft passing low over the Moon's surface

If the Moon were a smooth ball the impact might occur at the lowest approach. However, the Moon is not so smooth. In fact, it is quite rough, with jagged surface features thrown up by countless meteoroid impacts, undiminished by wind or rain. If a spacecraft comes streaking by and strikes the surface, that impact will likely be on a piece of high terrain, perhaps the side of a mountain or a crater wall. To work out the location, we’ll need a good elevation model of the Moon’s terrain. Fortunately, these are freely available, with resolution as high as 512 points per degree, which works out to one elevation point for every 100 feet or so.

We also need the simulator to give us a full “ground track” record, instead of just the lowest point of each orbit. The ground track is a list of latitude, longitude, and altitude points and typically a point is recorded for every 10-20 seconds of simulated time, as in the example shown below. Given that the spacecraft is traveling at about one mile per second, there is a lot of ground between each point. It’s not enough detail to locate the impact exactly, but it shows us the places where the spacecraft is close to the surface…places where we can zoom in for a closer look. As we go through this exercise, we will be zooming in on the points highlighted in green.

Figure 2: Ground track file excerpt. The terrain and "AGL" altitude data (in km) was added by post-processing the output from the simulator.

The first thing we need to do is to “post-process” the ground track file, looking up the height of the surface for each point in the file. For this method I am greatly indebted to a space enthusiast named Daniel Estevez, who ran simulations to try to estimate the impact location of a lunar satellite and posted his results here. I use a modified version of his method, wherein I run two passes on the ground track file.

Step one is to go through the ground track, one line at a time. From the latitude and longitude, we can look up the nearest terrain altitude point in the elevation model. Once we know the spacecraft altitude and the terrain height, we can calculate its “Above Ground Level” altitude. I write out a new copy of the ground track file with the extra terrain altitude and “AGL” data points added to each line, like the yellow values shown in the figure above. To limit the size of the new file I discard any point where the spacecraft is more than 5 km above the surface.

Here is a plot of a ground track file showing two low revolutions of a spacecraft over an area of the Moon. One thing to notice right away, even though this is covering 30 degrees of longitude, or a distance of about 900 km, the "zero" altitude point is flat, and the satellite trajectory curves upward, away from the Moon. This is just to make it easier to plot out the data. I promise the Moon is NOT flat, and the spacecraft is always curving towards the center of the Moon, as in Figure 1 above. The flattening of the Moon for this chart doesn't affect our ability to find the impact point. Another thing to keep in mind is that the vertical scale is greatly exaggerated. This chart is 900 km wide and just 8 km high.

Figure 3: A "flattened" plot of low passes of a spacecraft over the Moon. The area in the green box depicts the values highlighted in green from Figure 2.

Figure 3 allows us to see the areas where the spacecraft is coming close to the surface of the Moon. In particular, the points in the small green box highlight the closest approach visible at this resolution, and the closest point shows a separation of 449 meters above the ground. Given that these two data points are separated by a distance of over 20 km, we need to zoom in and take a closer look.

Figure 4: A "zoomed in" look at the region of the green box from Figure 3. We see that the spacecraft altitude is lower than the terrain altitude at 98.97°. Kaboom!

The figure above shows the zoomed in view. The two red dots are the points from the green box of Figure 3, the same data points highlighted in the ground track file in Figure 2.  What we have done is to make a straight line between these points, and break that line into 100 shorter segments, like the dotted blue line. (This process is called linear interpolation.) For each blue dot we can again look up the terrain altitude and compare it to the spacecraft altitude. Sure enough, in that intervening 20 km between the two red points there was a mountain, about 800 meters tall, and the spacecraft (moving from right to left in this example) strikes it near its top, at around 98.97°. 

How do we know there wasn't another mountain lurking somewhere further to the East? We don't! We have to check. In my code, posted here, I check any time I find a point that is within 3 km of the ground. (I also tried higher thresholds, but 3 km seems to be sufficient to catch all the lurking mountains in my tests so far.)

This is how I have used GMAT to estimate the impact location of the Apollo 16 Particles and Fields Subsatellite, the notorious (in some circles) PFS-2. Now that I have this tool working, I am interested to use it to investigate another Apollo impact. Yes, there is another spacecraft from the Apollo era whose final resting place is unknown...the ascent stage of the Apollo 16 Lunar Module "Orion". As I write these words the 50th anniversary of that mission is fast approaching. Stand by for further updates.

Monday, February 7, 2022

A Reality Check

 What about that Apollo 16 subsatellite?

