The orbit time for Tiangong 1 is 89 minutes, so that's 16 orbits in a day, and with error bars of 4+ days on the deorbit time, that's 64 orbits... so I think you can use the equation in the linked PDF to provide a decent likelihood plot.
It's unclear to me, but I think the error bars aren't ever going to get lower than, guessing 16 orbits. So the long term plot of likelihood probably still applies.
Meithan: the Space Station spends slightly more time near the lower and upper latitude "edges" of the zone.
However, the most important factor in where it will come down is not so much dwell time, but the position of the point of perigee: reentries tend to happen just after crossing through perigee.
I made a plot of Tiangong-1's current ground track extended for 100 days,
https://meithan.net/images/Tiangong1_track.png
and computed a histogram for the latitudes over which it flies, with bins around 1° of latitude wide:
https://meithan.net/images/Tiangong1_histo.png
Seems the station loiters over the last degree of latitude around 6 times longer than over equatorial latitudes. But the probability is only increased in a narrow band at the very edges of the range.
(This reminds me of the position probability plot for the classical harmonic oscillator ... which isn't surprising considering the orbit is almost circular, and the ground track is close enough to the equator that it resembles a sinusoid. There must be an exact result for that probability distribution.)
If the probability plot is plotted on a sphere, there is no more likely deorbit position than any other on the path (neglecting apogee/perigee, of course). The increased likelihoods at certain latitudes are simply issues of projection of the sphere onto a flat page.
@Christopher Becke: kind of. It's more a consequence of how we define geographic coordinates (which is determined by the spherical nature of Earth, yes). But it's not an illusion: the loitering time *does* peak near the edge of the latitude band.
If you measured the ground track speed in terms of *degrees of latitude per unit time*, the station does move faster (in these terms) near the equator than near the edges of its latitude range.
Do we have a plot or list of expected lat/long positions corresponding to the points of perigee for the next 2 weeks or so?
A neat plot would be those points, smeared out along the track a few hundred miles. Those would probably be a good guess as to the most likely deorbit positions.
The point-smear glyphs could be copies of a single vector graphics icon that could auto-adjust width and length in a custom gmaps plot of the earth (the orientation would be set for each - tied to the track at that point). Then you could leverage the built in gmaps data and interface to make it user friendly and fun for people to interact with.
I just asked PyEphem and apparently the current perigee (from the latest elset, dated 2018/3/20 07:49:52) occurs around 12°S latitude. If reentry is to occur close to the current perigee, then locations in the 10°S - 15°S latitude band should be more likely. But I just don't know if the current perigee is a good predictor of where it will reenter.
Continuing the idea that the latitude of the current perigee is a good predictor of the final latitude of reentry (is that so historically? Good question for Dr. Langbroek!), places in the 10°S - 15°S latitude band include Peru, Bolivia, southern Brazil, Angola, Zambia, Mozambique, northern Madagascar, and the northern tips of Australia -- and large areas of ocean, of course.
If I'm doing this right, I'm seeing the sat's orbit process relative to the surface of the earth by about 23.5 degrees long each orbit. I don't know the orbit's relative inclination to the axis of the earth, or where that 12degS was in its own orbit, but over many orbits, the range of latitudes covered by the sat ground track is about 82 degrees, centered on the equator. I guess that means its orbit is inclined by about 41 degrees....
Kevin: the orbital inclination of Tiangong-1 is 42.75 degrees. Meithan: the position of perigee is *not* stable, it changes over time. Exactly how it changes, depends on the actual orbital evolution, and is difficult to model for an object near reentry. We'll have to wait untill the last few hours of Tiangong-1's existence before we can start to maked educated guesses about the point of reentry.
and the period of the sat's orbit is about 89 minutes. that equates to 22.24 degrees of the earth rotating about it's axis, so my 23.5 degrees procession per orbit seems good, and (this is probably for my own spatial confirmation) the sat's orbit isn't processing relative to the earth's axis (neglecting the earth's slight wobble). so, as you say, i guess the range of 10degS to 14degS is a good rule, until we find out if the perigee is on the down or up stroke of the orbit, in which case we can drop that range by half.
Well... we can still play fun games by knowing the perigee position now, very conservatively extrapolating from the changes per orbit we see now to model how the perigee might change over the next two weeks (clearly the further out the worse the model), and plot those perigee positions on a map of the surface of the earth. after deorbit, we can see how the model deviated from reality.
I guess it depends on how quickly updates to the elsat get pushed out and how often you check this (and possibly other) websites that track those things... perhaps automatically.
I'm not sure if anyone has set up a text message or email or other alert that might trigger on updates to the models, 24 hour, 12 hour, and 2 hour alerts, etc.
@Kevin White: here, I downloaded all available TLEs from SpaceTrack (which cover the whole life of the station from launch in 2011), and extracted perigee/apogee altitude as well as perigee latitude/longitude data using PyEphem:
https://meithan.net/tiangong1/index.html
You can download the data in CSV by clicking on the icon. The first line (which starts with a "#" contains the definitions of the columns).
It's interesting that the latitude of perigee oscillates naturally from -inc to +inc with a very stable period of around 48 days (clearly visible when there are no re-boosts).
Dr. Langbroek: will this very clean periodicity hold as the station approaches reentry? Because if it does, one could use it to obtain an estimate of the latitude of reentry as a function of when it reenters.
The uncertainty in the exact reentry date still represents a big error in perigee latitude, around ~7.5 degrees per day. But at least some estimate could be made, and a predicted reentry uncertainty of +/3 days (as it currently stands) would narrow down the possible latitudes a bit. (And apologies if I'm overlooking a bunch of important factors here; I'm no expert in satellite reentry.)
