Stage Orbit Basics

In this post I will show the behavior of the stage in the first days, weeks, and months after it was jettisoned on May 22, 1969.

The stage was jettisoned into the "Phasing" orbit, which rose to around 352 kilometers high on the far side of the moon, and dropped down to around 22 km on the near side. The low point in the orbit, called the perilune, was near the Sea of Tranquility where Apollo 11 would be landing in two months.

Using the GMAT simulator I described earlier, you can enter the orbital parameters from the Mission Report, Table 6-II, and run the simulation for a single orbit. First off, here is the GroundTrack view that GMAT generates:

You see the stage in a low inclination orbit, very closely following the lunar equator. I added a small red dot showing where Apollo 11 landed, and you see that they passed just south of that site, just right of the center of this plot.

Here is GMAT's "Default Orbit View" of the same orbit, with a view from above the moon's north pole.

You see that the orbit drops down closer to the surface on the lower left, and then rises higher around on the far side. The red axis points towards Earth, and the blue axis is the north polar axis. In this view the orbit looks very nearly circular, which is indeed the case. The eccentricity of the orbit is actually not so high, relatively speaking.

Finally, here is a GMAT X-Y plot of the stage Altitude versus elapsed seconds.

Now the low and high points of the orbit are much more exaggerated. The "Altitude" is relative to the "mean lunar radius", which is sort of like "sea level"...the size the moon would be if it melted into a perfect sphere. (This altitude does not take into account lunar terrain.) The orbit drops down to within 22 km, and then rises up to around 350 km. (BTW, that "0" down in the lower left corner is zero seconds, not zero km.) This is one complete orbit, and the total time, i.e. the period, is around 7611 seconds...just over 2 hours.

So what happens when you run the simulation out longer? Here is a similar plot showing the altitude over the first 5 days.

You see the same highs and lows, but a new pattern begins to emerge. The lows are slowly getting higher, while the highs are getting lower. The orbit is becoming more circular, and less eccentric. This seems to be one of the first reasons that the stage does not quickly decay out of orbit. Later I will post the results of a study that shows more about this pattern.

OK, now let's run even longer, simulating the first 60 days in orbit. This will put the simulated time into late July, 1969, when Apollo 11 returned to the moon.

The first thing to notice is that the stage is still in orbit at the time of the Apollo 11 landing. Something might have happened since then to bring the stage down, but I feel quite certain that it was still orbiting the moon during Apollo 11. Then notice the pattern of oscillation in the eccentricity. The orbit becomes more circular for the first 12 days or so, but then starts to become more eccentric again. After about 25 days the orbit is nearly back to its original apolune/perilune. (But not quite, you notice.) This 25 day period of oscillation of the eccentricity is a pattern that will continue, and when I run simulations out to the present, this same 25 day oscillation remains a key feature of the stage orbit.

How to run simulations

When I started looking for the stage, I had no idea how to go about it. I assumed there were good simulators out there, and I understood that there were good models for lunar gravity. I just didn't know where to find these things.

Eventually I ran across a post discussing the merits of different simulation environments, and learned about GMAT, or the "General Mission Analysis Tool". This is a free, open-source package, developed by NASA, that has been used to design real missions. Since August of last year I have been learning the ins and outs of this environment, and using it to search for Snoopy. Unfortunately the acronym for this package is shared with another important "GMAT", the test that people take to get into graduate school. If you go searching the internet for this package, you may find you have better luck spelling out its name in full.

You can download GMAT here. There is a youtube channel with tutorials on how to use it here. Documentation for GMAT exists in various places, but I find this to be the easiest to use. As the name implies, it is a general tool, that can simulate objects in Earth orbit, Mars missions, etc.

One of the first things you will want to do with GMAT for any lunar simulation work is to upgrade the lunar gravity model. The gravity field of the moon is notoriously "lumpy", due to mass concentrations, or "mascons". The gravity model accounts for this lumpiness by decomposing the field using spherical harmonics, and there are a few things you need to know about it. The model that is installed by default is a decent model, named LP165P, but you should upgrade to a GRAIL model. GRAIL models derive from data gathered by a pair of lunar satellites, named Ebb and Flow, that tracked each other around the moon for several years. The resulting data has been processed into a series of ever-more-detailed gravity models. I have been using this one. In order to use it you download the file, save it as "jggrx_0420a_sha.tab", and copy it into the lunar gravity file directory in your GMAT installation. On my installation it is at ...\AppData\Local\GMAT\R2018a\data\gravity\luna\