In this blog I have shown that two Apollo spacecraft were left in orbits that are stable over decades. That’s really surprising and unexpected. Some people have asked if I can simulate an object that is known to have decayed out of orbit, as a reality check, to show that these simulations aren’t out of whack. That’s what we’ll do in this post.

One very notable case is the Apollo 16 Particles and Fields Subsatellite, otherwise known as PFS-2, which decayed out of lunar orbit in 1972 after only 5 weeks in orbit. Weighing just 36 kg, it was jettisoned from the Apollo 16 Service Module not long before the crew left lunar orbit to return to Earth. Originally it was planned to raise the orbit of Apollo 16, so that PFS-2 would remain in orbit for a year. Due to problems during the mission, that orbit change was skipped, and the expected orbital lifetime of PFS-2 was cut down to a few months. PFS-2 was equipped with a transmitter so that it could be tracked, and its data could be sent back to Earth. Only 34 days after it was jettisoned, the transmissions ceased, and PFS-2 impacted the Moon. 

Let’s run a simulation of PFS-2 and see what happens. As with previous simulations we can get the initial conditions from the Mission Report. The Figure 1 shows the data from the report. I believe the report is showing the state of the Command-Service Module (CSM) rather than the PFS-2, but it should be close enough to see if we are in the right ballpark. After converting the parameters to metric and getting them into the right coordinate frame, I get a GMAT script like this one, posted on GitHub.

Figure 1: Showing the initial conditions of PFS-2 from the Mission Report.

For starters, we’ll just record the low point in each revolution, as we have done previously. Figure 2 shows how it looks over time. We see the minimum altitude dropping for several weeks, and then there is a reversal and it starts to rise up again around the middle of May. About a week later the orbit starts to become more eccentric, and the perilune altitude begins dropping again. Sure enough, just 5 weeks after jettison, at the end of May 1972, the low point of the orbit is below the average radius of the altitude...and that is a sure sign that impact has occurred. (The simulator doesn’t check for impact while it is running…it will happily simulate an object that is actually beneath the surface, so we’ll have to look in greater detail to see exactly when and where the impact occurs. I’ll explain how to do that in a future blog post.)

Figure 2: Simulated perilune altitude.

A more detailed analysis of the simulation results gives the location and time of impact, and it comes out as below. Tracking data from the satellite ended shortly after 10:31 PM on May 29th, with an estimated impact at 111° East longitude, and 10° North latitude. This simulation puts the impact about 14 hours later, and about 13 degrees further west. That's not bad! 

Figure 3: Impact times and locations reported by NASA and estimated by simulation

There is another source of information on the PFS-2 initial orbit, at this page. It describes the orbit in a different way, and the parameters don’t completely agree with those in the Mission Report. If we run again with those initial conditions, we get the results labelled “Nominal 2”. This time we get closer to the 1972 estimated impact location and time…impacting about three hours earlier and about 4° more to the west, with the latitude agreeing almost exactly.

In my view, the basic answer is “yes”, these simulations do compare well against reality. We are able to predict the impact of PFS-2 within a few hours of the actual time, and within a few degrees of the estimated location. Considering the uncertainty of the initial conditions, with two different NASA sources that don’t agree, errors of a few hours either way don’t seem too surprising. Having gone through this exercise, I have even greater confidence in the results obtained for Eagle and Snoopy.

By the way, if you are looking for a lunar sleuthing challenge, the actual impact crater of PFS-2 has never been located. This web page states that the original raw PFS-2 tracking data has been preserved, and if you were to obtain that data and fit a simulation to it, I suspect you would be able to map out a very small area where the PFS-2 impact occurred on the surface of the Moon almost 50 years ago. You might be the person to identify the final resting place of the infamous short-lived Apollo subsatellite. Good luck and happy hunting!

Monday, January 17, 2022

Feedback and Stability

The Moon’s uneven gravity field causes most lunar orbits to be unstable. Over time the orbits increase in eccentricity, which is to say that the high part of the orbit gets higher, and the low part gets lower, until the object strikes the lunar surface. In this blog I have described the orbits of two different Apollo artifacts that show long-term stability in their orbits. (The Eagle and Snoopy.) They somehow manage to evade the instability that dooms most lunar satellites. How could that be? In this post we’ll dig in deeper to try to understand what is going on in greater detail.