Here's a rough prediction assuming the periodicity in the perigee latitude will hold up until reentry -- which is probably not true, but hey, it's a prediction:
I obtained the model of the quasi-periodic perigee latitude variations by fitting a cosine with a linearly varying period to the last 6 cycles. Then, I extrapolated that periodic variation till the currently predicted reentry time, and got the predicted reentry latitude bounds from that.
The predicted reentry latitude range is about 1/3 of the full latitude range of the ground track (due to inclination), so even if the prediction turns out to be good it could be just lack. But I had fun.
One question, above you say that perigee was at ~-12deg lat on 2018/3/20 07:49:52, but the data on your website seems to say that on 3/20 it was closer to -40deg lat.
Are we pretty sure perigee data from the csv link (and your plot on that page) is the correct one?
Assuming your csv data is the better set, then while the perigee data does look a little bit noisier recently, the shape through the most recent trough of the sinusoid is still within about 1.6% of the width/shape of the immediately preceding trough at about 1/28/2018.
So, that means that we can probably use a fit to the sinusoid since 1/1/2016 to guesstimate where the perigees will be over the next 2 weeks, at least as far as lat is concerned. I haven't looked at long...
hmm. that's going to take a different approach. I've looked at the incremental sum of the differences between adjacent longs in your csv, and there's some weird artifacts here and there, but it looks pretty linear in time, at least recently, so we can use that line since about 1/1/18 to extrapolate out where the longs will be for each projected perigee. the slope of that line is about 20.4 deg/hour, if I've done math right.
I think that's about all we need to guess a series of perigees out a few weeks, with error bars steadily increasing over that time.
tie that in with the modeled decay day provided by Marco, and you'll have a selection of 20 or so perigees for that day, and corresponding lat longs.
On second thought, I'm not sure I'm analyzing the longs correctly. I don't think I'm unwinding the longs so as to get the correct angle between adjacent long measurements.
If I redid things correctly, perigee longitude changes by about -15.34 deg/hour (that's the slope of the linear change in long for perigee since early feb).
Looking at the csv data again, it shows perigee positions only 3-4 times a day, but the orbital period for the sat is closer to 90min, which would mean 16 orbits a day, with each orbit necessarily including a perigee. I guess that tells us how often the elsats are updated? Or maybe that's the resolution of the model?
In any event, I think we have very rough evolutions of the position of the perigee relative to the surface of the earth, as a function of time. however, we don't yet have the times when the satellite itself passes through the perigee of the orbit.
@Kevin White: regarding the previously reported perigee latitude of ~-12deg for 3/20, you're right, there's indeed a discrepancy with the newer values.
I used different methods to compute the latitude. For that initial estimate I just looked at an altitude vs. latitude diagram and eyeballed the value. For the more recent values in the CSV and plots on my website, I used the orbital parameters (specifically: the mean anomaly) to compute the exact time of perigee, and then obtained lat/long at that time. So the CSV values should be more reliable, but let me double-check the latest calculations to make sure they're indeed correct.
As for the longitude of perigee, I did not try to make a prediction for it because it changes much faster than the latitude (as you said: around 15 degrees per hour, as opposed to around 7 degrees *per day* for the latitude). With a reentry date with ~3 days of uncertainty on either side, the longitude of reentry could be anything.
The 3-4 values per day is just the update frequency of the elsets. They're not updated once per orbit.
The times of perigee are included in the CSV; they're in column 4.
Hi Meithan: what would be helpful that's missing from your perigee latitude time evolution plot is whether perigee is occurring on the ascending node or descending node. For instance, at present perigee is occurring on the ascending node. Another thing to note is the interplay between orbital perigee (i.e. minimum radial distance) and minimum altitude. The two are only the same when perigee occurs at zero latitude. At all other latitudes, minimum altitude will occur at some latitude that differs somewhat from the latitude of perigee due to earth oblateness. --Rob Matson
@Rob - lets ignore that the earth is more squat by about 22km on radius. More important is the orbital perigee itself, and maybe the bulging of the atmosphere. Those two datum together would make some perigees "hotter" than others in the this totally seat of the pants analysis.
@Meithan - thanks. I think we can probably extract whatever time evolution there is in the timing of the perigees from the partial data and the known orbital period. We're pretty close!
Hi Kevin: I don't think you can ignore the earth's oblateness in even a first-order analysis. At the satellite's latitude extremes, the earth radius is 10 km less than it is at the equator. That's almost 50% of the current difference between perigee and apogee. --Rob
Just popping in to say I love your blog and your contributions to the SeeSat list (of which I understand nothing). First thing I do every morning at work is check both. Much enjoyment had! Thank you!!
@Rob - for what Marco is doing, you need to account for the density of the atmosphere along the orbit, which would probably have to take into account how the terrestrial bulge and the atmospheric bulge and maybe even the tidal bulge change that density. But, that's what's necessary to model and pinpoint a single time of reentry, and I'm fairly sure the atmospheric models Marco is already using account for those.
Aside from that, however, Marco mentioned that deorbits often happen right after an orbit perigee, not after an equatorial transit. And, while the altitude might change 10km when transiting the equator, it's unclear what effect that has on the atmospheric density or drag the sat sees at its current (and expected, before divebomb reentry) altitude, in light of all the other effects (including solar wind, etc.).
So, in the interest of keeping it simple, and using an alternative less rigorous method (cause Marco has the more rigorous method in hand), I think we may get pretty close to the more rigorous method by generating a plot of the orbital perigee positions over the earth for the next two weeks, even assuming a lot of things that aren't necessarily good to assume as this thing dives into the atmosphere. I'm interested in seeing how close we do get, or how far off we are.
Anyway, once we have that plot, we can highlight perigees that are closer to the equatorial crossings as more likely deorbit spots in the Orbital-Perigee-First Model. Also, it will be clear from that plot whether the perigee is leading into or out of an orbital transit (see Meithan's plot, for example).
