Three trajectory models of the Chelyabinsk meteoroid compared

[April 5: Help scientists to more accurately calculate the trajectory. Visit www.russianmeteor2013.org to contribute videos or help with the analysis.]

I now have three trajectory models of the Chelyabinsk meteoroid to share in Google Earth, from the three teams I am aware of who have published detailed results. The resulting KMZ file comes with a useful new feature: I’ve added geopositioned screenshots of the most useful videos, so you can now “fly” into each vantage point to check how the computed trajectories compare to the view in each video from the location it was taken. Here’s a quick tour on YouTube of the KMZ file:

Briefly, here’s what I’ve done: Initially, Google Earth allowed us to locate and measure YouTube videos to determine the angles of shadows, which enabled trajectory calculations, which have now been visualized in Google Earth. These trajectories can in turn be inspected visually from the vantage point of any number of geopositioned videos, resulting in an interesting additional method for verifying the accuracy of diverging trajectory calculations, short of going to these locations and making measurements in situ.

Before I do a walk-through of the trajectories and the videos, an exciting piece of news: A week or two ago, Jorge Zuluaga and Ignacio Ferrín — the duo calculating the trajectory of the meteoroid at the Physics Institute at the Univeristy of Antioquia in Medellín, Colombia — got in touch to discuss my original blog post on the use of Google Earth and YouTube as an ad-hoc sensor network for raw data on the meteoroid. They had taken my method and given it a rigorous mathematical make-over, aggregating information from four especially useful videos, including those contributed by commenters on Ogle Earth in the days after the event. From this trajectory, they calculated an orbit, concluding that the Chelyabinsk meteoroid was an Apollo-class Near Earth Asteroid.

In a classy move, Jorge and Ignacio asked me to co-author the paper they were writing, for having originally come up with the method which they then greatly improved upon. In the ensuing collaboration we identified additional useful videos, worked on the included Google Earth visualizations, and honed the prose. The paper, The orbit of the Chelyabinsk event impactor as reconstructed from amateur and public footage, has just been published to arxiv.org (here’s the PDF). The KMZ file discussed in this post (download and open in Google Earth) is the one attached to the paper. Note that the paper makes a point of thanking several commenters by name for their contributions to the original blog post. Citizen science FTW!

Now for some notes on the different trajectories:

Screen Shot 2013-03-09 at 9 Mar 14.48

Accuracy I: The NASA trajectory (in red) is derived from coordinates courtesy of Sebastien Pauleau, who calculated them from a close study of the trajectory map NASA released here, modeling the result on a WGS84 datum globe. He reports that while the accuracy of his model is calculated to 4 decimal points (an error of within 10m around Chelyabinsk, the limit of Google Earth’s accuracy with respect to the positioning of its imagery), it’s not possible right now to know how accurately NASA plotted its map. The Colombian trajectories (pink, green, black, orange), are also plotted to 4 decimal points, while the Czech results (blue) are plotted to 3 decimal points (within 100m), though of course the real error bars are a lot larger in at least all-but-one case (or else all the calculated trajectories would all have to lie within 100m of each other). The Colombian coordinates were shared directly; the Czech coordinates were published here.

Landing sites: We know that a good-sized chunk landed in Lake Chebarkul, and in the original coarse calculation I used that information as an input, fixing the lake as an endpoint for the trajectory. None of these more accurate “pro” trajectories make this assumption, and it is clear from subsequent news articles that the landing area extends beyond and around the lake. As a result, all calculated trajectories overshoot Lake Chebarkul, intersecting Earth just past the town of Miass.

Accuracy II: Because all these calculated trajectories are straight lines, there is an important caveat: From having looked closely at many geopositioned photos and videos, it seems clear that the real trajectory of the meteoroid changes as a result of the main explosion just south of Chelyabinsk. The post-explosion path seems to aim at bit more steeply at Earth, and may even have changed its azimuth (direction). Also, as the meteoroid slows down through atmospheric friction, it will begin to “fall” in a more classic arc. No one straight line can model such a more complex path with complete accuracy.

Screen Shot 2013-03-09 at 9 Mar 14.49
Miass, near Chimney

As a result, I think all current calculated trajectories overshoot the real landing site. I suspect most of the meteor mass landed between Lake Chebarkul and Miass, not beyond Miass. There are no videos from Miass showing a path flying overhead, though the calculated trajectories do assume such a path. One Miass video in particular (“Miass, near chimney” shows the contrail almost perfectly head-on, suggesting the the main part of the meteoroid landed in front of the viewpoint (towards Chebarkul).

