From what altitude does space debris drop vertically?

While gearing up for the CZ-5B reentry in the first week of May, an interesting exchange developed on Twitter between @SpaceTrackOrg, @DutchSpace and me, regarding the way space debris falls down in the last few tens of kilometers before hitting ground surface. 

It was triggered by the comment by @SpaceTrackOrg that the coordinates in their TIP messages typically refer to the object at 10 km altitude, not ground level:

As I pointed out in the Twitter thread, increasing drag acting on the fragments during reentry will not only make them start to ablate (and fragment), but will also slow them down, to a point where they finally have lost all initial forward momentum. From that point onwards they drop straight down.

During that tweet exchange, I decided to prove my point to initial disbelievers with a General Missions Analysis Tool (GMAT) model. I constructed an orbit for a hypothetical satellite about to reenter. I next ran this object through a GMAT model, modelling descent through the MSISE90 model atmosphere: initially for a 10 kg mass and 1 m² drag surface, but later I ran the model for 5 kg and 50 kg masses too, capturing a range of area-to-mass ratio's. The initial speed was orbital (7.4 km/s) and the starting orbital altitude was 80 km, just below the tipping point between orbital and suborbital altitude (in this way, rapid reentry in the model was assured).

The movement in latitude and longitude from the model output was next converted to movement in meters at the earth surface (I did this in QGIS), i.e. horizontal displacement, yielding this diagram that maps the horizontal component of movement of each fragment against atmospheric altitude:

click diagram to enlarge

As can be seen, all three objects indeed reach a point where horizontal movement becomes essentially zero - they drop down vertically from a certain point. 

These points where the horizontal movement becomes zero are located at about 45 km altitude for a 5 kg object  (with a 1 m² drag surface), about 35 km for a 10 kg object (with 1 m² drag surface), and about 25 km for a 50 kg object  (with 1 m² drag surface).

So our GMAT model demonstrates what I argued: from a certain point, well above 10 km atmospheric altitude, fragments from a reentry loose their forward momentum and basically start to drop down vertically, essentially a free fall.

But the reality is, of course, a bit different and more complex than this model suggests. Apart from atmospheric drag and gravity, there is another force that starts to act on these fragments once in the (upper) atmosphere, one that GMAT does not account for. The force in question is high altitude winds, which above 50 km altitude can be very strong.

So the reality is, that these high altitude winds at a certain point start to become the main force of horizontal displacement - fragments are litterally being blown away by these winds. As a result, the actual fall from the mentioned altitudes is not straigth down: falling fragments can be blown away laterally from the initial trajectory, or foward along the trajectory, and even be blown backwards along the initial trajectory, depending on the direction of the high altitude winds! The displacement, especially for fragments that are relatively large for their mass (space debris fragments usually are, as they usually are not solid), can be many kilometers.

This effect is well known to meteor astronomers, as it is a complicating factor in calculating where any meteorite fragments from a fireball might have landed. Like space debris, meteorites likewise are slowed down once descending through the atmosphere, and from ~25 to ~15 km altitude (their initial speed is faster than that of space debris and they are more dense, hence they penetrate deeper before losing their cosmic speed) they start the same kind of free fall, moving primarily under the effects of high altitude winds.

As an aside: I would love to see someone add the capability to import and effect high altitude wind profiles into GMAT, so this kind of displacement could be modelled in GMAT!

Note that, in interpreting the diagram above, one should realise that it maps horizontal displacement relative to altitude in the atmosphere. The modelled fragments do not end up in the same geographic location. 

For a given drag surface, low mass objects will come down earlier along the trajectory than heavier objects. This can be seen in the diagram below, which also shows you that the debris footprint of a reentry can easily be hundreds of kilometers long, something to keep in mind when looking at reentry coordinates in TIP messages:

 

click diagram to enlarge

It takes quite a while for these objects to come down through the lower layers of the atmosphere too, especially if they are large but lightweight:

click diagram to enlarge

The actual fall durations are heavily influenced by the area-to-mass-ratio. Relatively solid fragments (low area-to-mass) will come down faster, sheet-like or hollow objects (high area-to-mass) will come down slower. Surviving fragments will trickle down over tens of minutes. This is one reason why the time windows given for hazard areas during a controlled rocket stage reentry are usually an hour or so in duration.