Also, see: Generally, depth and thickness of the atmosphere are measured in terms of its lowest layer, the troposphere. The troposphere extends from the Earth’s surface upward to between about 6 and 20 kilometers (4 and 12 miles). The exact extent depends on location. The troposphere is shallowest -- or narrowest -- at the poles, and deepest -- or thickest -- at the equator. At the geographic North and South Poles, the troposphere reaches only 6 kilometers (4 miles) high, while at the equator, it extends nearly 20 kilometers (12 miles) high. Depths and degree of thickness gradually shift between these two extremes in the middle latitudes. For instance, at 50 degrees latitude, roughly the latitude of Seattle, Washington, the atmosphere is just under 10 kilometers (6 miles) thick.
Hi Kevin: you wrote "Marco mentioned that deorbits often happen right after an orbit perigee, not after an equatorial transit" -- what isn't captured in that historical analysis is the most relevant factor: NOT the latitude of perigee, but rather the latitude of lowest altitude in the orbits leading up to reentry. Based on Tiangong's orbit right now, propagating forward, I will say the odds of reentry over the northern hemisphere are greater than over the southern hemisphere. This is not so much a consequence of the projected latitude of minimum altitude; rather, it is that the minimum altitude is likely to occur within +/- 15 degrees latitude, combined with the fact that perigee is occurring on the ascending node. Reentry will happen in less than two weeks. It is unlikely in that short window that perigee (and minimum altitude) will transition from occurring during the ascending node to during the descending node. This increases the odds of a reentry over land.
@Meithan - I've seen your updated Tiangong 1 page - nice plots!
The thing I don't understand from the plot of reentry is how you determined/selected the time of reentry on the bottom plot - I don't see any data points, just a curve. The perigee of the orbital path is moving continuously, but it only intersects with the actual position of the satellite at specific times - is that point one of the times, and you chose March 31 as linked in with Marco's work?
Also, I'm just curious - did you need that many variables to fit a cos to the data? I also note that due to dwell time, the +- peaks are weighted much more heavily than the transits... and you can see the curve misses the transits pretty regularly as a result. There might be a better way to weight the fit so that it follows the transits better.
@Rob Matson: Very good remarks. I was just starting to look at elevation data, as opposed to simply using the orbital elements, and indeed there are some differences in computed latitudes. In fact, this explains the discrepancy that Mark White spotted in latitude values I quoted earlier: one of the values was obtained by looking at the latitude of minimum elevation while the other was the latitude of orbital perigee proper; they differ substantially.
I think I do agree with Rob in that any attempt of predicting the latitude of reentry should be based on *elevation* data, since atmospheric density scales with it, and that is what ultimately causes reentry. But I don't want to get too deep into atmospheric details, as Dr. Langbroek's models already do so and it would be futile to try and re-create those models "by hand".
I've already produced a simple prediction (which I can update effortlessly as the predicted time of reentry is updated) based on the latitude of the orbital perigee. Let's see now what comes out using elevation data instead, i.e., by determining the latitude of the point of lowest elevation in each orbit. I have all the required data; it's just a matter of crunching it.
@Kevin White: Your second guess is correct: I'm taking the time of reentry directly from Dr. Langbroek's predictions.
The goal was converting the time-of-reentry prediction, with its uncertainty, into a prediction for the latitude of reentry, which is something Dr. Langbroek doesn't report (probably because it's impossible to predict at the moment, and we're simply having fun with data here ;) ). In that plot, the red curve is the fitted model, and the blue curve is the extrapolation into the future using that model. I realize that the model is not perfect, in part because I used the last 6 cycles to fit it, so in a sense it's an "average model". Perhaps I could use only the last few weeks to get a more "local" model?
About the cosine fit: well, generally a simple cosine fit requires 3 parameters already (amplitude, frequency/period and phase constant). Since the cycle is not exactly periodic, I added a fourth parameter to account for time-varying period (by making the simplest assumption, i.e. that it changes linearly, if at all). That fourth parameter (T1) turned out to be small, so a constant-period model would also do.
Thanks for your reply, Meithan -- I'm pleased that you agree (or at least recognize the potential) that the most relevant parameter for predicting reentry latitude is the evolving latitude of minimum geodetic altitude. I look forward to seeing your analysis based on that metric. In parallel with our efforts, I'm writing a little bit of code to spit out that predicted progression of that latitude from a given TLE.
We must remind ourselves that the atmosphere of Earth has the approximate form of a rectangle, because at higher latitudes, the atmosphere rises further from the surface of earth than in the equator; the atmosphere at the equator is denser than a pont at same height closer to the poles. So maybe that is one contributing factor as to why higher probabilities of reentry at higher latitudes.
I just found that throughout all of 2018 the perigee has occurred around 1pm local time at the longitude of perigee. Does that mean we can predict a re-entry between 2pm and 6pm local time? Does this mean there will be no night-time fireball?
Hi Paul: I don't think perigee for Tiangong-1 can maintain a constant 1 pm local time at perigee longitude since the satellite is not in a sunsynchronous orbit. For instance, we have local, low elevation, predawn sunlit passes of the station on its ascending node visible from southern California this morning and tomorrow morning. I believe those passes were each not that long after perigee (or at least not long after minimum geodetic altitude), so that's quite far from 1 pm local time.
OK, here's finally an updated latitude prediction based on two models:
https://meithan.net/tiangong1/
The two models (red and orange data/lines) are:
1) The latitude at each perigee 2) The latitude at which minimum geodetic elevation occurs along each orbit
Both models (cosines of the form A*cos(2*pi*t/T + phi) + B) were fitted with recent data starting 1 March. The data sets -one data point per orbit- were generated from the TLEs using PyEphem.
The blue curves are meant to show how elevation at perigee is not always the minimum elevation in the orbit because the Earth is wider at the equator. When the perigee occurs at high northern/southern latitudes the point of minimum elevation along the orbit does not occur at perigee (but closer to the equator instead).
