# Tianwen-1 DSM final trajectory

A few days ago I spoke about the deep space manoeuvre that Tianwen-1 had executed on 2020-10-09. As remarked in that post, the data we had from that manoeuvre came from extrapolating state vectors from before and after the burn. The state vectors that the spacecraft was broadcasting after the burn most likely came from a prediction rather than from the actual result of the burn. In a few days, we would see a small change in the trajectory as the Chinese DSN performed precise orbit determination and uploaded the results to the spacecraft.

In fact, we saw that change the next day. The figure below is generated in the following way. I have taken the first state vector that we have received after the burn, and propagated its trajectory in GMAT. Then I compute and plot the error in each of the ICRF coordinates between the state vectors broadcast by the spacecraft in the telemetry and this GMAT trajectory. This allows us to see whether the trajectory broadcast by the spacecraft has changed slightly at some point.

As we can see, during the first day the error is close to zero. Afterwards, the trajectory deviates and the error starts growing to several hundreds of km. The new trajectory seems to be stable over the last few days (sorry about the lack of data on the night between the 11th and 12th). This is best shown in the figure below, where the state vector used as a seed to generate the GMAT trajectory is taken from the UTC evening of 2020-10-10. The error is only a fraction of a km. Therefore, we can consider final this new trajectory.

I have updated the calculations I did in the last post to use a state vector from the updated final trajectory. The results don’t change much. The calculations now locate the burn (approximated as an impulse burn) at 15:03:54 UTC with a delta-V of

`[-31.08193895,  40.28872314, 308.12845989]`

in ICRF coordinates, while my previous calculations estimated a burn at 15:03:59 with a delta-V of

`[-31.49477234,  39.29765307, 308.11690616]`

The state vector describing the updated post-DSM trajectory in heliocentric ICRF coordinates and UTC epoch is

`Tianwen1.Epoch = '10 Oct 2020 19:08:50.122';Tianwen1.X = 172262669.5024532Tianwen1.Y = 42536664.64589398Tianwen1.Z = 21989467.534531824Tianwen1.VX = -1.7753279668677469Tianwen1.VY = 25.966616665124505Tianwen1.VZ = 11.810575717885476`

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