Showing posts with label NASA. Show all posts
Showing posts with label NASA. Show all posts

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, January 25, 2020

How could Snoopy be found?

If you've read my earlier posts you have seen how simulations of the Apollo 10 Lunar Module descent stage...aka "Snoopy" that the stage might still be in lunar orbit today, despite widespread expectations to the contrary.

If, indeed, by some miracle the stage orbit never did decay, and is still in orbit, how might we locate it? Experts have told me that optical methods won't work. However, there is another method that has been proven to work, and was used to locate a "lost" Indian lunar satellite in 2017. This method uses radar. Specifically, a dish in Goldstone is used as a transmitter, and another dish in Green Bank is used as a receiver.

In 2017, they knew that the lost satellite was in a polar orbit, so they could aim the radar just off of the moon's pole and wait for it to appear. Objects orbiting the moon come around about every two hours, so even if they were unlucky and the thing had just passed by when they turned on the machine, they would have to watch for two hours at the most.

How about Snoopy? If you read my earlier post about the stage orbit, you know that the stage is in a low inclination orbit...i.e. it follows the lunar equator. So to look for the stage they would aim the beam just above the rim of the moon, right at the lunar equator. And wait. And hope. For two hours at most? Not quite.

The same face of the moon is always facing the Earth. (Mostly.) Using the simulator, we can record the latitude and altitude of the stage as it crosses 90 degrees East longitude, that is, as it comes around from the back side of the moon. Here is a plot showing how that might have looked over 6 months of 2018. I have also drawn in a circle representing the size of the radar beam at lunar distance, which I was told is about 200 km wide.

Each orange dot represents one crossing of the stage above the lunar horizon, so there are two hours between each dot. Some days the stage is coming "over the hill" at a low altitude, below 100 km, and then other days it is coming over at a higher altitude. At this point, after 50 years, although the simulations give an idea that the stage is still in orbit, there is too much uncertainty to know exactly where it might be in its orbit, so you can take the above plot as a kind of "probability map" of how high the stage might be as it comes around on any given orbit. But the key takeaway here is that with a single two-hour radar observation, the stage might pass under the beam.

Aha, I have a brilliant idea! Aim the beam closer to the moon! Unfortunately, an expert told me that they need to aim the beam "several hundred kilometers" away from the surface, so that the receiver doesn't get overwhelmed with reflections of the moon itself. So how long would they need to observe with the radar to either find the stage or conclusively prove it was not there? To answer this question, you need to look at how the altitude at the limb changes with time.

As the moon rotates once each month, always keeping one face towards the Earth, it also rotates under the eccentricity of the stage orbit. So the altitude of the stage as it comes into view slowly varies, over the course of a month, from the lowest part of the orbit to the highest, and back again. So if the first attempted radar observation happened to be on a "low horizon-crossing altitude" day, and found nothing, they could wait half a month and try again. And oh, by the way, when the orbit is crossing the eastern limb of the moon at low altitude, it is crossing the western limb at high altitude, so another strategy would be to observe each equatorial horizon of the moon for two hours on a single night.

Wouldn't it be awesome to locate this amazing artifact after 50 years? Please tweet a link to this post to @NASAJPL if you agree.

Simulating Decades

Using a simulation environment developed by NASA, and a highly accurate lunar gravity model, we have seen how the orbit of the Apollo 10 Lunar Module ("Snoopy") descent stage behaved its first year in lunar orbit. Surprisingly, the simulation gives no sign of the orbital decay and lunar impact that was widely assumed. Now lets see what happens if we run longer simulations, out to 10 years, or 25, or even 50 the present. Surely the stage will decay out of orbit over decades.

OK, so here are the results for a simulation of the first 10 years of the stage orbit. On my laptop, using a GRAIL gravity model with degree/order set to 200/200, it takes about 9 hours to run this simulation. As described in an earlier post I am only plotting the low "perilune" points of each orbit.

We can still see the 25-day cycles of oscillation in the orbit eccentricity that we saw in the first year, but now they start to blur together. The longer 5-month cycles are still easy to discern. But the key point of this plot is that there is no downward trend. Here and there you see the perilune dropping below 20 km, but overall there is no sign that the stage will be impacting the surface any time soon.

If we zoom in to look at the data for year 10, the pattern closely resembles the pattern of the first year in orbit.