However, coincidentally the perigee if the currently predicted reentry date will be close to the equator, so the two models produce very similar predictions for the reentry latitude.
And, as said before, these predictions are probably completely wrong as the final latitude of reentry will depend on exactly when the station reenters (and not just on the projected latitude of perigee/min. elev.). But we're having fun here ;).
Now for Long! (now that we know the time of perigee(s), we can plot the projected longs at those same times, stretch them out along the orbital path about 2 minutes?, and those streaks are the most likely spots of deorbit.)
so, instead of a full set of ground tracks over the full reentry window, plot just the points along those ground tracks that correspond to perigee positions (or min elevation positions, i guess).
Thanks everyone for participating in this comment thread. I enjoyed it immensely. And thank YOU Marco for continuing to put up with us and to regularly update this blog entry with your thoughts and work. The tie-in with Humanity Star was excellent science.
It'll be interesting to see if anyone adjusts their models based on the last few hours of telemetry. I love those graphs.
2/4/18 20:41
[post last updated April 2, 3:00 UT, 3:45 UT, 16:50 UT and 21:30 UT]
[Image]
Final orbit and reentry position of Tiangong-1 (click map to enlarge)
TIANGONG-1 has reentered the atmosphere at 00:16 UT on April 2, over the central Pacific Ocean, JSpOC and the 18th Space Control Squadron have announced.
The decay message is, as expected, listing an uncertainty window of only +- 1 minute, indicating this determination was likely based on Space-Based observations by US Early Warning satellites (SBIRS).
*****
So, how did the final pre-reentry forecasts from various sources fare, compared to reality? Here is a map summarizing nominal last pre-reentry forecasts:
[Image]
click to enlarge map
Note how well the "amateurs" did compared to the professionals!
Note that the map only shows the nominal positions, ignoring the (hefty!) error bars. When the error bars are taken into account, all predictions overlap with the real position.
It gives you an idea about how much weight to attach to these nominal positions.
*****
I am currently issuing a daily estimate of the reentry date for the Chinese Space Station Tiangong-1 on Twitter. This current blog post consolidates these estimates and is daily updated. My current and previous predictions:
SatAna/SatEvo:Date issued Date predicted (UT)
April 1 III 2 April 00:56 ± 130 min (re-issue)
April 1 III 2 April 02:02 ± 150 min
April 1 II 2 April 00:52 ± 130 min
April 1 I 1 April 22:30 ± 5.6h
March 31 III 1 April 20:30 UT ± 7h
March 31 II 1 April 22:55 UT ± 9h
March 31 I 1 April 21:15 UT ± 11h
March 30 II 1 April 20:30 UT ± 14h
March 30 I 1.9 April ± 17h
March 29 II 1.5 April ± 0.7 day
March 29 I 1.4 April ± 0.8 day
March 28 1.1 April ± 1.0 day
March 27 II 1.3 April ± 1.2 days
March 27 I 1.1 April ± 1.3 days
March 26 1.1 April ± 1.6 days
March 25 1.2 April ± 1.9 days
March 24 2.6 April ± 2.4 days
March 23 3.5 April ± 3 days
March 22 2 April ± 3 days
March 21 31 March ± 3 days
March 20 31 March ± 3 days
March 19 3 April ± 4 days
March 18 1 April ± 4 days
March 17 1 April ± 4 days
March 16 4 April ± 4 days
March 15 7 April ± 5 days
March 14 6 April ± 5 days
March 13 13 April ± 6 days
GMAT:Date issued Date predicted(UT) April 1 III 2 April 00:36 ± 130 min (final)
April 1 II 2 April 00:21 ± 125 min
April 1 I 1 April 23:20 ± 5.8h
March 31 III 1 April 23:08 UT ± 8h
March 31 II 1 April 22:46 UT ± 9h
March 31 I 1 April 22:05 UT ± 11h
March 30 II 1 April 18:00 UT ± 13h
March 30 I 1.7 April ± 15h
March 29 II 1.6 April ± 0.7 day
March 29 I 1.6 April ± 0.9 day
March 28 1.6 April ± 1.1 day
March 27 II 1.6 April ± 1.3 days
March 27 I 1.7 April ± 1.5 days
March 26 2.2 April ± 1.8 days
March 25 2.3 April ± 2.2 days
March 24 3.6 April ± 2.6 days
March 23 3.8 April ± 3 days
March 22 3 April ± 3 days
(all times are in UT = GMT: while earlier predictions were expressed in
decimal days, I am issuing the latest predictions with a nominal time. Note the large error margin on this time, however!)
Currently indicated is a reentry late April 1 or early April 2 (in GMT ), depending on how the periodic atmospheric density
variation develops.
JSpOC, the US Military tracking organization, is issuing periodic TIP messages for Tiangong-1 on their Space-Track webportal. Their lastforecast (issued late April 1st) was 2 April 00:49 UT ± 2 h.
Their final post-reentry, post-mortem Decay Message gives reentry at 2 April, 00:16 UT +- 1 min.
[Image]
click diagram to enlarge
[Image]
click diagram to enlarge
The first set of forecasts is made using Alan Pickup's SatAna and SatEvo software, with current and predicted Solar F10.7 cm flux. The error margins are a standard 25% of the number of days between the last elset used for the estimate, and the estimated moment of reentry. This might be a bit conservative, certainly well before the actual reentry. Note that from March 23 onwards, I am using slightly different settings for SatEvo than before that date, in an attempt to correct for SatAna/SatEvo results being noted to be a bit on the early side using standard settings with recent reentries.
The second set of forecasts (the most reliable, it turns out) is made by modelling the orbital evolution in GMAT, using the MSISE90 model atmosphere, historic and predicted solar flux, and a Prince-Dormand78 integrator. Drag surface is taken from an ongoing analysis of the variation in apparent drag surface as indicated by the NDOT/2 value (see below). The error margins are a standard 25% of the number of days between the
last elset used for the estimate, and the estimated moment of reentry. In addition, nominal values for modelling at minimum and maximum drag surface are shown as grey crosses.
