Tianwen-1 TCM3 final trajectory

A few days ago I posted about TCM3, the fourth trajectory correction made by Tianwen-1 so far. After some days, the Chinese DSN has performed precise orbit determination and updated the on-board ephemerides, so that we are now seeing the final trajectory in the telemetry state vectors.

The figure below shows how the state vectors have been updated a couple of times following the TCM, as the DSN computes and uploads an improved trajectory solution. I have plotted this graph in the following way: I have taken the first state vector received after TCM3, on the UTC afternoon of 2020-10-28, and used it to propagate a trajectory in GMAT. The plot shows the difference between the state vectors and the GMAT trajectory.

TCM3 happened on 2020-10-28 at 14:00 UTC, so the reference trajectory computed in GMAT corresponds to the trajectory of the state vectors immediately following the TCM. These are based on a prediction of the burn performance, rather than on the actual results. The graph above shows clearly two changes in the trajectory, one on 2020-10-29, and another one on 2020-11-01.

Since we have already seen the same trajectory for three days without updates, I am confident that this trajectory is now final. The latest state vector we have today is

[0163f5396aeb] 2020-11-04 03:25:57.092300 160383830.37880394 94290296.68475787 45404213.83552203 -9.17821106231485 22.96506090856966 10.332601544380973

As always, this gives the UTC timestamp and the ICRF heliocentric position and velocity coordinates in km and km/s respectively.

I have re-run the calculations in the previous post by back-propagating a state vector from the UTC evening of 2020-11-01, which already belongs to the final trajectory. The change in delta-V in comparison to what I should in the previous post is small. The new delta-V is 2.13 m/s rather than 2.09 m/s, and the components have changed around 5%. The detailed calculations and data can be found in the updated Jupyter notebook.

Tianwen-1 TCM3

On 2020-10-28 at 14:00 UTC, Tianwen-1 has made its third trajectory correction manoeuvre. This has been the next manoeuvre after the deep space manoeuvre at the beginning of October. According to the press release, this was a firing of the eight 25N thrusters intended as a minor correction and as a test of this propulsion system. I haven’t found the duration of the burn in the news.

I have followed the same method as in previous burns to compute the moment of the burn and the delta-V vector by extrapolating the telemetry orbit state vectors received by AMSAT-DL in Bochum before and after the burn. This extrapolation locates the burn at 14:02:28 UTC. Note that this time is an approximation for the mid-point of the burn.

The delta-V vector was, in m/s

[-0.6575566 , -0.11513034,  1.97535319],

and the magnitude was 2.09m/s. Assuming a mass of 5000kg and eight 25N thrusters, it would take a burn of 52 seconds to achieve this delta-V.

Update 2020-10-30: according to this news article, the duration of the burn was 42.8 seconds which is some 18% smaller than my estimate. Note that my estimate didn’t take into account the mass of fuel spent by the deep space manoeuvre, which I estimated to be 457kg (giving a decrease in mass of 9%).

Apparently this burn has lowered the periares height significantly in comparison to the trajectory following the deep space manoeuvre, which was around 18000km. Thanks to Achim Vollhardt for noticing this. It’s difficult for me to give a good estimate of the new periares height, because it is quite sensitive to orbit perturbations. I’ve obtained anything between 30 and 800 km by enabling and disabling solar radiation pressure in the GMAT propagator, and we don’t have a good estimate of the spacecraft’s cross-section and reflection coefficient.

The figure below shows one of the GMAT simulations. Note that the periares is near the equator, which is good for insertion into a low inclination orbit.

Periares passage in GMAT

Keep in mind that according to the media still one more trajectory correction manoeuvre remains and that the data used in this post comes straight from the spacecraft’s telemetry, and as such is most likely based on a prediction of the burn rather than on the actual performance of the burn. In a few days, I will publish a new post when the Chinese DSN perform precise orbit determination and upload updated orbital information to the spacecraft.

The data and plots for this post can be found in this Jupyter notebook.

Tianwen-1 post–TCM-1 state vectors

Yesterday I reported about Tianwen-1’s first trajectory correction manoeuvre, TCM-1. In that post I commented the possibility that the updated state vectors that we saw on the telemetry after TCM-1 might come from a prediction or planning rather than take into account the actual performance of the burn.

The figure below shows the error between the state vectors collected after TCM-1 over the last two days, and a trajectory propagated in GMAT, using the following state vector, which is one of the first received after TCM-1.

[0151059eb9ea] 2020-08-02 00:17:06.711400 100230220.21360767 -106145016.11787066 -45441035.07405791 25.581827920522485 18.240707152437626 8.567874276424218

We see that on the UTC night between August 1 and 2 the state vectors deviate very little from the GMAT trajectory. However, on the UTC night between August 2 and 3 we see a slightly different trajectory in the state vectors. We have no data in between, as the spacecraft is not visible in Europe, so we don’t know the precise moment of change. The gap in telemetry around 2020-08-03 00:45 UTC is due to a transmission of high-speed data.

It seems reasonable to think that after TCM-1 the Chinese DSN performed precise ranging of the spacecraft to determine the new orbit accurately and then uploaded a correction to the state vectors on-board Tianwen-1.

The state vectors from last night all describe the same trajectory, as shown in the plot below which uses

[0151322e67d0] 2020-08-02 21:03:08.078400 102132184.96868199 -104770375.00352533 -44795830.46284772 25.29849580646669 18.532513218789806 8.692135086385246

to propagate a trajectory in GMAT. There is a small jump of a few hundred meters at some point. We usually see one or two these jumps per day, but we don’t understand well why they happen.

