By Duncan Steel 09/09/2019

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The Indian lunar lander and the rover it was carrying appear to have been destroyed when they plummeted to the surface after contact with them was lost when about 2 km up and a few minutes from the planned soft touchdown. Here I examine what one can deduce about what happened, and when, from the TV coverage of the situation in the mission control centre. 

Earlier today I posted an update to my blog concerning the space mission Chandrayaan-2 which had been sent to the Moon by the Indian Space Research Organisation. That mission has three component parts: an Orbiter, which is still working well, a lander named Vikram, and a small rover vehicle named Pragyan which was to be deployed once Vikram had landed safely. Unfortunately it seems that contact was lost with the lander when it was still more than 2 km above the lunar surface, and so one presumes that both Vikram and Pragyan have been destroyed. In that update I estimated, based on various assumptions, the speed with which the pair would have struck the surface of the Moon, the answer being about 300 kilometres per hour. One cannot, therefore, hold up much hope for their survival unless my assumptions were incorrect; of course I sincerely hope that they were, and that somehow an autonomous system brought the lander gently onto the surface.

In the present blog post I offer some further analysis of what may have occurred.

News media coverage of the unfortunate (apparent) crash of the Vikram lunar lander continues, though that coverage seems to lack some core information about what happened. ISRO personnel have (quite rightly) said that the available data need to be interpreted.

In fact even sat here in New Zealand it is possible to gather some useful data from the YouTube video of the events as played out in the Mission Operations Complex at ISTRAC (ISRO Telemetry, Tracking and Command Network) in Bangalore. Here is my interpretation.

To drop Vikram from lunar orbit down onto the surface a series of rocket motor burns were scheduled, causing braking and therefore a descent. The initial orbital (horizontal) speed of Vikram was above 1,600 m/sec, and that needed to be reduced essentially to zero so as to enable a soft (vertical) landing.

For the sequence of interest at present we begin with the Rough Braking phase that cut the major part off of the orbital speed; that brought Vikram down to an altitude of 7.4 km. There is then essentially a gap (the Coasting phase) until the Fine Braking was begun at an altitude near 5 km. That phase was planned to bring the lander down to an altitude of only 400 metres, whereupon it was to hover on its rocket engines whilst an onboard optical system selected the best place to land.

In the YouTube video it happens, rather conveniently, that the time marks on the recording are precisely one hour and 31 minutes in excess of the ISTRAC time marks which label the mission phase as an elapsed time since the Rough Braking was initiated; thus 1:40:21 on the video implies 9 minutes and 21 seconds after the de-orbiting began. The Rough Braking ends on the video at about 1:42:00 (note the applause subsequent to 1:42:10 and continuing for about 40 seconds).

A note on the times indicated and what ‘now’ means: On September 7 the Moon was slightly closer to apogee than perigee, around 390,000 km from Earth. The actual distance needing to be travelled by any radio signal from Earth to Vikram would depend on the location of the ground station and also the small time delays in the electronics. I have not looked it up, but it may well be that the limited longitude range of ground stations operated by ISRO mandated that they use a communications satellite to relay commands from ISTRAC to Vikram, introducing further delays.

The overall delay from uploading any command from ISTRAC to Vikram was therefore about 1.5 seconds, with a similar delay in receiving data back from the probe. This means that one is never seeing what is happening on the probe instantaneously, and it also indicates that the lander needed to be able to act autonomously to some extent, at least. That is, it is not feasible for someone to sit in Bangalore with a joystick or a computer terminal and manually set a lander down on the lunar surface: the three second time-delay is too much.

By looking through the video recording for periods (sometimes only a few seconds) during which one can see the horizontal and vertical speeds of Vikram on one of the mission control centre’s display screens, I was able to construct the following speed history. As to whether the times indicate instants at the Vikram probe, or 1.5 (or 3) seconds later, is not a matter to worry us here. Everything is relative.

What does all this tell us? The first indication of trouble, at least to the viewer of this TV coverage, occurs (in retrospect) at 1:42:55: the reported trajectory of Vikram (green line) deviates from the planned path (red line), and again in retrospect I suppose they should have used those colours in reverse (though Indian tradition might well, for all I know, be quite different to what I am implying there).

Statements so far from ISRO have said that communication with Vikram was lost when it was 2.1 km above the surface. My first thought, looking at the animation that is seen for 15 seconds from 1:42:40, was that as the probe was rotated around so as to point its rocket engines downwards perhaps the radio link to Earth was lost because the relevant antenna(s) failed to maintain the correct pointing angle as the spacecraft swivelled. But read on.