Here is the GMAT prediction diagram in a bit more detail, with the actual moment of the reentry indicated by a red x:
[Image]
click diagram to enlarge
The rest of this post below was written pre-reentry and not updated post-reentry:
Uncertainties
The diagrams above shows you how the GMAT and SatAna/SatEvo predictions develop. When the reentry is still several days away, there will remains quite an uncertainty and prediction-to-prediction shift in the estimated moment of reentry, mostly due to periodic variations in the atmospheric density not well represented in the F10.7 cm solar flux variation that is used by most atmospheric models to account for solar activity.
Solar activity has a strong influence on the density of the upper atmosphere - and from that on the drag that the space station experiences. For a forecast, solar activity over the coming days has to be estimated - and those estimates might be off. One -unpredictable- solar flare can completely change the situation.
In addition, the drag surface of Tiangong-1 is unknown and might vary over time (see below, where I discuss an attempt to get some grip on this. And we do know it is spinning). And there is also some leeway in the current mass of Tiangong-1. These all combine to create uncertainty, even with the best reentry models.
As the predicted reentry moment comes nearer, the uncertainties become less. Still even 1-2 hours before a reentry, uncertainties in the moment of reentry (and from that in the position) can still be many tens of minutes. AS these objects move at almost 8 km/s, a 10 minute uncertainty in time amounts to thousands of kilometers uncertainty in the position.
Within the uncertainty of the current JSpOC TIP message, this is the resulting track, i.e. the
line where Tiangong 1 could currently come down. Cities with
populations of more than 1 million people between 42.8 North and 42.8 South
latitude are marked on the map as well, with those under or very near the projected trajectory indicated by white dots:
[Image]
click map to enlarge
A note about "Live" tracking websites
There are several websites
where you can (seemingly) "Live" track objects like Tiangong-1. They
are often causing confusion after reentries: people still see the object
orbiting on such websites even when it already has come down, and as a result mistakenly think it must still be on-orbit!
How is that possible? Well, contrary to what many people assume, these sites doNOTlive track the object. The positions on their maps are not based on a live feed of data.
Instead, the positions on their map are predictions
based on orbital elements gathered earlier in the day by the US
tracking network and released through JSpOC's webportal. These elements
are hence always "old", at least a few hours and sometimes half a day or
more.
So even after it has come down, these websites
sometimes still depict a spacecraft as on-orbit for a while (untill they
update their orbit database). But they show you a ghost!
So never rely on on-line tracking websites to judge whether Tiangong-1 is still on-orbit or not.
Drag variability
There is a periodic variability in the drag parameter B*, which is due to a periodic atmospheric density variation under the influence of periodic solar wind speed variations that are not well represented by the F10.7 cm solar flux variation (see below), as can be seen in the diagram below. It is a complex variation of periodicities dominated by ~5.5 and ~6.8 day periods. I expect the reentry prediction to rock back-and-forth a bit with a similar periodicity.
[Image]
click diagram to enlarge
If fact, the daily shift in SatAna/SatEvo reentry estimates indeed clearly mimics this periodicity:
[Image]
click diagram to enlarge
Drag surface reconstruction
For the orbital data of the past weeks I have calculated area-to-mass ratio's, in an attempt to get some grip on the drag surface to be used in my reentry modelling.
I initially used a mass for Tiangong-1 of 8500 kg, but in an e-mail discussion with Jon Mikkel, he convinced me that that mass
might be too high as that value likely refers to a fully
fueled Tiangong-1. If we assume ~1000 kg of fuel initially at launch but now spent, i.e. a mass of 7500 kg, the resulting drag surface is lower, varying between 16 m2 and 31 m2 for a 7500 kg mass.
In the diagram below, apparent drag surface
values for a 7500 kg mass are shown:
[Image]
click diagram to enlarge
The calculation was done using the MSISE90 model atmosphere as incorporated in GMAT. For each elset, one full revolution was modelled in GMAT, and atmospheric model densities sampled over that revolution. These values were then averaged to get an average atmospheric density. This density was used in this area-to-mass equation:
(where n is the Mean Motion taken from the orbital elements; rho is the atmospheric density as modelled in GMAT; Cd a drag coefficient (2.2); and NDOT/2 is taken from the orbital elements)
The drag surface thus modelled from the data between March 4 and March 28 appears to vary between 16 m2 and 31 m2 (for a mass of 7500 kg). These seem reasonable values: the body of Tiangong-1 measures 10.4 x 3.35 meter (this is excluding the solar panels however), which gives an approximate maximum cross section of 35 m2.
My initial (wrong!) interpretation was that over the two week analytical timespan, the drag surface varied between ~90% and ~50% of the maximum surface, suggesting that the attitude of Tiangong-1 appeared to be slowly varying. As will be discussed below, this was a misinterpretation.
It turns out he is right! The diagram below plots the drag of Tiangong-1, and that of the Humanity Star (2018-010F, which reentered 22 March near 13:15 UT). The Humanity Star is a nice test object, because it was orbiting low in the atmosphere too and more importantly, it was semi-globular, i.e. we know it had no variation in drag surface. Any variation in drag visible in the data for Humanity Star therefore must be atmospheric in origin.
[Image]
click diagram to enlarge
As can be seen, the periodic variation in drag of the Humanity Star and Tiangong-1 closely mimics each other. So the cause is NOT attitude variation of Tiangong-1 (a variable drag surface due to a slow spin, as I initially interpreted it), but periodic variations in atmospheric density that are not well represented in the MSISE90 model atmosphere.
After all, to quote Monty Python: "It is only a model...!".
