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.