This image was derived from GRAIL data and shows the local "lumpy" variations in the moon's gravity field. The "lumps" are likely from heavy objects that hit the moon and then stayed close to it's surface, creating mass concentrations or "mascons"

The model above has "420" in the name because it can run with the degree and order set as high as 420. This is how many spherical harmonics can be used to simulate the field, and more is better in terms of the fidelity. However, more is also slower, in terms of simulation time. I once ran a simulation with a high-fidelity model, with the degree and order set to 1000. This simulation ran for about a week on my computer, simulating a month in orbit. This is too slow for most of what I do, and it does not seem to be required. By running the same simulation with higher degree/order, I have noticed that there are diminishing returns, i.e. very small differences in the results, above degree/order setting of 150/150.

Introduction

The descent stage of the Apollo 10 Lunar Module ("Snoopy") may still be in lunar orbit today. This defies conventional wisdom. It goes against all expectation about how things behave in lunar orbit. It is the last thing I expected to find when I set out to look for an impact crater that I assumed would be the final resting place of the stage. Nonetheless, this is what simulations of the stage orbit show. In this blog I will show how I arrived at this surprising conclusion.

This picture of the descent stage ladder and footpad comes from the 16mm "DAC" film taken on May 22, 1969, during the dramatic moments when the stage was jettisoned. 

Snoopy's tail was jettisoned into lunar orbit on May 22, 1969, during a daring mission that paved the way for the first moon landing less than two months later. Apollo 10 was the first mission to take a Lunar Module to the moon; the first test of all the hardware and procedures. All except landing. It was the first demonstration of Lunar Orbit Rendezvous, the risky, radical, "sine qua non" of Apollo. 

When I started looking for the stage, I was expecting a quick orbital decay. Everything I read said that's what happened. I thought this would mean less uncertainty about the impact point...a smaller search area. So I was disappointed when I started running simulations, showing that the stage stayed in orbit for months. That was not helpful for finding a crater. My remaining hope was that some high piece of lunar terrain might have snatched the stage if it slowly drifted down to lower and lower altitudes. Perhaps I could focus the search on lunar mountaintops. So I kept looking.

The stage orbit was unusual, in terms of Apollo orbits. In order to demonstrate undocking, firing the LM descent engine to approach the moon, and then firing the ascent engine for the rendezvous, NASA had a problem. Without any landing, they needed a way to arrange for the right timing of the maneuvers. The descent would put the LM in a lower orbit, moving it ahead of the Command Service Module. (The "CSM".) Demonstrating the ascent and rendezvous required that the CSM be leading the LM. The solution was the "Phasing" maneuver. This special burn, never performed by any other Apollo mission, would raise the high side of the LM orbit to 190 nautical miles above the far side of the moon, slowing down the LM's orbital period enough to allow the CSM to overtake it.

This plot of the LM position relative to the Command Module, from mission planning documents, shows how the "Phasing" burn pushed the LM into a higher orbit, so that it would drop behind the CM, giving the right alignment for rendezvous.

While the LM was in the Phasing orbit, 12 n.m. at its low point, and 190 at the high point, the descent stage was jettisoned, with an initial velocity relative to the ascent stage of around 2 feet per second. (Both parts were zipping along at a mile a second at this point.) The goal was to kick the stage forward, but unexpected problems with the attitude controls during staging altered this, and the stage was pushed "upward" relative to the local horizontal at the time of staging. (Notice that the moon is "upside down" in the picture above taken during staging...it wasn't supposed to be this way.) Regardless of the extra drama, ten minutes later, the stage was at a safe distance, and the crew fired the ascent engine, slowing their velocity and lowering the high side of their orbit, putting them on track for a successful rendezvous and docking. The stage was left behind in the phasing orbit. It was assumed that this orbit would quickly decay, impacting the moon within days or weeks.

As I starting running simulations of the stage orbit, the hope for a quick demise did not pan out. I ran the simulations out longer and longer, out 10 years, and still the stage kept going. Finally I decided to run the simulation out to the present. This took about 40 hours on my laptop. At the end, the stage remained in orbit all the way to the present, with no sign of decay or orbital instability. As I build out this blog I will share more details, and show you how to try it to see for yourself.