Screen Shot 2013-03-09 at 9 Mar 18.27
Miass, near plant

Other viewpoints in Miass (“Miass, near plant” especially) suggest that some of the calculated trajectories do a better job of modeling the pre-explosion path, while others are more accurate for the latter part of the path. It’s important to note that around Miass, because the meteoroid was so close to Earth, very small differences in the calculated path can have a very large perceived effect, with changes of just a few hundred meters radically altering the perceived view.

From what I understand, it’s possible to construct even more accurate trajectory models that do not assume a single straight line, and I think this is where astronomers’ efforts will lie in the future.

Screen Shot 2013-03-09 at 9 Mar 18.28
Road near Miass

Accuracy III: One word of caution about the geopositioned screenshots in the KMZ file: It’s not possible to accurately compensate for fish-eye effects and other distortions in Google Earth beyond basic field-of-view adjustments, and the videos do not always contain sufficient environmental references to precisely measure the heading, tilt and roll of the camera viewpoint. So these videos cannot be used for detail work, though they do work well when trajectories diverge greatly, as is the case near Miass.

Interact: The KMZ file is fully editable, so feel free to edit the embedded screenshots (Right-click an item in the Places sidebar, select Get Info) to see if you can get a better fit against the calculated trajectories. Although it is tempting, I tried not to align the meteoroid path in the video capture with the calculated trajectories in Google Earth, relying instead on clues from the surrounding environment. It’s possible to infer quite a lot from aligning the placement and angles of objects in the geopositioned video capture with imagery on the ground.

Interact II: Do play with the opacity slider at the bottom of the Places sidebar (click the gradient button, if you need to); this makes it much easier to make comparisons (watch the video above to see how). Finally, if you’re wondering how I managed to fly around so smoothly in Google Earth — I use this to navigate 3D space.

[April 5: Help scientists to more accurately calculate the trajectory. Visit www.russianmeteor2013.org to contribute videos or help with the analysis.]

40 thoughts on “Three trajectory models of the Chelyabinsk meteoroid compared”

  1. Great Post Stefan. The embedded video captures really help. Alone ‘Road near Miass’ seems to confirm the average colombian trajectory. What puzzles me is that the two most reknown teams (Czech and NASA) have two very intricated trajectories that both seem to be slightly off the real thing.

  2. “Excellent work and updated model, Stefan: Interesting to see how your ‘amateur footage’ and calculations/projections compares with the ‘professional trajectory announcements’ from the relevant organisations/authorities too, and which are also quite vague in some respects…. (but to be fair they appear to have relied primarily on infrasonic monitoring, which may account for such vagueness?).

    Clearly not all the (reportedly evaporated) 11KT of the initial mass (plus the 100Kg of small meteorites found so far) accounts for it all….Again those videos show a large incandescent object surviving past the airburst/s (and it did not all go in the Lake…) – My own calculations predicted this larger fragment landed halfway to Ukraine (but my cold air resistance/density gradient and gravitational assumptions etc may be incorrect !) Now all we have to do is wait for the snow to melt so these possible impact sites can be properly investigated. “

    The NASA calculations are extremely approximate and seem to have been based mainly on a mixture of the blast size and/or trajectory via the infrasound detection system (which as you know is usually used for Nuclear activity purposes). Indeed NASA themselves accept this data as very approximate (and even state the blast size as between the radiated (ie. detected) energy and the total (including kinetic) energy as 90-440KT of course).

    In my opinion it is much more intelligent (these days) to take those ‘amateur visuals’ and other data and thence extrapolate on that basis: Even with a given range of trajectory estimates the errors in such calculations are reduced (and also largely quantifiable, too !)

    When I did my own calculations about the remaining (major) segment from this event I also (reasonably) took into consideration the increasing density of the air as the altitude reduced and also the air resistance variations at various heights/temperatures, too. As you will probably know these factors result in a rather curved (and increasingly steep) path, and also that at some point a terminal velocity is achieved… The biggest errors however are in determining the likely ‘vector’ effects (ie. both in terms of velocity and direction) on the surviving segments as may be caused by a c.100KT airburst… Thus I was led (or possibly misled…) into believing an impact site for a major segment could well be much further west and further south (than Miass) was possible…. We will see !

    I will re-work my data if/when more details emerge and let you know !