I’ll start by focusing on the Eagle, and then at the end we can do a similar analysis for Snoopy. To start, as a reminder, look at the way the perilune altitude varies over time in the figure below. (Remember, perilune altitude is the lowest point of each revolution.) You see a cycle that repeats as the minimum altitude dips lower then climbs higher about every 25 days. I showed in a previous post that this 25-day cycle reflects the way the orbit changes as the Moon rotates underneath. The lowest lows always occur on the near side of the Moon. The fact that the cycle completes in 25 days, while the Moon completes a full rotation in 27.32 days, means that the Eagles orbit is also precessing. (This is also sometimes called “Apsidal advance”.) In this way the long axis of the Eagle’s orbit, called the Apse Line, does a complete circuit of the Moon in about 25 days, and this drives the short-period variation.

Figure 1: Minimum altitude of the Eagle in the first year after jettison. Notice the shorter variations every 25 days, and the longer variation every 4-5 months.

What about that longer variation in the perilune altitude? Notice how every 4-5 months the minimum altitude goes higher and then lower. What’s going on there? If you look at the figure above, notice that the minimum altitude is nearly the same at point A and point B, but somehow this system “knows” that at point A the longer cycle is increasing, and at point B the longer cycle is decreasing. Somehow there is “state” information being stored in the system, so that it “remembers” where it is in the long-period cycle. Let’s dig in and look for that “state” signal.

Figure 2: Showing the time (in days) between the peaks of the first 4 complete cycles for the Eagle. Notice that the time between peaks increases as the altitudes move lower.

For starters, let's look for differences between the “low” cycles and “high” cycles. One thing to measure is the “period” of the cycle, i.e., how many days it takes to complete a cycle. We can measure the time between the highest point in each cycle. In figure 2 above, I show the time (in days) to go from one peak to the next for the first 4 complete cycles of the Eagle’s orbit back in 1969. Do you notice anything interesting? As the altitudes get higher, the times get a bit shorter. As the altitudes get lower, the times get a bit longer. We can plot these on a graph that makes the relationship easier to see, and in the figure below I show the first 14 cycles…the first year of the Eagle after jettison. If I plotted out the data for 52 years you would see that the same relationship continues to the present day. This is a persistent feature of the Eagle's orbit.

Figure 3: Cycle length and end peak altitude for 14 Eagle cycles during its first year in lunar orbit.

The next thing to notice about these cycles is how they relate to the Moon. The plot below shows perilune altitude versus the Moon’s longitude, for one year. As the Moon rotates underneath the orbit, we see 14 tracks wrapping around. Each of the blue dots represents the lowest point of one revolution, and the longitude where that low point occurs above the Moon. What’s interesting is that the lowest parts of the cycles always occur on the near side of the Moon, near 30 degrees East, while the highest parts occur on the lunar far side. (From Earth we can only see lunar longitudes between -98° and +98°.)

Figure 4: Mapping how perilune altitude varies with lunar longitude. Eccentricity of the orbit is highest when perilune occurs on the near side of the Moon.

You might also notice some “sloshing” back and forth in that pattern in Figure 4. Notice on the left part of the figure where the highest points in each cycle are marked with red dots. The dots actually form a loop. It's even more interesting to connect the successive dots, as in Figure 5 below. In this figure I’m only showing the highest points of each cycle, like the red dots above, but now I added a dotted blue line showing the sequence. You can see that over the course of a year these dots trace out a series of loops. And these loops tie back to the slower 4- to 5-month variation you see that first figure above. Now we can see the difference between points A and B in the first figure. I’ve marked them again in Figure 5. Point A occurs about 30 degrees farther to the East than point B. This longitudinal variation is how the system stores its “state” information…how it “remembers” whether the short cycles are increasing or decreasing. And just to be clear, this is another pattern that is stable over decades. On the left in Figure 5, notice how this variation looks over a 50-year period. It doesn’t expand or contract or drift away. It remains centered on this longitude.

Figure 5: These plots show the lunar longitude where the perilune cycle peaks occur. Points A and B on the left are the same ones marked in Figure 1. All the red points on the left are also marked in red in Figure 4. Data for 50 years is plotted on the right, showing the long-term stability of the pattern.

We’ve seen how the eccentricity variation of the orbit stays locked to lunar longitude over decades. How can that be? There must be some feedback mechanism that prevents it from drifting away. It’s interesting to look at the rate that the perilune longitude point changes. To do that, for every revolution, we have to measure how far Eastward the perilune point shifted and compare that to the elapsed time. If we divide the longitude change by the elapsed time, we get a measure of the rate. (The elapsed time is nearly constant…about 1 hour and 58 minutes per revolution, but it’s a spreadsheet doing the math, so why not recalculate it for each point.) I’ll call this measurement the “precession rate”. That’s kind of a misnomer…the longitude is mostly changing because of the Moon’s rotation under the orbit, which is not really precession. (This component is also constant, because the rate of the Moons rotation is constant.) But there is an additional precession in the orbit so there is some variation in this precession rate. Here it is...