So it seems possible that as John Young guided the first Space Shuttle flight to a successful landing in 1981, the stage he had last seen in lunar orbit ten years earlier might still have been orbiting the moon.

All right then, let's run this simulation out to the present day. The 50th anniversary of the mission was in May of 2019, and that is when I first got the hair-brained idea to go looking for this stage.

At the resolution of this image, the individual 25-day oscillations are no longer visible, and the 5-month oscillations are nearly lost. We see the orbit dipping below 20 km four or five times in any given decade. But the key takeaway from this plot is that the simulation gives no hint of any decay of the stage orbit.

And once more, zooming in on the results of the simulation for the year leading up to the 50th anniversary of Apollo 10, there is nothing to distinguish the behavior of the orbit in that year from the first year or the tenth. The same pattern of oscillating eccentricity is present.

It seems possible from this result that on the 50th anniversary of the mission, in May of 2019, the stage was still orbiting the moon, screaming along at over a mile a second, just as easily, as silently, as majestically as it was in May of 1969.

Could this really be true? If the stage were still in orbit, isn't there some way to detect it? That will be the subject of my next post.

Thursday, January 23, 2020

Running Longer Simulations

Last time I posted an XY plot generated by GMAT, showing the stage altitude versus time. If you run the simulation yourself you will notice that GMAT spends a lot of time drawing and redrawing this plot while the simulation is running, and it is not very efficient.

For longer simulations, simulating months or years, I have found that it is better to shut down the XY plot, and instead use the GMAT "report" function to capture the data into a csv data file, which can then be processed after the simulation finishes to generate plots, etc. Here is an example of the GUI to set it up:

The next thing I do for longer simulations is to cut down on the number of data points that go into the report file. I am mostly interested in the minimum altitude, i.e. the perilune, for each orbit, so in the setup of the GMAT mission I build a loop that propagates the orbit around to the perilune and records that point. In that way I get a single line in the report file for every two hours of the stage simulation. That's 12 points per simulated day, or about 4300 per year. That keeps the report files manageable for longer simulations.

The other thing about saving the data to a csv file is that I can import it into a spreadsheet to generate more meaningful plots. Compare the XY plot from GMAT with a plot of the same simulation generated with a spreadsheet program. I overlaid the blue line on the GMAT plot so that you can see how it relates to my plot. 

In my plot I can control the labeling and scaling of the of the axes to make things more clear.

This chart is a bit more abstract, in that it is only showing how the low point of the orbit evolves over time, and ignoring the higher parts of the orbit. On the other hand, the labeling makes it easier to relate to what it means, and its easier to see some important features. The GMAT XY plot appears to show the altitude as "0" in the lower left corner, but that is really "0 elapsed days", and the initial altitude of 20+ km is not clear. In my plot the altitude is much more clearly labelled. The other thing that is much easier to notice is that the perilune is showing an upward trend! Unexpectedly, not only was the stage still in orbit on July 20 when the Eagle landed, its perilune altitude was apparently HIGHER than at any time since staging, two months earlier.

One misleading thing about plotting only the perilune points is that it appears the stage is defying gravity by rising in its orbit, but look back up at the GMAT XY plot. As the perilune rises, the apolune is dropping. Another way of saying this is that the energy of the stage orbit is conserved. A bump in the perilune altitude is always accompanied by the dip in the apolune, and vice versa. The eccentricity of the orbit is oscillating, but the overall average height of the orbit remains the same. Keep that in mind when looking at the perilune plots.

OK, lets run the simulation out a full year to see if the trend of the first two months continues.

Now we see a new aspect of the oscillation of the orbit. The initial upward trend in the perilune doesn't hold up. Over about 5 months, the oscillations drop back down, and the minimum altitude of the stage is actually lower than it was in May, for the first time. But then it starts trending up again, so that by November, while Pete Conrad and Al Bean were down on the surface standing next to Surveyor, with Dick Gordon orbiting overhead, the stage was still whizzing around.

If you were hoping to find a crater marking the final resting place of the stage, as I was when I began this exercise, at this point you are realizing that these simulations won't be very helpful. (Actually there is a pattern in this data, which I will explain in a later post, that did give me some slim hope. What can I say...I am an optimist!) 

Next time I will show what happens when you run the simulations out 10 years and more.

Tuesday, January 21, 2020

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.

Monday, January 20, 2020

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 "", 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.


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 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.