The trajectory according to the state vectors from 00:17:06 and from 21:03:08 are very similar. For example, at the closest approach to Mars they only differ in 1197km. For comparison, the difference between the new trajectory and the pre–TCM-1 trajectory is 126529km (again, at the closest approach to Mars).

I have generated a new table of right-ascension, declination and distance coordinates based on the updated state vectors. Note that this table doesn’t include light-time delay to the spacecraft.

Thanks to AMSAT-DL‘s Bochum observatory team and to Paul Marsh M0EYT for their continuous effort in tracking Tianwen-1. The data used in this post has come from their observations.

Tianwen-1 TCM-1

On 2020-08-01 23:00 UTC, Tianwen-1 made its first correction manoeuvre, called TCM-1. The manoeuvre was observed by Amateur trackers, such as Edgar Kaiser DF2MZ, Paul Marsh M0EYT, and the 20m antenna at Bochum observatory, operated by AMSAT-DL. The news of the successful manoeuvre appeared in Chinese media, and in the German Wikipedia article for Tianwen-1 (thanks to Achim Vollhardt DH2VA for sharing this information).

Since Tianwen-1 transmits its own real time orbit state vectors in the telemetry, by comparing the vectors transmitted before and after TCM-1, and also by studying the Doppler observed by groundstations on Earth, we can learn more about the manoeuvre.

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Tracking Tianwen-1’s orbit to Mars: part II

Yesterday I published a post explaining how Tianwen-1 is transmitting real time state vectors for its own orbit in its telemetry and how we’ve used those to propagate its orbit and track the spacecraft with the Bochum observatory 20m dish. However, there seemed to be some problem in the way we were interpreting the state vectors, since the ephemerides derived from these had a pointing error of a few degrees when compared with observations from Bochum and other smaller Amateur stations.

As of writing that post, I believe I have found the problem. It has to do with the way that the timestamps from the state vectors are interpreted. After correcting this problem I am getting an orbit that matches the observations well. Here I explain this problem and show some more details about the corrected ephemerides.

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Tracking Tianwen-1’s orbit to Mars

Last Thursday 2020-07-23 at 04:41 UTC, Tianwen-1, a Chinese mission to Mars consisting of an orbiter, a lander and a rover, launched from Wenchang. Usually, I would be posting an analysis of a recording of the telemetry signal, made by Paul Marsh M0EYT or another of my Amateur DSN contributors, as I did a few days ago for the Emirates Mars Mission. However, something amazing has happened that has kept me quite busy. Rest assured that the analysis of the signal will come in a future post, but here I’m going to tell a story about Tianwen-1’s orbit.

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Advances with delta-range and delta-range rate observations in GMAT

A month ago I started modifying the GMAT EstimationPlugin to support delta-range observations. This work is needed in order to perform orbit determination with the VLBI observations that we did with DSLWP-B (Longjiang-2) during its mission. Now I have a version which is able to use both delta-range and delta-range rate observations in simulation and estimation. This is pretty much all that’s needed for the DSLWP-B VLBI observations.

The modified GMAT version and accompanying GMAT scripts for this project can be found in the gmat-dslwp Github repository. This post is an account of the work I’ve made.

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Simulating delta-range observations in GMAT

During the DSLWP-B (Longjiang-2) mission, we made a number of VLBI observations of the spacecraft’s UHF signal by performing GPS-synchronized recordings at Dwingeloo (The Netherlands), Shahe and Harbin (China), and Wakayama (Japan). The basic measurement for these observations is the time difference of arrival (TDOA), which measures the differences between the time that it takes the spacecraft’s signal to arrive to each of the groundstations. This can be interpreted in terms of the difference of distances between the spacecraft and each groundstation, so this measurement is also called delta-range.

One very interesting practical application of the VLBI observations is to perform orbit determination. The delta-range measurements can be used to constrain and determine the state vector of the spacecraft. This would give us an autonomous means of tracking Amateur deep-space satellites, without relying on ranging by a professional deep-space network. Even though the measurements we made showed good agreement with the ephemerides computed by the Chinese deep-space network, during the mission we never ran orbit determination with the VLBI observations, mainly due to the lack of appropriate software.

While GMAT has good support for orbit determination, it doesn’t support delta-range measurements. Its basic orbit determination data type is two-way round-trip time between a groundstation (or two) and the satellite, as shown in the orbit determination tutorial.

I have started to modify GMAT in the gmat-dswlp Github repository to implement the support for this kind of VLBI observations. As a first step, I am now able to create and simulate delta-range observations.

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Trying to find the DSLWP-B crash site

As you may well know, DSLWP-B, the Chinese lunar orbiting Amateur satellite crashed with the Moon on July 31 as a way to end its mission without leaving debris in orbit. I made a post with my prediction, which showed the impact point southeast of Mare Moscoviense, in the far side of the Moon. Phil Stooke was more precise and located the impact point near the Van Gent crater.

Our plan is to get in contact with the LRO team and try to find the crash site in future LRO images. We are confident that this can be done, since they were able to locate the Beresheet impact site a few months ago. However, to help in the search we need to compute the location of the impact point as accurately as possible, and also come up with some estimate of the error to define a search area where we are likely to find the crash. This post is a detailed account of my calculations.

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