Figure 6: The "Precession Rate" varies depending on perilune altitude.

What is interesting here is that the rate gets much faster as the perilune altitude gets higher. Put another way, the precession rate varies inversely with eccentricity. As the orbit becomes more eccentric, the rate slows down. As the rate slows down, the Moon's gravity begins to drive the eccentricity lower. Lower eccentricity causes the rate to speed up, and the cycle repeats. Again, and again. For decades.

OK we found an interesting pattern in the orbit of the Eagle that persists for decades and can plausibly explain its long-term stability. (“Explain” is a strong word here…I believe there are more layers to this onion.) How about the Snoopy descent stage? If we go through the same exercise with Snoopy, we see very similar patterns. Compare the figures below for Snoopy’s orbit to those above for the Eagle. There is something about these retrograde equatorial orbits that leads to long-term stability, somehow evading the unstable fate of most other lunar satellites. Pretty cool, eh?

Figure 7: These plots of Snoopy's orbit data show similar patterns to those of the Eagle. A similar feedback mechanism seems to be responsible for the long-term stability displayed by both orbits.

Sunday, August 8, 2021

Start Here

I started this blog to document my search for the descent stage of "Snoopy", the Apollo 10 Lunar Module. I thought that I could simulate its orbit and maybe find the crater where it hit the moon. To my surprise, I found instead that Snoopy's orbit was stable over decades. This blog was my attempt to show what I had done, and how I had done it, and hopefully get some feedback on anything I missed. I have to say that traffic was quite light.

I then turned to the ascent stage of the Apollo 11 one knows what became of that little piece of history either. And again, amazingly, the simulated orbit shows a long-term stability very similar to that of the Snoopy stage. Wow! That was in September of 2020, and you might notice that the blog posts stopped around that time. Instead, I focused on writing up the results for peer review and publication, and after some fits and starts I am proud to say that the paper is published.

My intent now is to expand on the Eagle results and continue looking for other interesting objects from that era. 

You can page through the blog posts in order for a "tutorial" on the process I went through. Or skip around to whatever looks interesting.

Love it? Hate it? Don't believe it? Post your (respectful) comments.

Hope you enjoy the material!


Sunday, September 6, 2020

Has the Eagle Landed?

 No one knows what became of the Eagle. That seems wrong. 

After it carried Neil Armstrong and Buzz Aldrin back from the surface of the Moon in 1969, the ascent stage of the Apollo 11 Lunar Module "Eagle" was jettisoned into lunar orbit. The astronauts watched out the window as it drifted away. The NASA tracking network followed it for a few revolutions, until they lost the signal. Since then no one has seen or heard from the Eagle. Without question it is one of the most important machines ever created by humanity. Not knowing her fate is a terrible wrong which must be righted.

The assumption has always been that the Moon's lumpy gravity caused the Eagle's orbit to decay, and she impacted the Moon at an unknown location. In this post I will go through the last known orbital state of the Eagle, and show the results of simulating that orbit with the best gravity models available. Spoiler alert: as I found previously with "Snoopy", the orbit is quasi-stable. Lunar gravity alone may not have brought the Eagle down.

For the orbital state of the Eagle at the time it was jettisoned, we look to the Apollo 11 Mission Report. Table 7-II lists information about the spacecraft at various points in the mission, and in particular there is an entry for "Ascent stage jettison" as below.

Orbital State of the Eagle at jettison, from the Mission Report

As I have described in a previous post, I use a simulation tool developed by NASA, and gravity models derived from GRAIL data. It's fairly straightforward to plug in the values from the table and simulate the stage. There is one problem with the Mission Report, though. It's wrong! When you think back to 1969, a world where word processing does not yet exist, and data processing is cumbersome, it isn't shocking that there is a problem in the table. But if you know a bit about the Apollo 11 orbit, the error is rather glaring.

All of the Apollo missions followed orbits that were low in inclination...that is, they stayed close to the lunar equator. It means that their "Space-fixed heading angle East of South" in degrees was never far from -90 degrees. If we use the value in the table, the orbit is inclined to the lunar equator by about 8 can't be right.