      1. Submitted as additional information on behalf of davew:

        My post above was (also !) slightly vague -as it was originally intended just as a note for Stefan- but here are some more of my views/comments/data on this for anyone else contemplating such calculations:-

        -As we know the object impacted the atmosphere at a shallow angle, ~17 degrees from horizontal; first became visible at ~90Km altitude, and then ablated for the next 10 seconds or so before exploding at a height of ~30Km and (parts) continued to be visible for about another 7 seconds or so. This is well represented/recorded and thus the video evidence has produced several excellent extrapolations, as explained extensively within the video:

        http://www.youtube.com/watch?v=lmjawUCkO84

        The path of the object (even at 17km/s) curves gradually (and increasingly) however once the object hits the atmosphere and resultant ablation rapidly occurs, and the curving worsens as the air density increases of course. Thus the object loses a high percentage of its original mass en route through the atmosphere, typically 90% under these circumstances (but which would also thus mean there is c.50,000Kg as yet not ‘fully accounted for’ ?).

        Calculating the (final) curved path is complicated therefore by the rate of mass loss and this relies on estimates of the initial mass size/shape/composition, (the latter assumed from the pieces recovered so far to be an ordinary chondrite), the various gravitational effects on this shrinking/slowing mass and also the increase in air density as the altitude decreases; Overall quite an equation, however….

        The operative word above is ‘estimates’ of course, with resultant approximations and calculation errors… including the fact that in falling the remaining c.30Km the surviving fragments will also attain a terminal velocity…

        For example, using the optical projections (only) and these kinds of estimates it is possible that ‘the’ surviving fragment is in Lake Chebarkul – ie it simply ‘dropped short’ of the projected impact sites due to the atmospheric effects mentioned.

        However, based on the likely size of the (any) fragment in the Lake it still does not explain what exactly happened to the remainder of the object as it ablated/evaporated/exploded ! Nor does it explain what happened to those emerging fragments which were not visible, either, in the ‘strewn field’ etc. Those parts which vapourised will be present (and distributed far and wide) as condensed spherules, too. Moreover it overall also still casts some doubts on estimates (and/or composition) of the original incident object..(?)

        Moving on one can only hope that as the snow melts many other pieces (of the meteoroid and the puzzle) are actually found !

        1. It seems to be coming more clear that the main explosion represents some sort of demarcation point. Flight before that point can be extended back into space to calculate the previous orbit and flight after that point may lead to where debris was strewn and any larger fragments may have impacted.

          There’s many more videos now listed at

          and

          several of which look useful for either timing or positioning and which haven’t been mentioned here before. Some of these have both visual and audible effects with timestamp, possibly allowing more distance calculations to be made.

          I am intrigued by /watch?v=c0AQmFnXQyQ and by /watch?v=v=y7VvBxJXG7E
          at 54° 50’ 56.53″ N 61° 33’ 15.14″ E (if I am reading the right comments)
          and by /watch?v=umBdOycWLDA
          at 54° 48′ 51.16″ N, 58° 26′ 0.97″ E.
          I’m fairly sure the main explosion ejected some fragments sideways to the left (as seen along the direction of travel) but I can’t prove it.

          Important note. Some links in this blog appear to no longer work, especially those to http://www.youtu.be/ but this is easily fixed. Delete the “www.” part from the URL and the link will be working again.

  3. There are voices that question some aspects of this meteorite:
    – narrow atmosphere horizontal entering angle: ~17 degrees (the lesser this angle is, the greater is the chance for the object to miss the Earth)
    – just one explosion in meteorite’s disintegration
    – explosion sound was not heard in ~90 km west of Chelyabinsk(by comparison, the Sikhote-Alin meteorite was heard from ~ 300 km)
    – brown trails left on the sky, similar with a burned fuel used for rockets
    So, the question would be: was it actually a nuclear rocket disguised in a meteorite-like form ?

    1. To my eye, hundreds of videos show it behaving exactly like a meteoroid is expected to behave.

      I also don’t see a relationship between angle of attack and probability of missing earth.

  4. The main point here is that all such events are essentially unique; Unfortunately comparisons are inevitable (even if inappropriate, as we have simply not seen enough such events): That said some aspects of this event are certainly ‘similar’ to the “Grand Teton” (’72) event, and which was a ‘grazer’ due to a very shallow angle of attack:

  5. @g1smd:
    A great compilation there – 450+ videos – unprecedented ! From all these additional visual extrapolation should certainly provide many more (‘straight line’) trajectory estimates and directional data approximations. Again the complete breaking up of the object (especially into ‘dark flight’ fragments) makes strewn field deductions more difficult of course.
    -That fragmentary diversion ‘to the left’ you mentioned is why I suggested looking further south (and west) for the larger fragments, too !

    1. - and in answer to the ‘nuclear rocket’ question above and (in spite of Chelyabinsk’s long association with nuclear research) there is -unfortunately- no such technology (and neither is there ever likely to be which could be used to launch from Earth). There are ION rockets which can be used once in space, however these are only suitable for very slowly-accelerating spacecraft, and can be powered from a small ‘nuclear’ source (akin to a ‘thermocouple battery’) which I suspect is why sometime folks refer to ‘nuclear rockets’ – or similar !

