On January 3, 2019, 02:26 UTC Chang’e 4 landed on the far side of the Moon ending over a fortnight of tracking the trajectory of the mission as it left Earth, arrived in lunar orbit made orbital adjustments and then finally landed. I discuss the results of our tracking attempts focusing mostly on the final analysis where the landing time was predicted and compare that to a final analysis performed after reviewing the crumbs of data shared from Chinese state media videos to see how close we got.
Orbital Changes in Lunar Orbit
Chang’e 4 made two significant orbital changes while in orbit around the Moon that where not related to the final decent and landing. It’s initial orbit around the Moon was 100x400km. It changed it’s orbit as follows:
December 26th, 2018 – 100x100km
December 30th, 2018 – 100x15km
During these phases of operations we where able to compare the orbit and determine the relative orientation of the orbital plane and get a decent sense of the location of the space craft along the plane using Doppler analysis. I discuss much of the early details in previous posts. What was a challenge was determining if we had the true RAAN of the orbit identified. I.e. did we guess wrong and was our value 180 degrees out.
From the Doppler data prior to the Dec 30th maneuver it was very challenging to determine the correct RAAN and after getting confirmation from Chinese state media of the Dec 30th maneuver I posted this element set based only on Doppler data from prior to the maneuver:
Epoch (MJD GMAT)=28482.58428964
But afterwards it became very clear due to subtle changes now observable in the acquisition and loss of signal displayed on the Doppler data obtained after the maneuver that I had made the wrong guess on the RAAN and was 180 degrees out. After adjusting it and the Argument of Periapsis and True Anomaly we had a pretty good estimate of the orbit which I posted to Twitter as we awaited confirmation of a landing.
Epoch (MJD GMAT) = 28482.58428964
SMA = 1794.5
ECC = 0.023683477
INC = 87.0
RAAN = 65.0
AOP = 225.0
TA = 35.0
A Few Notes on the Process…
Fitting the Doppler data to develop the above orbital elements was a tedious and time consuming process. Namely because there are no convenient tools that have been written that are publicly available to perform or automate the fitting process. The following sections detail our challenges and provide some incite into the process.
Collection of Doppler Data
Doppler data was primarily collected from the radio tracking station operated by Edgar Kaiser @DF2MZ in Northern Germany. Paul Marsh @UHF_Satcom in England also contributed key data sets.
Collecting Doppler data from a satellite in lunar orbit is no easy feat. There are no off the shelf radios or antennas that amateurs can reasonably access to do this type of work so it requires considerable skill to collect the unique parts, assemble the station and operate it.
These station operators don’t normally collect Doppler data of analysis of deep space radio signals so the methods they had to provide their data differed. This create another significant technical step in the project.
Doppler Data Reduction
Edgar provided data in the form and images called a waterfall display. A waterfall display provides a time and frequency plot of a radio signal and is used by the operator of a station to visualize the radio signals they are hearing. While a highly convenient way to observe radio signals in real time and make operational adjustments with reducing data from a screen capture of these waterfall display produced a challenge for our team.
This is where a member of the SatNogs team offered support to create software that could reduce the Doppler data from the images Edgar generated into a tabular format conducive for analysis.
Fabian P. Schmidt, known as Kerel in the SatNogs community, developed a number of techniques and a process to confirm the quality of the data he reduced from Edgar’s waterfall images and in the process also created an accessible archive of those techniques and data in the open source spirit of the Libre Space Foundation.
Meanwhile, Paul Marsh was providing tabular data from his station; however, the format and volume of data didn’t lend itself to a simple conversion from his format to the format we needed to analyze it without crashing Excel… We needed to convert the time to Modified Julian Date, add an offset to get the correct frequency etc. So I spent a day or so learning Python and wrote a script to convert that data into what we call STRF format.
2018-12-15 19:10:02 470002746 -81.54 dB
2018-12-15 19:10:03 470002730 -82.42 dB
2018-12-15 19:10:04 470002711 -83.64 dB
58467.798715 8470002746.000 -81.540 9996
58467.798727 8470002730.000 -82.420 9996
58467.798738 8470002711.000 -83.640 9996
Modeling a Satellite in Lunar Orbit
With the data now in a format that analysis could be done we needed a technique and the tools to properly model a satellite in lunar orbit. Fortunately NASA provides a wonderful tool free of charge called General Mission Analysis Tool or GMAT. With GMAT one can easily create scripts to model a mission in space even outside of the Earth’s gravity well. So it was capable of modeling a satellite in lunar orbit.
Unfortunately, it doesn’t allow one to compare their Doppler data directly with it’s output options.
But as luck would have it Daniel Estévez, @ea4gpz, and I had collaborated on tracking DSLWP-B while in lunar orbit after it and Queqiao where launched in May of 2018.
Daniel developed a wonderfully elegant set of scripts to compare Doppler data to the expected Doppler from a given lunar orbit model from GMAT. This and writing a couple of different scripts for GMAT myself allowed me to fit the Doppler data to orbital parameters and then propagate the results over time to determine if it all made sense and ultimately to make ‘educated’ guesses at the landing time.