What to do? Fortunately there is another source. This paper from 1970 lists orbit data for several Apollo missions, including Apollo 11. In particular, it lists the inclination for several revolutions leading up to the moment the Eagle was cast off. By plotting out the values and extrapolating, one can find an accurate inclination at that moment...178.817 degrees. (Inclination would be 0 degrees for an orbit following the lunar equator, in the direction the Moon rotates. Because the orbit is "against" the rotation, the inclination is close to 180 degrees.) Using GMAT this inclination can be translated into a heading angle...-89.63 degrees.

Extrapolating to find the inclination at the moment of jettison

Plugging this value into GMAT, along with the other values from table 7-II leads to a simulated orbit that matches up nicely to what is known about the mission. For instance the ground track of the orbit matches up well with those depicted in the Mission Report; the apolune and perilune values agree with values reported by Public Affairs Officer during the mission; and longitude values from the simulation agree well with Aquisition Of Signal and Loss Of Signal (AOS/LOS) times reported by tracking.

So what happens to our simulated Eagle? Let's look at the first five days after jettison. The stage was initially in an orbit that was "63.3 by 56 nautical miles", according to a P.A.O. announcement a few hours after jettison. That's a nearly circular orbit that is 117.2 kilometers at the high point and 103.7 km at the low point. From there we can see that our simulated stage is pulled into a more eccentric orbit, with higher highs and lower lows over the next 5 days.

If this trend were to continue, the Eagle would have indeed impacted the moon within a few weeks. However, as I have seen in previous simulations of Snoopy, there is a pattern that takes hold, and the orbit cycles through periods of higher and lower eccentricity, completing one cycle about every 22 days. In the plot below we see that after about 10 days, the orbit begins to return to a more circular pattern, with lower highs and higher lows, until around August 13th, when it is nearly back to the original state. Then a new cycle begins and we see the minimum altitude dropping again.

For simplicity in the plots below, I will ignore the higher parts just focus on the lowest points of each orbit, following the lower envelope of the plot. If I plot out these low points (the "perilune" points) for the first year, we see that the orbit continues to oscillate throughout the year.

What is exciting about this simulation is that there is no impact! Across the first three cycles of eccentricity, the low point of the orbit drops down to within 20 km of the surface in September of 1969. Then the trend reverses, and the minimum altitude begins trending higher. We see that there is a slower cycle of highs and lows superimposed on the 22 day cycle, which repeats about every 4 months. 

These cycles are very similar to the behavior of Snoopy's descent stage, and the cycles of eccentricity are can be explained by precession of the major axis of the orbit around the Moon. For whatever reason, the orbit always reaches it's highest eccentricity when the perilune point is above the near side of the moon. For Snoopy a cycle of precession takes about 25 days, while for the Eagle, in a lower orbit, it is about 22 days.

Now the big question. What happens if we run the simulation longer? When does the stage impact the moon? The answer, very surprisingly, is NEVER! I ran the simulation out to the present, which took about a week to complete on my home laptop. Here is a plot of the perilune points of the Eagle, simulated to the present...

Simulation of Eagle to the present shows no contact with the Moon!

The cycles of high and low eccentricity are almost completely lost in this graph, but there is no secular trend...the closest approach to the surface in 1969 is about the same as the closest approach in 2020. If the simulation is to be believed, then lunar gravity did not bring the Eagle down.

I have posted the simulation script and other information on GitHub, and I welcome you do try it yourself.

 It sounds crazy, but there is some possibility that the Eagle never impacted the Moon. Wouldn't it be amazing if we could find this amazing little vessel and bring her back to Earth!!!!

Saturday, August 15, 2020

The Staging Disaster (That Never Happened)

Among people who celebrate the Apollo program, there is a group that can recite the details of a near disaster during Apollo 10. They talk about the Lunar Module spinning out of control, seconds from impacting the moon. A chaotic staging in the middle of engine firings. It's a dramatic story, no doubt. Fortunately, for the men on board at the time, the story is largely false. The dramatic events actually never occurred, at least not in the way they have come to be described.

A still from the 16mm film taken as the descent stage moves away during staging. Notice that the lunar horizon is "upside down".

I can't blame people for believing in this mythology. Take a look at this excerpt of a video that has been shown on the Discovery Channel. We see the LM apparently in the midst of a rehearsal for landing. The descent engine is running. Then suddenly we see the stages separate and the ascent stage goes in a rapid, wild tumble. These are powerful images.

I am sure that the Discovery Channel showed this animation over and over to attract attention to their show. I don't know if the people who produced it knew it wasn't real, but for sure, if they had spent a few hours researching the mission records, they would have known it was a false telling of the tale. 