      The ‘brown trails’ as observed here were simply vapourised rock/particles, ie. NOT a vapourised rocket…

  6. Latest reports emerging from the Russian press are now stating that the object was ‘initially 10,000-18,000 tonnes – and the size 17-20m, with around 10% reaching the Earth’ (=1,000-2,000 tonnes) but that ‘Chelyabinsk was only exposed to “about 1 kiloton of energy”….’

    So, just a few thousand tonnes still ‘missing’, then ?

  7. As you mentioned davew, the strewn field makes it ‘easier’ to find fragments everywhere, for a strewn field is usually elliptical and broad. The 3 or 4 biggest visible remains from the videos might nevertheless stay on one of the main calculated trajectory.

  8. @SebastienP; I agree, plus the ‘Strewn Field’ here is even greater and more diverse than for a ‘standard’ break-up – due to the explosion/s of course – and so may well cover an area over 10K square km… It will be interesting to see just what is found (and when); For example if there *is* a fragment in the Lake it will probably be a lot less than 2m diameter, though ?!

  9. Maybe the attached link, for a ‘typical’ chondrite, gives an idea of just what we could expect to find (in the Lake), although this fragment is ‘only’ c.90Kg & measures c.50X40cm; Note the fragile/cracked nature of the object, due in part to ablation/cooling effects in transit through the atmosphere: There would originally have been a much more burned/blackened appearance of course (but this has been ‘weathered off’, as this one fell to Earth 10K+ years ago)…

    http://www.lpi.usra.edu/meteor/metbull.php?code=56144
    Image: http://theheritagetrust.files.wordpress.com/2012/08/stonehenge-meteorite.jpg
    – Alternatively (image) search on ‘Wiltshire Meteorite’ or ‘Lake House Meteorite’

  10. Hi Stefan,hi all, there is another aspect we could talk about and perhaps investigate… Mysterious electrophonic noises have been heard at the very moment the Chelyabinsk meteor was entering the atmosphere. 27 people have reported it within a week of the Chelyabinsk fireball. Normaly, no sound of explosion can be heard before dozens of seconds. But the electrophonic sound appeared to some when the meteor was still flying. This is a known phenomenon, not yet understood that we could analyse in this thread if we find the source of the reports (sadly, not linked in the article below).

    http://www.astronomy.com/en/Web%20Extras/2013/04/The%20whispering%20bolide.aspx

    “Within a week of the Chelyabinsk fireball, a Russian website collecting testimonials had 27 independent reports of people hearing weak but clear hissing sounds during its flight. Many compared the sound to a “Bengal sparkler,” a type of hand-held firework popular in Russia. And one person described the noise as “a low-level crackling hum very similar to what you hear near high-voltage power lines.”

    Most of those who heard sounds noted that they could not determine either the source of the hissing or its direction — precisely the features that had puzzled previous observers. One witness, however, was certain the noise came from a telephone cable running from a street pole to her house.

    The reports seem to have come only from observers in quiet rural areas. In the city itself, and in the vehicles carrying the now-ubiquitous dashcams, background mechanical noises appear to have masked the meteor’s sounds.”

  11. Yes, it is an interesting phenomenon (and similar observations have been made ever since telegraph/phone lines have been in use, particularly from lightning sources…)

    Basically as a bolide impinges on the ionosphere (and then atmosphere) multiple-frequency Radio Waves are produced of course – particularly including VLF RF – and these can interact with such wires, and other objects, which act as ‘receivers’/secondary radiators (as the RF energy is demodulated into sound); This is why the source is indistinct, as such receivers/radiators/demodulators can be located anywhere/everywhere around the observers/s !

  12. Yes Davew, this is I think the status of research. But this hypothesis is only resulting of the analysis of witnesses’s reports. And for now, as far as I know, nobody ever measured the incoming RF as a sound was being heard. I’d like to think that the RF are interfering with wires, but I know at least of one case in a car (no cables, not really a quite place either) so that I’m not sure at all. Some think that this is only the surprise of witnessing something highly unusual. And indeed, the two witnesses I personnaly know of have only witnessed one meteorite in their lives, whereas friends astronomers of mine that have seen dozens of bolides have heard it only once or even none. To better find out, I think it would help if the Electrophonics sounds databases around the web would be “open”. Because all I’ve said can be contradicted as there is no casuistic available really.