This periodic density variation of the atmosphere is the result of periodic variations in the solar wind speed, which in turn are the result of the distribution of coronal holes over the solar surface. The 5.5-6.8 day periodicities I find are actually quite typical values for this variation. More can be read in this paper.
Note that the same variation is not present in the F10.7 cm solar
flux, which most models use to calculate atmospheric density variations
under the influence of solar activity. This is why it appears as an
apparent drag surface variation in the area-to-mass ratio analysis.
For me, this case has thus produced an interesting lesson regarding area-to-mass ratio analysis: variations in apparent drag surface can in reality reflect atmospheric variations not well represented in the model atmosphere, rather than real drag surface variations. In other words: one should be very careful in interpretating the results of an area-to-mass ratio analysis. Lesson learned!
Spinning
We do know that Tiangong-1 is spinning, as a matter of fact: high resolution RADAR data gathered by Fraunhofer FHR with their TIRA radar shows that the space station is in a flat spin with a period that was about 4 minutes a week ago, and is about 2.5 minutes currently. TIRA by the way also captured amazingly detailed RADAR images of Tiangong-1, which can be seen here.
[Image]
click diagram to enlarge
Perigee of the Tiangong-1 orbit is currently below 145 km altitude and rapidly decreasing.
[Image]
click diagram to enlarge
This diagram shows the frequent orbital raising manoeuvres, ending late 2015, after which the station goes steadily down:
[Image]
click diagram to enlarge
The rate of decay, clearly going up:
[Image]
click diagram to enlarge
Where can Tiangong-1 come down?
The map below shows the area where Tiangong-1 potentially can come down: included land areas at risk are southern Eurasia, Australia and New Zealand, Africa, South America, Meso-America and the United States. Northwest Europe including my country (the Netherlands) is not at risk.
In theory, the extreme margins of this zone (i.e. near 42.8 S and 42.8 N) have an elevated risk. In reality, it is notably the position of the perigee which matters, as reentries tend to happen just after perigee passage.
Note that at this moment, the uncertainty in the reentry estimates is that large, that it is not meaningful to provide nominal estimated reentry positions. Any newspaper claims that it will reenter over a particular region, are simply false.
[Image]
click map to enlarge
Within the uncertainty window of the current JSpOC TIP, the lines on the
map below are where Tiangong-1 could come down (cities with populations lager than 1 million people between latitude 42.8 N and 42.8 S are also
shown: those under or very near the trajectory of Tiangong-1 are indicated by white dots):
[Image]
click map to enlarge
Only during the very last few hours before the actual moment of reentry,
we can start to point to a particular part of the orbit where it might
reenter. But even then, uncertainties in location still will remain
large. Satellites near atmospheric reentry move at speeds of almost 8 km/s,
so a mere 10 minutes uncertainty in time on either side of the
nominally predicted time already means an uncertainty in position of
almost 8500 km! And usually, short before reentry the uncertainty is
still much larger than 10 minutes...
An article in the International Business Times has recently appeared which suggests that Chinese officials claim to still have control of Tiangong-1, and that they will do a deliberate deorbit over a designated Ocean area.
In that case, I would expect to see a NOTAM and Maritime Broadcast Warning
being issued in advance by Chinese authorities for a specified location
and time window. No such NOTAM or Maritime Broadcast Warning has been
issued so far, so for the moment I am skeptic of the claim.
What if...?
Tiangong-1 is big enough to almost certainly see pieces survive reentry and hit the ground or the Ocean surface.
Surviving elements of reentries are often parts of the rocket engines and fuel- and inert gas tanks.
The tank below is an example: this was part of the second stage of a Falcon 9 rocket (2014-052B) that reentered over Brazil on 28 December 2014. This tank impacted on Brasilian farmland and was subsequently recovered:
[Image]
photograph (c) Cris Ribeiro, Brasil
The chances of being hit by falling space debris are however very slim: you have a much higher chance of being struck by lightning.
In fact, the biggest risk of freshly reentered space debris is not being hit, but curious people checking out the fallen objects. If the part in question contains a fuel tank with remnants of fuel still in it, this can be very dangerous. Most rocket fuels are highly toxic, and fumes from a ruptured tank still containing some remnant fuel could easily kill you. It can also do nasty things when your skin or eyes come into contact with it.
The video below shows a spent rocket stage that came down downrange from a launch in China in January (this is not "space debris" persé: but rather "launch debris" as it concerns a primary stage that was jettisoned early in the launch, so the stage itself stayed suborbital).
In the second part of the video, you can see people filming the burning wreckage from close by. DON'T DO THIS! This is extremely dangerous...!
So if by change the reentry does occur over your region and you come upon debris lying in the field, hold your distance and call the emergency services. Let them deal with it.
At the same time, do not worry too much about the risks. It is still most likely that Tiangong-1 will come down over the Ocean, as most of our planet is Ocean.
And finally...
To get into the mood, here is the Hollywood version of a Tiangong reentry for you... ;-)
(Tiangong-1 in reality is much smaller by the way)
Note: this post has been updated, and parts added or rewritten, repeatedly. Text and figures are updated daily
Note 2: a very nice background piece on my reentry estimate efforts was written for Atlas Obscura by Jessica Leigh Hester.
posted by SatTrackCam Leiden at 23:50 on 02-Apr-2018
"Updated Tiangong-1 reentry forecasts (updated April 2)"
44 Comments -
WooT!
17/3/18 00:18
How much more likely is it that reentry occurs near the edges of the latitude band than near the center?
19/3/18 15:53
I think this has some good info from which to calculate the distribution of liklihood.
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080045805.pdf
The orbit time for Tiangong 1 is 89 minutes, so that's 16 orbits in a day, and with error bars of 4+ days on the deorbit time, that's 64 orbits... so I think you can use the equation in the linked PDF to provide a decent likelihood plot.