From meteoric fireball studies, we know that as a rule of thumb, ablation (mass loss, i.e. burning up) of fragments stops once their speed is below ~3 km/s. Note that for low melting point materials like aluminium, the speed might actually be somewhat lower (meteorites are rock or iron with melting points at ~1100-1500 C, while aluminium has a melting point at ~660 C).

For the three modelled fragments (all modelled for a drag surface of 1 m²), the 5 kg fragment reaches this point at 77 km altitude; the 10 kg fragment at 73 km altitude; the 50 kg fragment at 61 km altitude. Note that the results will be different when modelling with the same masses but a different drag surface (for a smaller drag surface, the altitudes for a given mass will get lower, as they don't slow down as rapidly). Also note my earlier remark about materials with low melting point temperatures. But in general: anything that survives to below ~50 km in the atmosphere, will probably reach ground surface.

Guest Post: Modelling of Starlink trail brightness and comparison to observations

(The following post is a Guest Post written by Richard Cole)

Observers have been reporting ‘missing passes’ of Starlink trains since the Starlink L1.1 launch, the first of the operational spacecraft. A missing pass is where an examination of the NORAD or SpaceX orbital elements, or a prediction from one of the Starlink websites, would indicate that multiple spacecraft should be expected to be visible but none appear on time.

An observer in Argentina noted missing passes to their south in late February, local summer. Initially, I thought that perhaps the spacecraft had been temporarily placed into the operational low brightness mode (that brightness having been seen on the prototypes after deployment in mid-2019) but this did not match other observers seeing the same spacecraft at normal brightness at similar times. This phenomenon affected spacecraft in the holding orbit at 350-380km, not the operational spacecraft at 550km.

Recently, the images of the spacecraft on-orbit by Ralf Vandebergh and Szabolc Nagy showed its large solar panel of the solar array was facing the Earth when the spacecraft were overhead and explained the normally high brightness of the spacecraft as seen from the ground. The longer dimension of the panel was observed to be parallel to the velocity vector of the orbit, i.e. the orbit path.

SpaceX had referred in communications to a low-drag mode which was consistent with the observed appearance. This raised the question of how this mode of operation would deal with acquiring enough solar power. Would the panel always face upwards to the zenith, or would the spacecraft be rolled around the velocity vector to get more sunlight onto the panel?

During April 2020 more observers saw missing passes. I had personally tweeted a prediction for a late evening pass of the Starlink L1.5 train to the north of my site in southern UK on April 20th, but the spacecraft were only magnitude 6, needing binoculars to be seen at all. Observers in northern UK reported they had visually seen spacecraft on that pass. It was clear that the spacecraft were indeed being rolled around the velocity vector and by such an angle they were nearly directly facing the Sun, now towards the north in Spring, and observers to the south were just seeing the shadowed back of the panel.

Since it was clear that further analysis was needed to accurately predict visible passes, early on April 21st I created a simple model of the spacecraft panel pointing axis assuming the panel long axis was the velocity vector and the spacecraft was being rolled so that the Sun was in a plane normal to the panel and through the long axis (figure 1). Usually the panel cannot directly face the Sun, but is at some offset angle, in azimuth and elevation.

Figure 1: Spacecraft Roll-Angle concept.  Click diagram to enlarge

This concept allows calculation of the angle between the direction the panel is pointing and the observed Starlink direction for a particular observer on the ground, for the same time. This ‘panel view angle’ will be different for each possible observer of the same spacecraft at the same time, some will see a large part of the sunlit side of the panel, some will see only a little of the same side and some will see only the back of the panel away from Sun, which is dark.

The model gave panel view angles consistent with recorded occasions of observed train non-appearances.

Marco Langbroek’s excellent observation and images of the L1.5 train from Leiden on 2020 April 21 (the same day as the first version of the model was written, as it turned out) provided a useful test of the model. Further, more recent information from SpaceX has confirmed this behaviour and suggested that the actual roll-angle used on-board many not be exactly as calculated above.

In the image below (figure 2) I plot the calculated glancing angles to the sunlit side of the solar panel (so a glancing angle of zero means the view angle of the panel is to the edge of the panel, an angle of 90 would be face on). I have done this for two altitudes (elevations) in Marco's image, 50° and 70°. The roll-angle was as calculated above.