    This is the article that spoke of 27 witnesses in last february:
    http://chelyabinsk.ru/text/newsline/625214.html

    The Cheliabinsk dedicated database that recorded the 27 witnesses but which is “closed” (or seems to be):
    http://www.chel-meteorit.youini.ru/

    1. Response by davew posted on his behalf (he had trouble posting here):

      As we know, this is simply an unusual event, and, with only c.30 witnesses out of (say) 300K observers here it is likely to be (and stay) relatively rare (and hence difficult to investigate in detail and in a truly scientific way) !

      As I stated It does not *only* happen with wires, RF radiation impinging on ‘other objects’ (metal or not) can produce this effect….

      Remember we are dealing with hypersonic vapourisation of rock/minerals/elements so we should thus expect some ‘interesting fireworks’ and ‘very unusual effects’ of course.

      I am not sure why you maybe think such effects are ‘secret’ either – as there is lots of (publicly-available) research on the high energies produced by ‘shock vapourisation’ (of rocks) etc. With bolides the levels of released energy *naturally* thus produce RF/light/heat/sound (and effects) galore !!

      However we also know that there are highly-sophisticated ‘sound monitoring systems’ around the world (to monitor terrestrial seismic event – including man-made ‘explosions’) so don’t be too surprised if the information about these systems is not so readily available: I am sure though you read the reports about the reverberations from this bolide lasting for many days for example (?)

  13. No, that I didn’t know. I only have hard times finding the relevant testimonies that I’d like to analyse myself – others would probably like too, from this particuliar bolide or any other that shows such reports. If you or anyone knows about an available reports database of electrophonics effects, I’d like to see it.

  14. SebastienP:

    I was referring to research on ‘shock vapourisation’ of rock, such as experiments/work like this (for example using lasers on quartz):

    http://www.fas.harvard.edu/~planets/sstewart/reprints/papers/50_Kraus_JGR_2012_Silica_Vaporization.pdf

    – and there is a long list of additional references at the end, too.

    As for any ‘database on electrophonics’ effects.. Again this is simply so rare that -unless we are lucky enough to have some suitable monitoring-equipment at a suitable location – will probably remain essentially anecdotal or speculative… Otherwise it is simply an electomagnetic-energy to sound-energy modulation/conversion as I explained above (?)

    1. Incidentally, back more on topic it seems that a meteorite fragment (c.60cm/300Kgm) has now finally been detected at the bottom of Lake Chebarkul – but not yet raised…..

      Also interesting to note that some of the other (small) fragments found will be incorporated into the Gold Medals for the Winter Olympics !!

  15. Still waiting for that biggest fragment (so far) to be recovered….

    ‘In other news’ there has been a statement that the meteor fragments that have been found have a characteristic ‘dark surface’ … and that this – in part – is why we ‘did not see it coming’. Considering the size/speed/original trajectory/etc of the object then with all due respect it seems rather naive to blame this ‘oversight’ on the colour …. ?

    There have been some interesting images of the bolide from satellites however:-

    http://www.planetary.org/blogs/guest-blogs/2013/20131004-egorov-elektro-l-chelyabinsk.html

      1. News today regarding recovery of the large fragment:-

        http://www.nst.com.my/latest/russia-pulls-huge-chelyabinsk-meteor-chunk-from-lake-1.377423

        Authenticity yet to be confirmed but other photos/videos of this I have seen look genuine enough (!)…. and it is also definitely ‘shock fractured’ too.

        Now all they have to do is to find those pieces I predicted/expected from the (larger) strewn field; Smaller pieces to the East of Lake Chebarkul, bigger ones to the West !(?)

  16. An interesting video – it *almost* captured the impact ! I had to watch several times to discern that ice/snow/water ‘ejecta’ cloud though…

    More analysis/extrapolations have now been published in ‘Nature’ :-
    http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12671.html – Note how the extrapolations were complicated by those quickly-rising ‘vapour trails’

    Similarly the predictions for the fragments (and see Table ‘d’):-
    http://www.nature.com/nature/journal/vaop/ncurrent/fig_tab/nature12671_SF6.html – I am a little biased but I suspect they are also now intrigued as to how such a huge object has apparently produced such a small strewn field, too !?

  17. At the AGU Meeting (December 9) it was in fact described as an ‘Airburst':-

    http://www.youtube.com/watch?v=6uU2i65aKUA

    As for the ‘Lessons Learned’ ? IMHO that we can *not * accurately predict such events, in part because they are all essentially unique – and even if we could ‘see them coming early enough’ there is actually -so far- very little we could do about it quickly enough to avoid the related terrestrial destruction and damage (?!). Yes, Nature can be cruel sometimes…..

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