It's unclear to me, but I think the error bars aren't ever going to get lower than, guessing 16 orbits. So the long term plot of likelihood probably still applies.
19/3/18 19:04
Meithan: the Space Station spends slightly more time near the lower and upper latitude "edges" of the zone.
However, the most important factor in where it will come down is not so much dwell time, but the position of the point of perigee: reentries tend to happen just after crossing through perigee.
20/3/18 13:47
Thank you, SatTrackCam!
I made a plot of Tiangong-1's current ground track extended for 100 days,
https://meithan.net/images/Tiangong1_track.png
and computed a histogram for the latitudes over which it flies, with bins around 1° of latitude wide:
https://meithan.net/images/Tiangong1_histo.png
Seems the station loiters over the last degree of latitude around 6 times longer than over equatorial latitudes. But the probability is only increased in a narrow band at the very edges of the range.
(This reminds me of the position probability plot for the classical harmonic oscillator ... which isn't surprising considering the orbit is almost circular, and the ground track is close enough to the equator that it resembles a sinusoid. There must be an exact result for that probability distribution.)
20/3/18 16:14
If the probability plot is plotted on a sphere, there is no more likely deorbit position than any other on the path (neglecting apogee/perigee, of course). The increased likelihoods at certain latitudes are simply issues of projection of the sphere onto a flat page.
At least that's how I understand it.
20/3/18 16:18
@Christopher Becke: kind of. It's more a consequence of how we define geographic coordinates (which is determined by the spherical nature of Earth, yes). But it's not an illusion: the loitering time *does* peak near the edge of the latitude band.
If you measured the ground track speed in terms of *degrees of latitude per unit time*, the station does move faster (in these terms) near the equator than near the edges of its latitude range.
20/3/18 16:43
Do we have a plot or list of expected lat/long positions corresponding to the points of perigee for the next 2 weeks or so?
A neat plot would be those points, smeared out along the track a few hundred miles. Those would probably be a good guess as to the most likely deorbit positions.
The point-smear glyphs could be copies of a single vector graphics icon that could auto-adjust width and length in a custom gmaps plot of the earth (the orientation would be set for each - tied to the track at that point). Then you could leverage the built in gmaps data and interface to make it user friendly and fun for people to interact with.
20/3/18 20:54
I just asked PyEphem and apparently the current perigee (from the latest elset, dated 2018/3/20 07:49:52) occurs around 12°S latitude. If reentry is to occur close to the current perigee, then locations in the 10°S - 15°S latitude band should be more likely. But I just don't know if the current perigee is a good predictor of where it will reenter.
20/3/18 22:16
Continuing the idea that the latitude of the current perigee is a good predictor of the final latitude of reentry (is that so historically? Good question for Dr. Langbroek!), places in the 10°S - 15°S latitude band include Peru, Bolivia, southern Brazil, Angola, Zambia, Mozambique, northern Madagascar, and the northern tips of Australia -- and large areas of ocean, of course.
20/3/18 22:36
If I'm doing this right, I'm seeing the sat's orbit process relative to the surface of the earth by about 23.5 degrees long each orbit. I don't know the orbit's relative inclination to the axis of the earth, or where that 12degS was in its own orbit, but over many orbits, the range of latitudes covered by the sat ground track is about 82 degrees, centered on the equator. I guess that means its orbit is inclined by about 41 degrees....
20/3/18 22:58
Kevin: the orbital inclination of Tiangong-1 is 42.75 degrees.
Meithan: the position of perigee is *not* stable, it changes over time. Exactly how it changes, depends on the actual orbital evolution, and is difficult to model for an object near reentry.
We'll have to wait untill the last few hours of Tiangong-1's existence before we can start to maked educated guesses about the point of reentry.
20/3/18 23:14
and the period of the sat's orbit is about 89 minutes. that equates to 22.24 degrees of the earth rotating about it's axis, so my 23.5 degrees procession per orbit seems good, and (this is probably for my own spatial confirmation) the sat's orbit isn't processing relative to the earth's axis (neglecting the earth's slight wobble). so, as you say, i guess the range of 10degS to 14degS is a good rule, until we find out if the perigee is on the down or up stroke of the orbit, in which case we can drop that range by half.
20/3/18 23:17
ah, ok - thanks for the clarification on the perigee position not necessarily being stable.
20/3/18 23:21
@SatTrackCam: I see. Oh well, we'll just have to wait and see.
21/3/18 00:08
Well... we can still play fun games by knowing the perigee position now, very conservatively extrapolating from the changes per orbit we see now to model how the perigee might change over the next two weeks (clearly the further out the worse the model), and plot those perigee positions on a map of the surface of the earth. after deorbit, we can see how the model deviated from reality.
21/3/18 00:46
So I will have at least 30 minutes to take cover in case it is going to hit my area?
21/3/18 17:34
I guess it depends on how quickly updates to the elsat get pushed out and how often you check this (and possibly other) websites that track those things... perhaps automatically.
I'm not sure if anyone has set up a text message or email or other alert that might trigger on updates to the models, 24 hour, 12 hour, and 2 hour alerts, etc.
21/3/18 19:25
Marco, is there a way we can dredge up the perigee ground track positions over the past few weeks? I'd love to grab that data and plot it.
21/3/18 19:27
@Kevin White: here, I downloaded all available TLEs from SpaceTrack (which cover the whole life of the station from launch in 2011), and extracted perigee/apogee altitude as well as perigee latitude/longitude data using PyEphem:
https://meithan.net/tiangong1/index.html
You can download the data in CSV by clicking on the icon. The first line (which starts with a "#" contains the definitions of the columns).
It's interesting that the latitude of perigee oscillates naturally from -inc to +inc with a very stable period of around 48 days (clearly visible when there are no re-boosts).