Just to be clear, something did go wrong at staging. At the moment it occurred, in May of 1969, no one knew exactly what was happening, and there is no doubt it was a frightening incident. Both Tom Stafford and Gene Cernan, the astronauts aboard, deserve great credit for quickly recovering and keeping their mission on track. In this post I will look at some of the fictionalized accounts online, and then go back to the original records to piece together what really happened that day. The exaggerations that have been popularized in recent years don't honor the true courage and flying skills of these brave men.

First lets look at more of the false accounts.

Here is a YouTube video from "Seeker", which claims that "the spacecraft could have slammed into the Moon." In fact the astronauts were in a stable orbit, and slamming into the surface was simply not something that would have happened in any scenario. 
Sadly, even the Draper Corporation has joined in the fiction-fest. This company descended from the MIT instrumentation lab that designed the guidance and wrote the software for the Moon landings! But this web site, which Draper sponsors, joins the chorus of bogus descriptions of the staging incident. They claim that the crew was "seconds from crashing into the moon when they successfully regained control." Fortunately for the Apollo crews, Draper's standards for reality-checking were tighter back in 1969. No doubt Charles Stark Draper is spinning in his grave faster than an out-of-control LEM.

Here is one more misleading account of the event, and again one would hope for better fact-checking from the source...Smithsonian Magazine. While I appreciate their effort to draw attention to an overlooked Apollo mission, the claim that the staging gyration took place "after the ignition of the ascent engine" is simply false, as a few minutes of online research will quickly prove.

Surprisingly, it seems that the over-dramatized accounts of the staging incident tie back to someone who was there - Gene Cernan, the Apollo 10 Lunar Module Pilot. Back in1969 his descriptions of the events related well to the facts of the mission. By 2009, 40 years later, his sense of drama appears to have enhanced his memories, and the tale he tells has grown. He recounts "seeing the lunar horizon go by 8 times in 15 seconds". No wonder the event mythology has become so exaggerated. Eyewitness testimony! While I have great respect for Gene and all of his contributions to the space program, in this case we unfortunately need to doubt his words.

Let's go back to May of 1969 and uncover what really happened. There are a number of great sources to help understand the event, including film taken out the LM window, on-board audio recordings, telemetry data, the crew debrief, and the "anomaly" investigation report.

For starters, one fun video from the time is the live coverage that was being broadcast by CBS. They were "all in" on the Apollo program, and invested heavily in animations to complement the audio they were getting from NASA. Famously, there was no 7-second delay in those days, and we clearly hear Gene cussing on live television as things go south in the LM. In the video I linked above, Cernan recounts how his wife admonished him about his "salty" language when he got back to Houston. However even from the live coverage, it's clear something went wrong during staging, resulting in a "wild gyration".

Cernan's mic was "live", so his words went straight to Houston, and on to CBS, which is why he was tagged as the "salty" one. Meanwhile, an on-board tape recorder captured audio from both Cernan and Stafford. From the transcript of the tape produced by NASA, we see that Stafford (labelled "CDR" in the transcript) had a few choice words of his own. Fortunately for all concerned these words were not broadcast live. 

This excerpt from the LM transcript captures the tense moments of the staging incident.

To understand what really happened, there is one truly outstanding source - the Apollo Flight Journal. Robin Wheeler of the AFJ put together a video that combines the film, the on-board audio, and telemetry data, aligned to a mission timer. Anyone interested in the true story of this incident needs to watch this video. When I watch it I have to really admire the crew as they quickly and effectively dealt with a very unexpected situation. Clearly they are a great team, with years of experience training and flying together. Listen to the great communication as they keep each other apprised as events unfold.

From the video it's clear that the LM did not tumble or spin in the dramatic fashion of the Discovery Channel animation. The lunar horizon does not go by "8 times in 15 seconds" as Gene claimed. What we see in the video matches up much more closely to what Tom and Gene described in the crew debrief interview they gave when they got home. In that interview Tom states that "We got the vehicle under control after about, I'd estimate, a 360-degree maneuver." Gene's account is more conservative, saying that "We could have maneuvered 30 degrees or we could have maneuvered 90 degrees. All I know is that it was fairly slow." Then he added "whether we did a 360-degree maneuver is difficult for me to say." The account Gene gives years later, is very different, and is probably one of the the main reasons that the staging mythology grew. 
This chart shows the spin rates at the time of staging. The peak in the Z-axis (roll) was around 26 degrees per second...about 13 RPM.  Source

It's important to understand that neither the descent engine or the ascent engine was fired during the staging maneuver. The plan was to use the small "RCS" jets to speed up by 2 feet per second, kick off the stage, then slow back down to the original speed. This is basically what happened, but the unexpected attitude changes meant that the stage was kicked off more upwards than backwards. Robin Wheeler at the Apollo Flight Journal undertook a detailed analysis of the film and prepared this image showing the planned and actual staging attitudes.