Based on what is seen in the TV coverage and the timeline presented in the table above, it seems that something did go wrong as the lander dropped through 2.1 km altitude: this is evidenced by the trajectory plot lasting 15 seconds from 1:42:55 as seen in the video. However, the trajectory data could only be available if Vikram was continuing to telemeter its position and speed back to Earth. The downlink appears to have still been working, then, to below 400 metres (the nominal altitude at which hovering was due to commence, and the landing site then quickly chosen).

The speed trend appears to make sense in terms of a controlled descent if one compares the values at 1:42:28 with those at 1:41:23, in that both the horizontal and vertical speeds have reduced. During the subsequent minute, though, something seems to have gone awry: the horizontal speed has reduced (which is fine) but the vertical speed increased (from 42.9 to 59.0 m/sec) whereas one might expect it to have been decremented (i.e. descent slowed by retrorockets). I note also that these speed components (at 1:43:25) are not seen to change at any future time, and so they may have been attained earlier (than 1:43:25) and I would interpret them as being the final speeds telemetered back to Earth by Vikram before its impact.

The final altitude indicated was 335 metres (at 1:43:27 in the video record, but this does not mean that was the altitude at that instant: it was quite likely the last altitude telemetered back, in my interpretation). Let us now plug in some figures.

The last received velocity components (48.1 and 59.0 m/sec) indicate an overall speed of 76.1 m/sec, obtained by adding those in quadrature. I assume that to be the speed at altitude 335 metres. Using the normal equations of uniformly-accelerated motion (see my update to this post) the fall from 335 metres to the surface (assumed altitude zero) increases the vertical speed to 67.6 m/sec, and the overall speed to 82.9 m/sec (the horizontal speed being taken to be unaltered). That would be the speed at which Vikram (and Pragyam) would hit the surface under my interpretation. This is close to the 300 kilometres per hour I estimated previously based on an assumption (not a good one) that Vikram was stationary at 2.1 km altitude and fell vertically without anything to slow it down.

It is also straightforward to calculate the time it would take Vikram to hit the surface under this scenario (an unrestrained drop from 335 metres with initial velocity components as above). The answer is 4.7 seconds. Earlier I discussed the time-delay inherent in communicating with the probe from Earth (a three-second round-trip time at least), and so perhaps we have an answer here as to why there was no further signal received from Vikram after the last communication of its location and speed when at altitude 335 metres.

What do I think went wrong? My interpretation – and I would be pleased to be shown to be wrong in some way – is that although the downlink (from Vikram to ISTRAC) continued to function until altitude 335 metres, ceasing after that time due to the spacecraft slamming into the lunar surface at high speed, the loss of the mission was due to the uplink (ISTRAC to Vikram) perhaps being lost as the module rotated to point its rocket nozzles downwards as it passed altitude 2.1 km. From there, already having a vertical speed of about 40 m/sec (from the table above, a slight reduction assumed in the value at 1:42:28), it would have taken only 32 seconds to hit the surface. Any glitch in the autonomous landing software, or the need for an update or input from ISTRAC, could have been fatal for the lander part of the mission at that late stage in the descent.

I would anticipate that skilled ISRO personnel are on top of this already, but I’ve found it interesting to try to come up with some answer as to what may have gone wrong using the very sparse information available to me: a recording of the live TV coverage available on YouTube.

Addendum, September 10: I awoke during the night thinking “Hang on, my estimate of a 32 second uncontrolled drop to the surface is inconsistent with the 15 seconds of video of the green path deviating from the red path” (starting at 1:42:55 in the table above). And so I went back to look at the video recording yet again.

At time stamp 1:42:47 (in the animation of the lander’s progress) the altitude of Vikram is given as 2.06 km, and we recall that the time may well be out by a second or two. At time stamp 1:43:12 (in the altitude plot: red and green lines) it appears that Vikram has reached the point at which the last telemetered position was received; on that plot it appears to be slightly under 0.4 km altitude (the height at which the red line becomes vertical), and the value is given as 0.335 km in the animation frame appearing at 1:43:21 (by which time I think that Vikram had actually hit the surface).

Based on the above, it appears that Vikram fell from 2.06 km at 1:42:47 to 0.335 km at 1:43:12, a time difference of 25 seconds. I would posit that to be not inconsistent with my estimate of 32 seconds for an unimpeded drop from 2.1 km to the surface, given the uncertainties in these time evaluations at the one/two second level.

Addendum 2: My old buddy Scott Manley (we worked together at Armagh Observatory in Northern Ireland around two decades ago) has a useful commentary on YouTube regarding the loss of the Vikram lander. Much recommended.

0 Responses to “How the Indian lunar lander was lost”

  • Thanks for the analysis. Definitely plausible, and sounds likely.