Figure 2: Marco Langbroek's image of Starlink 5 passes, with the calculated panel glancing angles overlaid. Click to enlarge

The trend of a reducing glancing angle with Starlink brightness is correct, so as the Starlinks passed further north (to the right of the image) of Marco at Leiden, less and less of the panel sunlit surface was visible until nothing could be seen. There was one predicted Starlink that passed on the right of the image (further north) but is only detectable by image analysis, it can’t be seen in the original camera image because very little of the sunlit side was facing the camera:

Figure 3: the extra and faint track of a predicted Starlink satellite in the image. Click to enlarge

I was observing the same pass from southern UK a few minutes earlier than Marco and saw the same behaviour of reducing Starlink brightness as each Starlink passed further to the north. I was very pleased to see he had recorded it in his image.

However, the fit is not perfect so I tried changing the roll-angle by a small amount from that calculated. The fit was best for a deviation of nine degrees from the model, that is the actual roll-angle was nine degrees less that the simple model predicts and the panel is pointing slightly higher in the sky. This gave a better fit:

Figure 4: the same image with the changed panel glancing angles overlaid, using an offset of nine degrees in the solar panel pointing direction. Click to enlarge

SpaceX is now promising to change the roll-angle model used on-board to minimise the Starlink brightness as seen from the ground. The panel will be rotated, at periods when the Starlink can be seen from the ground, so the sun falls on the edge of the panel, not on its face as in figure 1. This is a small portion of each orbit and as Starlinks at low altitude are not using their communication equipment, they will need less power to keep functioning.

Richard Cole
Twitter: @richard_e_cole

The fabrications of Masami Kuramoto (again on MH17 and the suspect Russian MoD pictures)

In January, I posted an analysis of images provided by the Russian MoD during a press conference in July 2014, a few days after the shootdown of Malaysian Airlines flight MH17 over the Ukraine. These images purport to show Ukrainian BUK installations in a field near Zaroshchens’ke.

In my investigation of these images, I showed that the images are suspect because the satellite-to-ground geometry of the satellite and target area on the moment the images were purportedly taken, do not appear to match.

In short: the satellite could only image these targets with clearly obligue angles with the horizontal at the target location, angles between 45 and 57.5 degrees. The Russian imagery however, appears to show these purported "BUK's" as if taken from a much higher angle,almost from straight above. There also appear to be inconsistencies in the shadow directions.

I noted this in the context of checking which satelite made the purported imagery (the only candidate is the Resurs P-1 satellite). For more details, read my earlier post with the original analysis.

The authenticity of these same Russian satellite images had already come under fire from the side of the Bellingcat collective earlier, based on an analysis with the photoforensic tool FotoForensics. More recently (15 July 2016) the authenticity of the images in question again came under fire, this time by the people from the Arms Control Wonk blog, using another photoforensic package, Tungstène.

Both of these photoforensic analysis are not without criticasters (most notably Neal Krawetz, the author of the FotoForensics photoforensic tools). There are however other reasons as well to be cautious with respect to this Russian imagery.

My own analysis, approached the issue from (pun intended) another angle, and came (predictably) under fire from a number of Twitter trolls, the most persistent of which was and is an anonymous  Twitter known under the nickname 'Masami Kuramoto' (they always are anonymous, and that itself tells you something). I earlier replied to his criticism in a blog post in February.

'Masami Kuramoto' initially seemed to have given up after my rebuttal, but more recently has stepped up his antics again. He has posted an analysis on his brand new blog, called "Facts versus Truthers", in which he purports to show that my model is incorrect, claiming that I published a model that was "misaligned and pointing downhill". He also tried to smear me by suggesting I am a "truther" (really a very odd insult given the positions I take).

The truth is that Masami Kuramoto's own points of view have very little to do with "facts". As I was tired of arguing with trolls I have ignored him for a while (I have better, more useful things to do), but as the antics are stepped up in the debates in the aftermath of the appearance of the Arms Control Wonk study, and Masami publicly purports he has rebutted me and proven my reconstruction "false", I will briefly discuss Masami Kuramoto's fabrications and show the malicious manipulative perversity of it all.