The confusion about the engine firings probably arises because the LM was designed to be able to perform staging "hot", during descent. This "Fire In The Hole" capability had been tested with the first unmanned LM flight during Apollo 5. For Apollo 10, no such risk was taken with men aboard. The descent engine had been deactivated after the Phasing burn, two hours before. The ascent engine would be fired for the first time 10 minutes after staging, as the crew began their rendezvous with "Charlie Brown".

This table from the Mission Report shows the Phasing Burn that preceded staging and the Insertion Burn that occurred about 10 minutes after staging. We also see that the LM was in a 190-by-12 nautical mile orbit...with no risk of impacting the surface

Another point of confusion about the staging mishap concerns the altitude above the lunar surface when it occurred. Prior to the Phasing Burn, the LM had been in an orbit that took it to within 8.5 nautical miles of the surface. However, at the time of staging, one can see from the Mission Report that they were at an altitude of 31.4 nautical miles. They were never in danger of impacting the Moon.

Table 6-II from the Mission Report, showing the altitude of 31 miles at the time of staging

All of the original documents point to the staging event as much less dramatic than the one so widely depicted online these days. That bothers me. Although the mission was a success overall, there were plenty of challenges, and plenty of surprises for the talented crew to overcome, and they met them all in grand fashion. Thanks to the fantastic job by Gene, Tom, and John, Apollo 10 was an amazing success, which paved the way for the first landing on the Moon less than two months later. There is no need to exaggerate the mission to celebrate its triumphs.

Saturday, May 16, 2020


Snoopy's descent stage was jettisoned into lunar orbit with more than 8 tons of hypergolic propellants still aboard. If the stage orbit was long lived, what happened to all this fuel? This might be the thing that brought the stage out of orbit, so in this post I will examine the possible outcomes.

Descent Stage Cutaway View  Source
The mission was a rehearsal for the Apollo 11, without the landing. They undocked, then did the Descent Orbit Insertion (DOI) burn to drop the orbit closer to the surface, as Apollo 11 would. Then they did an additional "phasing burn" to get the right alignment with the command module for the rendezvous. One orbit later the stage was jettisoned. These two short maneuvers used only a small fraction of the fuel, leaving the tanks at about 96% of their capacity

This excerpt from the Mission Report shows the quantities of propellants loaded and consumed
The stage was not designed for long life, so no one knows exactly what might have happened. There are some facts in various NASA reports that offer clues, so we'll map out the clues and then make some guesses about the eventual outcome.

In a previous post I showed a simplified model of the Descent Propulsion System, or DPS. It was a simple, reliable system with tanks fed by pressurized helium. The tanks of fuel and oxidizer led to the combustion chamber, so when a valve was opened, the propellants mixed, ignited, and burned, creating thrust. In the earlier post I described how the main "supercritical" helium tank likely vented to space within a few days after staging. Then what?

Here is a complete schematic of the DPS plumbing. There are actually two helium tanks, plus various valves, burst disks, and so forth.
In order to analyze what happened, its useful to simplify things, as I show below. The "Squib valves" were sealed during flight and then opened using small explosive charges when the engine was activated. Once opened, they never close, so it's cleaner to show them as open pipes. One set of squib valves was used to vent the propellants on the lunar surface, so for Apollo 10 these remained sealed. I believe they can be ignored. (I don't think it's possible that they could activate themselves.) So I eliminated those as well. The Supercritical Helium tank no doubt vented within a few days after staging, so I also eliminated that from the diagram, showing instead an opening to the vacuum of space. Here is the simplified schematic:

What do we know about this system when it was cast off? We know that the fuel and oxidizer tanks were pressurized to 247 PSI at 70 degrees. We know the tanks were still 96% full. The small Helium tank in the schematic is the high pressure "start bottle". (It was used to initially pressurize the tanks and start pushing fuel through the heat exchanger.) We know this tank had a slow leak. We know that the burst disks were rated to open between 260 and 275 PSI. We know the quad check valves might have had leakage rates up to 100 standard cubic centimeters per hour. We know that even without the main helium pressurization system, the DPS could operate from existing tank pressures, in "blowdown" mode, generating significant thrust.

