Continued radio monitoring of Chang’e 4 in orbit around the Moon has allowed amateurs to develop an orbital model and propagate that model to predict a tentative landing date and time. Data supplied by radio amateurs Edgar Kaiser, DF2MZ and Paul Marsh, M0EYT suggest a possible first landing window of early January 1st or 2nd, 2019. So is it time to start a friendly betting pool at the office?
Fitting the orbit to Amateur Data
As discussed in earlier posts an orbital model demonstrating the general orbit of Chang’e 4 was developed and as more data has come in that model has been refined. Edgar Kaiser’s data from December 14, 2018, is of particular value as it occurred around the time the plane of the orbit of Chang’e 4 started to eclipse the Moon, wasn’t compensated for the effect Earth introduces on the Doppler effect and Chang’e 4 was relatively inactive that day with Earth ground stations.
The timing of the eclipse of the spacecraft behind the Moon is naturally very sensitive to the RAAN of the orbit and this allowed me to get a fairly decent estimate of the orbital plane while fitting to the data provided. Getting the RAAN right will allow us to be able to propagate the orbit to when it over flies the landing zone with some accuracy.
One challenging factor in using Edgar’s data is that it was reduced from waterfall plots and has scaling errors. The calculated time error is at least +/- 3 minutes. Frequency error is not known to great certainty and after adjusting the frequency offset the data fit the orbit as follows fairly well based on a manual successive approximation approach to fitting the respective Keplerian parameters:
MAT CE4.Epoch = ‘28464.864’;
GMAT CE4.CoordinateSystem = LunaInertial;
GMAT CE4.DisplayStateType = Keplerian;
GMAT CE4.SMA = 2030;
GMAT CE4.ECC = 0.0754900689;
GMAT CE4.INC = 85;
GMAT CE4.RAAN = 220;
GMAT CE4.AOP = 0;
GMAT CE4.TA = 210;
Most of the other data obtained to date has artifacts of Earth in communication with the spacecraft and is difficult to use for orbital analysis purposes.
Propagating the Orbit to Von Karman…
The landing site has been announced as Von Karman crater located on at 179.245 degrees East and 44.451 degrees South on the lunar far side.
The image below shows the landing site illumination and location for January 1st, 2019 which looks good and should produce high contrast visual lighting if that is required.
The following table provides an estimate of over flight timings of the target landing zone for January 1st around 1030UTC based on the above orbit for a landing window:
This timing places the Moon well for the tracking station in Argentina.
Lets consider the look angle at the Earth as surely going to have the Moon well over mainland China to ensure the ground control of the Chinese A-team is on duty. This will certainly be something to consider when testing the confidence of a model as so far in the mission all major events have occurred with China pretty much directly under the Moon.
Now back to reality, this model provides us with a way to find a window based on some observations and those observations and my analysis are far from rigorous, after all I’m an amateur just figuring this stuff out as I do it… I feel that given our orbital estimate is VERY rough and the Chinese will likely refine the orbit a bit will result in a timing of first landing opportunity occurring while the Moon is well over China either on January 1st or 2nd, 2019 which is around 0100-0200UTC for these dates.
Given we know the plane of the orbit pretty well and it is unlikely the Chinese will expend valuable fuel changing it with a significant non-co-planar maneuver to significantly change inclination and RAAN the landing window seems reasonable based on the data we have to date.
As we make more measurements and possibly note correction maneuvers we will update our Chang’e 4 landing estimates for those involved in a pool and placing their bets around the water cooler. Yes, this is what geeks bet on…