As I have mentioned in several posts, the trajectory in which Tianwen-1 was launched had a closest approach to Mars of around 3 million km, so at some point a large correction manoeuvre was needed. We had already seen small manoeuvres TCM-1 and TCM-2, but we were expecting soon enough this large correction, which is called DSM (deep space manoeuvre). Some sources placed the DSM around the beginning of October, while others were more precise and mentioned that it would happen right after the Mid-Autumn festival holiday season, which this year ended on October 8.
After the Bochum 20m antenna was able to acquire the spacecraft’s signal and gather telemetry at 19:09 UTC, we were able to confirm the manoeuvre in the state vectors transmitted by the spacecraft. Paul Marsh M0EYT was also able to receive telemetry confirming this, starting at 18:18 UTC. This post is an analysis of the data.
Since the manoeuvre happened when the spacecraft was not in view from Europe, we have no Doppler data to measure the burn directly. Thus, I have relied only on the state vectors from the telemetry, using the same method as for TCM-2. This method involves propagating forward the last state vector received before the burn and propagating backwards the first sate vector received after the burn. The intersection of the two trajectories gives the moment and delta-V of the burn.
I have used this GMAT script, which uses the following state vectors for the pre-burn and a post-burn trajectories.
Tianwen1_preTCM.Epoch = '09 Oct 2020 04:08:32.068'; Tianwen1_preTCM.X = 172471096.37504846 Tianwen1_preTCM.Y = 38882565.02362641 Tianwen1_preTCM.Z = 20338235.36580359 Tianwen1_preTCM.VX = -1.1782259639276798 Tianwen1_preTCM.VY = 26.05998493933646 Tianwen1_preTCM.VZ = 11.571927755891284 Tianwen1_postTCM.Epoch = '09 Oct 2020 19:09:40.777'; Tianwen1_postTCM.X = 172401001.66836962 Tianwen1_postTCM.Y = 40290822.63279648 Tianwen1_postTCM.Z = 20967750.693616968 Tianwen1_postTCM.VX = -1.4286845530882641 Tianwen1_postTCM.VY = 26.04901896207726 Tianwen1_postTCM.VZ = 11.853820044831242
The results of this GMAT script are processed in this Jupyter notebook. The figure below shows the distance between the pre-burn and post-burn trajectories. The point where the distance is minimal is at 15:03:59 UTC, with a distance of 556 m.
Given that this method of locating the burn approximates the burn as an impulsive burn, it makes sense that it will actually locate the midpoint of the burn. The media quote a burn length of 480 seconds (8 minutes) at 15:00 UTC, so the fact that my study locates the burn at 15:04 UTC seems about right.
The delta-V vector in ICRF coordinates and m/s is
-31.49477234, 39.29765307, 308.11690616
The magnitude of this vector is 312.2 m/s. The engine is said to have a force of 3kN, and the mass of the spacecraft is around 5000kg. Applying this force to this mass for 480 seconds produces a delta-V of 288 m/s. This doesn’t take into account the mass of the fuel spent during the burn (which we don’t know how much was), which would make the produced delta-V somewhat higher. Therefore, the delta-V measured from the state vectors seems to match the data in the press release.
Something interesting is that the angle between this delta-V vector and the delta-V vector from TCM-2 is only 2.8 degrees. This makes me think that both burns happened in exactly the same direction, and that TCM-2 was some kind of test for this large burn. In fact, TCM-2 was also done at 15:00 UTC. Recall that TCM-2 was a short burn of four 120N thrusters for 20 seconds.
After propagating the new trajectory in GMAT all the way to Mars, we see that the new trajectory is in fact quite adequate for Mars orbit injection. The periapsis altitude is around 18000km (give or take 1000km, since it is quite sensitive to the parameters of the propagator, so it is difficult to estimate accurately).
Still, two or three small corrections remain until arrival to Mars around 2021-02-10, to account for all the possible perturbations in the transfer orbit.
It is convenient to remark that the state vector data we are using in this post most likely comes from a prediction done before the burn and doesn’t reflect the actual performance of the burn. In a few days we will most likely see a small change in the trajectory described by the state vectors as the Chinese DSN performs ranging to determine the new trajectory accurately and uploads the data to the spacecraft. We have already seen something like this for TCM-1 and for TCM-2.
Congratulations to the Tianwen-1 team and China National Space Administration for their successful mission, and thanks to the AMSAT-DL people at Bochum and to Paul Marsh for their continuous effort in tracking this mission.