We also know that the stage was slowly tumbling in orbit. The dramatic film taken during staging captures the unplanned attitude excursions, and a post-mission guidance report shows the rates at the moment of staging in this chart:

At staging, Snoopy's tail had yaw, pitch, and roll rates of -9, -4, and +7 degrees per second. So that's one full yaw rotation every 40 seconds, one pitch rotation every 90 seconds, and one roll every 52 seconds.

So what happened? I think there are four possibilities. 1) Slow leaks might have allowed the tanks to depressurize, until the stage reached a stable state. 2) The tank pressures might have increased until the burst disks failed, allowing things to vent to space. 3) Propellants might have leaked back through the check valves, into common helium plumbing, which might have led to combustion or even a catastrophic explosion. 4) Something might have caused the throttle to open, allowing the engine to start generating thrust. Let's take these one by one, in reverse order.

If something caused the throttle to open up, residual pressure in the tanks would have allowed for significant thrust in "blowdown" mode. For example, as Apollo 13 was headed back to Earth, it was noted that the DPS could provide an 800 f.p.s. velocity change to the full LM-CM-SM stack in this mode. In the case of Snoopy, the volume of gas in the tanks was lower, reducing the possible burn time. However the stage was much lighter than the Apollo 13 stack. If the throttle opened up, it might have knocked the stage out of orbit.
Detailed view of the throttle assembly (source)

I really doubt this happened, because several things would need to fail for it to occur. One of the two actuator isolation valves would have to fail hard open, allowing pressurized fuel to flow into the valve actuator, forcing the main shutoff valves open. Then the "thrust control actuator" would have needed to fail into the open state. Designing a thrust control valve that could fail open doesn't sound like something that would have passed muster during Apollo. If you have deeper insights, please leave a comment. In my view, a spontaneous blowdown burn is unlikely.

How about reverse leakage through the check valves? This could create big problems because it would allow both fuel and oxidizer to flow into the common helium feed plumbing. A high profile explosion during a ground test of the Crew Dragon spacecraft in April of 2019 was attributed to oxidizer leaking into helium pipes. NASA documents do state that early check valves had a higher leak rate than originally intended. So could this leakage cause the stage to explode?

For the check vales to leak, there must be reduced pressure in the helium feed. The helium system was still being fed by the small ambient "start bottle", so it probably remained at 247 PSI for some time. During the flight, the ambient bottle pressure dropped 35 PSI in 97 hours, apparently due to a leak that developed during launch. At this rate, the bottle pressure would have dropped to 247 PSI in about one year. After the other helium system vented, the leak rate might have increased.

So once the pressure was low enough for leakage to occur, does that result in an explosion? Honestly I don't know how to evaluate this possibility. If the leakage was in gaseous form, any reaction would probably be low-power. If liquids leaked, and eventually flowed together, the reaction would be more violent, perhaps even powerful enough to blow out the plumbing, or even trigger the complete destruction of the stage. Leave a note in the comments if you have insight into this possibility.

How about venting through the burst disks? These disks were designed to open up if the pressure in a tank reached 270 PSI, give or take. The tank pressures could have reached this level if they heated up, since pressure increases with temperature. The temperature in the tanks was 70 F after the second burn, and a rise of 43 degrees would have raised the pressure up to the nominal burst pressure. Could this have occurred? It seems unlikely. Orbiting the moon every two hours, half of each orbit in searing sunlight and half in freezing darkness, it seems that the heavy tanks would slowly reach thermal equilibrium. The surface of the moon in sunlight actually is quite hot, and radiates a lot of heat out into space, adding to the direct heat from the sun. But it doesn't seem that this would be enough to raise the temperature of those tanks to 110 degrees. Perhaps the hot/cold temperature cycles could lead to failure of the burst disks at a lower pressure? Again, I don't know how to evaluate this.

If the burst disks did open up, I don't think the orbit would have been significantly affected. Due to the "thrust neutralizers" and the tumbling of the stage, the net thrust would have been low. I believe this case would be similar to what occurred when the helium tank vented.

Finally, what about slow leaks that allowed the tanks to depressurize? For the fuel side, at least, this could have occurred through the isolation valves and pilot valves of the shutoff valve assembly. For the oxidizer this path doesn't exist. That sets up the possibility that the ox tanks, still pressurized, could have leaked back through the helium plumbing and into the depressurized fuel tanks. Kaboom!

It bothers me to say it, but I just can't make any solid prediction about what happened to these propellants. Ultimately there are two possibilities. Either the stage reached an inert state, and remained in orbit, or it didn't. The only way to find out is to look, and I hope someday the looking will occur.