Last Sunday September 20, around 14:15 UTC, I published a post with an update on Tianwen-1‘s attitude during the mission. I mentioned that we were expecting to see an attitude change to prevent the high-gain antenna from exceeding its maximum slew range. I also mentioned that we were expecting the second trajectory correction manoeuvre (TCM-2) to happen sometime in September according to Chinese media.

Apparently the timing of my post was quite appropriate, because shortly afterwards, at 15:00 UTC (23:00 Beijing time), Tianwen-1 executed its TCM-2. However, news of this didn’t appear until the next morning, at 7:00 Beijing time (23:00 UTC). Unfortunately the manoeuvre happened when the spacecraft wasn’t in view from Europe, so we don’t have Doppler data as for TCM-1. In any case, we can use the state vectors transmitted in the telemetry to study the manoeuvre, by comparing the vectors received before the burn and those received after the burn. In this post I look at this and check if it matches the news report.

To study the burn, we take the last state vector received by Bochum 20m antenna before the burn, which is

2020-09-20 02:43:09.781400 168604889.56909633 -4841002.675037454 819828.1462429519 6.040570180355337 26.755173581997227 12.004667204918906

and the first state vector received after the burn, which is

2020-09-20 21:24:11.336300 169000645.7112682 -3041127.403723257 1627310.2280670837 5.727235944182077 26.76315619215232 12.006614891956165

Using GMAT, we can propagate the first vector forward in time and the second vector backwards in time and the two trajectories will approximately meet at the location and moment when the burn was made. By subtracting the velocity vectors of the two trajectories at that instant, we obtain the delta-V of the burn.

The GMAT script used for propagation is here, while the output files with the trajectories are in this folder. These output files are then loaded into this Jupyter notebook, which is used to do the calculations and plots.

The figure below shows the distance (difference in position vectors) between the two trajectories with respect to time. We see that the two trajectories meet at 15:00 UTC and diverge before and after this moment.

In fact, the moment when the distance is smaller is at 14:58:10 UTC, which is not too bad taking into account that the trajectories are computed in one minute steps and that this kind of calculations, as well as the news report, are not going to be very exact. The distance in this moment is 450m.

The delta-V obtained by subtracting the velocity vector of the post-TCM trajectory and the pre-TCM trajectory is, in ICRF coordinates and m/s

[-0.2795918 , 0.68354296, 4.23141581]

It is quite interesting that this is almost aligned with the Z axis. In fact, the angle between the delta-V vector and the Z axis is 9.9 degrees.

The magnitude of the delta-V vector is 4.3m/s, so we see that this was a small burn. In fact, the Chinese media state that

The robotic spacecraft ran its four 120-Newton thrusters for 20 seconds at around 11 pm after receiving control signals from its ground controllers, the administration said in a statement on Monday morning.

Source: Mars probe makes midcourse maneuver, at chinadaily.com.cn

This seems another test of the propulsion system. In fact, in TCM-1 the 3kN main thruster was fired for approximately 25 seconds, and this was described as a test by the Chinese media. Here we learn that Tianwen-1 has four auxiliary thrusters besides the main thruster.

It is interesting to check whether the delta-V we have computed from the state vectors matches the news report. The mass of the spacecraft is around 5000kg (this is mentioned in the same news article, for instance), so a force of 480N for 20 seconds would produce a delta-V of 1.9m/s, which is much less than the delta-V we have calculated.

Where could this difference come from? Well, I think it might have to do with the firing of ullage motors before the burn. These motors are used to accelerate the spacecraft slightly and drive the fuel to the bottom of the tank. Usually, the delta-V provided by the ullage motors can be disregarded in comparison with the much larger delta-V produced by the burn of the main engines. However, for such a short test burn, the ullage motors can produce a significant fraction of the total delta-V.

In fact, in TCM-1, where we observed the firing of the ullage motors in the Doppler of the X-band telemetry signal, we saw that a firing of the ullage motors for 194 seconds before the main burn produced a delta-V of approximately 2.2m/s (so the force of the ullage motors was around 50N). If we assume the same kind of ullage motor firing in TCM-2, we have a total delta-V of 4.1m/s between the 50N ullage motors and the four 120N thrusters. This is much closer to the value of 4.3m/s obtained with GMAT.

Since the delta-V of this manoeuvre is small, the trajectory hasn’t changed significantly. In fact, the closest approach to Mars is still 3 million km, roughly the same as during all the mission so far. Therefore, we are expecting another TCM that alters significantly the trajectory to drive it closer to Mars. In the news article there is a figure where future “Deep space maneuver” and “Third mid-course correction” appear, so it could be one of these.

It is quite interesting to note when these manoeuvres are being performed. Since apparently there is nothing very critical about there timings, one could expect that they are performed during normal business hours in China, to avoid having the controllers doing extra shifts. However, this is not the case: TCM-1 was done at 07:00 Beijing time on a Sunday and TCM-2 was done at 23:00 Beijing time also on a Sunday.

When doing any speculation about these, it is important to keep in mind that the Chinese DSN operates a world-wide network, so the local time in China might not be so important. Incidentally, the times at which both TCM happened were moments of the day in which the elevation of Tianwen-1 as seen from Beijing was quite high (above 50 degrees), although this may well be a coincidence.

Congratulations to the Tianwen-1 team and the China National Space Administration for this successful mission