It is as simple as comparing my original image (left) with the reproduction by Masami Kuramoto (right):

click to enlarge

It is immediately clear that he superimposed his block model on a severely distorted version of my reconstruction.

In fact, when we project Masami Kuramoto's block model (red) over my undistorted model, with both being rotated so that the Y-axis is north-south in order to match the North-South oriented Russian satellite image and the north-south alignments of the purported BUK on that image, we get the image below.

click to enlarge

As you can see, the two models actually match very well. There is no significant difference between my model and Masami Kuramoto's model, contra Masami Kuramoto's insistence. In fact, it only appeared that way because Masami Kuaramoto provided a distorted version of my model and compared his model to that, rather than my original.

Hence why I use the word "fabrication" to refer to Masami Kuramoto's attempt to rebut me. Masami Kuramoto's argument that my model is "misaligned and pointing downhill" is simply not true, the argument is fabricated.

Looking at the reconstructions above, it is also very clear that the BUKs in the Russian MoD image do not match both Masami's own model and my model in terms of what is visible of the west sides of the launch vehicles (the slanted look of the models due to the oblique viewing angle).

This of course was the original point of my analysis: the two BUK's seem to be shown too much from directly above these machines, whereas the image should show a clearly oblique angle (as the model reconstructions show)

I want to emphatically point out, that no amount of orthorectifications applied to the Russian image can make the exposed west sides that should have been imaged (but are not), somehow automagically disappear. Nor will it result in incompatible shadow directions.

So, I think my point is clear. And it is also clear that Masami Kuramoto is a malicious, insincere troll of the kind that is abundant in the MH17 debate.

I know enough of troll behaviour by now to have no illusion that this will stop Masami Kuramoto's attempts to discredit my findings by provided fabricated counter-arguments. He will try again, and in that sense, this will be a perpetual discussion. Remember however, the history of this discussion so far, in judging the veracity of any new bollocks he might come up with.

It is interesting to look at how this whole argument developed, as it contains several clues on how to identify a troll. Masami Kuramoto tried from the start to tear my analysis apart by any handle he could perceive. When several of these attempts failed, he went on to the next one, and then yet another one. This is the hallmark of someone with a strong bias, a bias with an origin in ideology. In brief order (see also the summary and discussion in my earlier post):

1) He tried to argue that the orbital elements for the satellite in question I used were incorrect, and hence my geometry reconstruction was incorrect. He argued that the US MoD had post-altered the orbital elements for this satellite, but was taken aback when I informed him that I (and several other satellite trackers) maintain a private archive of elements. I regularly save copies of the latest orbital elements released by JSpOC to a hard drive and have an archive of these going back many years, and that analysis of that archive showed no sign of post-MH17 fiddling with the orbital elements;

2) Then he tried to use a part of the Space-Track User Agreement, taken completely out of context, to (falsely) imply that the elements would not be accurate enough (the matter of fact is that the accuracy of JSpOC elements for the question at hand is not in dispute, see my earlier post);

3) He then tried that argument again by referring to a publication, without (wanting to) realize the inaccuracies pointed out in that paper were very small scale and completely neglicable for the discussion at hand;

4) He then came with the fabricated counter-evidence currently under discussion in this blog post.

In all cases, he insisted on maintaining his position even after being corrected on the matter. It was (and is) very clear he is desperately looking for handles to tackle my analysis because he wants to prove it wrong. Masami Kuramoto is pro-Russian and promotes a worldview where Russia is never wrong, so I must be. As we have seen, he is willing to fabricate arguments to sustain his point. All this, from the comfort of his anonimity.

There are a lot of people out there like Masami Kuramoto (and, to be clear, not just pro-Russian ones). They are annoying, and poisoning the debate. Around last week's 2-year anniversary of the MH17 tragedy, we have seen a lot of it again, both anonymous and not so anonymous, coming out of the woodwork. Most of these people are "useful idiots" blinded by ideology. Some are more sinister, as they deliberately fabricate disinformation on behalf of an involved party.


UPDATE 10 June 2020:

During the MH17 trial yesterday (9 June 2020), the prosecution also tore apart the dodgy Russian 'satellite evidence', presenting an analysis by ESA which shows these images cannot have been taken at the date the Russians claim.