Manual Successive Approximation
If you’ve ever tuned something like the ignition system in a car, a radio transmitter or even aimed a TV antenna at something you probably have used the technique called successive approximation to find the ‘best fit’ for the given problem.
In a nutshell, you make a guess at the final answer and observe the result, if undesirable then adjust the other way in a controlled systematic manner and observe the result. If the result got better but was wasn’t fully acceptable yet then half the adjustment you just made as you adjust back the other way. As you successively reduce the adjust the closer you get to the correct final answer (hopefully).
This technique works well in systems with a small number of variables. However, in a system where there are six independent variables (seven if you include time) then it can get a little hairy.
What I did was constrain the SMA and Eccentricity to the values calculated from Kelper’s equations using the information provided in Chinese public statements. So two variables didn’t need to move. Next, the inclination was known to be polar. Nothing is usually perfect so I had a look at the inclination of LRO a known lunar satellite in polar orbit and there was tons of data on how it’s orbital inclination oscillates from 85-89 degrees over the years. Given that changing the orbit plane is fuel intensive there was a good chance it wouldn’t change much so I decided to constrain my guess to 87 degrees.
This left only the Epoch and three other elements left to constrain from the Doppler data a much more manageable exercise but still very time consuming.
So using my understanding of orbital dynamics and what little public information was released I iterated the remaining elements until I was able to get a reasonable fit to the Doppler data we obtained.
It wasn’t until the last maneuver had occurred that I was able to see the correct orientation of the RAAN value and came to an orbit that fit all of the elements reasonably well and placed Chang’e 4 in the vicinity of the published landing site when all the rumours where swirling of when it was going to land.
The final challenge in the data was the fact it was often skewed or distorted by communication with Earth and multiple ground stations. This effectively prevents ever getting or knowing when you are looking at a pure Doppler only affected signals. It takes time and patience to find those elements of the data that you feel you can trust most to make your judgements on. All I can say is that just required a few years of experience with teasing info from Doppler data to do that…
The Final Comparison
Even after the successful landing of Chang’e 4 on the Moon, China has not released much in the way of real information about the mission. Coverage of the mission on state media was limited and we are left to interpret some video of the main control room at the time of landing to come to a final reasonable estimate of the orbital elements of Chang’e 4 before it landed.
A wide angle and blurry image was my first clue toward a final state vector for Chang’e 4 before it began descent.
The above image shows the time (Beijing local time) and the location of the spacecraft. And as it turns out the moment it would have departed from the 100x15km orbit to begin it’s descent to the landing site.
Another video segment at a different time in the mission sequence gives us the next important clues. The white dot must be something important as this, the spacecraft location and the landing site are marked.
This loosely translates to “power decline downhill point”. With my very limited knowledge of Chinese, I know that most words are two characters long so individual translation of these words gave me this translation.
So it’s a point that has some power going on and decline downhill… Seems pretty clear that is the perilune of the 100x15km orbit and the spot one would start a powered descent to a landing.
Conveniently they choose to have the 30 degree south latitude indicated which happens to be right where the mark is just east of the prime meridian line. I make this to be about 178.25 E, 30 S.
Also notice there is an inclination to the orbit it’s not perfectly polar (90 degrees). So my guess at 87 degrees seems reasonable by the method of inspection. The spacecraft’s location adjacent to Aitken Crater makes for a handy confirmation of position to give me some confidence in my assessment.
Next step was to go back to my orbital model and make some minor adjustments to the RAAN to shift the plane to fit this timing by two degrees. Next, I adjusted the Argument of Periapsis to match this point and finally tweaked the True Anomaly to place the spacecraft in the right position in the orbit at this time.
The following images show the moment described above after making the adjustments to the Doppler described orbital model.
Here is the final bit of Doppler data fit to the orbit. The stretched amplitude is due to the spacecraft being locked to probably two different Earth stations while data was collected. This as noted earlier presented a challenge for analysis.
Here is a table providing a comparison of the final orbital elements giving my final guess before landing and that produced as a result of this analysis.
Given the challenges of this exercise which included but are not limited too:
- Little or now public information from China,
- Limited number of radio stations capable of obtaining data,
- Difficulties in getting data into a usable format,
- Data being skewed by communication and ranging activities of the spacecraft,
- Time intensive manual approach to fitting the orbital elements to the data.
It shows that using amateur means a satellite can be reasonably accurately tracked while it is in orbit around the Moon. I believe given these experiences the next lunar mission results will only get better.
I also believe these techniques can be extended to other missions around the planet’s and asteroids that are currently be monitored by amateurs as well and could greatly enhance the learning of orbital dynamics in the radio astronomy and amateur radio hobbies with so many interesting targets to study.
Thanks again to everyone that helped, sent notes of gratitude and encouragement to keep going throughout the orbital phase of Chang’e 4 missions.
And finally, congratulations to the people of China on this achievement!