Dr. Langbroek: will this very clean periodicity hold as the station approaches reentry? Because if it does, one could use it to obtain an estimate of the latitude of reentry as a function of when it reenters.
The uncertainty in the exact reentry date still represents a big error in perigee latitude, around ~7.5 degrees per day. But at least some estimate could be made, and a predicted reentry uncertainty of +/3 days (as it currently stands) would narrow down the possible latitudes a bit. (And apologies if I'm overlooking a bunch of important factors here; I'm no expert in satellite reentry.)
22/3/18 01:52
Here's a rough prediction assuming the periodicity in the perigee latitude will hold up until reentry -- which is probably not true, but hey, it's a prediction:
https://meithan.net/tiangong1/Tiangong1_prediction.png
I obtained the model of the quasi-periodic perigee latitude variations by fitting a cosine with a linearly varying period to the last 6 cycles. Then, I extrapolated that periodic variation till the currently predicted reentry time, and got the predicted reentry latitude bounds from that.
The predicted reentry latitude range is about 1/3 of the full latitude range of the ground track (due to inclination), so even if the prediction turns out to be good it could be just lack. But I had fun.
22/3/18 06:58
Thanks!
I think we'd only look at 1-1-2016 and beyond.
One question, above you say that perigee was at ~-12deg lat on 2018/3/20 07:49:52, but the data on your website seems to say that on 3/20 it was closer to -40deg lat.
Are we pretty sure perigee data from the csv link (and your plot on that page) is the correct one?
Assuming your csv data is the better set, then while the perigee data does look a little bit noisier recently, the shape through the most recent trough of the sinusoid is still within about 1.6% of the width/shape of the immediately preceding trough at about 1/28/2018.
So, that means that we can probably use a fit to the sinusoid since 1/1/2016 to guesstimate where the perigees will be over the next 2 weeks, at least as far as lat is concerned. I haven't looked at long...
hmm. that's going to take a different approach. I've looked at the incremental sum of the differences between adjacent longs in your csv, and there's some weird artifacts here and there, but it looks pretty linear in time, at least recently, so we can use that line since about 1/1/18 to extrapolate out where the longs will be for each projected perigee. the slope of that line is about 20.4 deg/hour, if I've done math right.
I think that's about all we need to guess a series of perigees out a few weeks, with error bars steadily increasing over that time.
tie that in with the modeled decay day provided by Marco, and you'll have a selection of 20 or so perigees for that day, and corresponding lat longs.
22/3/18 08:16
On second thought, I'm not sure I'm analyzing the longs correctly. I don't think I'm unwinding the longs so as to get the correct angle between adjacent long measurements.
22/3/18 09:14
If I redid things correctly, perigee longitude changes by about -15.34 deg/hour (that's the slope of the linear change in long for perigee since early feb).
Looking at the csv data again, it shows perigee positions only 3-4 times a day, but the orbital period for the sat is closer to 90min, which would mean 16 orbits a day, with each orbit necessarily including a perigee. I guess that tells us how often the elsats are updated? Or maybe that's the resolution of the model?
In any event, I think we have very rough evolutions of the position of the perigee relative to the surface of the earth, as a function of time. however, we don't yet have the times when the satellite itself passes through the perigee of the orbit.
Thoughts?
22/3/18 10:05
@Kevin White: regarding the previously reported perigee latitude of ~-12deg for 3/20, you're right, there's indeed a discrepancy with the newer values.
I used different methods to compute the latitude. For that initial estimate I just looked at an altitude vs. latitude diagram and eyeballed the value. For the more recent values in the CSV and plots on my website, I used the orbital parameters (specifically: the mean anomaly) to compute the exact time of perigee, and then obtained lat/long at that time. So the CSV values should be more reliable, but let me double-check the latest calculations to make sure they're indeed correct.
As for the longitude of perigee, I did not try to make a prediction for it because it changes much faster than the latitude (as you said: around 15 degrees per hour, as opposed to around 7 degrees *per day* for the latitude). With a reentry date with ~3 days of uncertainty on either side, the longitude of reentry could be anything.
The 3-4 values per day is just the update frequency of the elsets. They're not updated once per orbit.
The times of perigee are included in the CSV; they're in column 4.
22/3/18 14:46
Hi Meithan: what would be helpful that's missing from your perigee latitude time evolution plot is whether perigee is occurring on the ascending node or descending node. For instance, at present perigee is occurring on the ascending node. Another thing to note is the interplay between orbital perigee (i.e. minimum radial distance) and minimum altitude. The two are only the same when perigee occurs at zero latitude. At all other latitudes, minimum altitude will occur at some latitude that differs somewhat from the latitude of perigee due to earth oblateness. --Rob Matson
22/3/18 20:31
@Rob - lets ignore that the earth is more squat by about 22km on radius. More important is the orbital perigee itself, and maybe the bulging of the atmosphere. Those two datum together would make some perigees "hotter" than others in the this totally seat of the pants analysis.
@Meithan - thanks. I think we can probably extract whatever time evolution there is in the timing of the perigees from the partial data and the known orbital period. We're pretty close!
22/3/18 22:13
Hi Kevin: I don't think you can ignore the earth's oblateness in even a first-order analysis. At the satellite's latitude extremes, the earth radius is 10 km less than it is at the equator. That's almost 50% of the current difference between perigee and apogee. --Rob
22/3/18 22:26
Just popping in to say I love your blog and your contributions to the SeeSat list (of which I understand nothing). First thing I do every morning at work is check both. Much enjoyment had! Thank you!!
23/3/18 00:08
@Rob - for what Marco is doing, you need to account for the density of the atmosphere along the orbit, which would probably have to take into account how the terrestrial bulge and the atmospheric bulge and maybe even the tidal bulge change that density. But, that's what's necessary to model and pinpoint a single time of reentry, and I'm fairly sure the atmospheric models Marco is already using account for those.
Aside from that, however, Marco mentioned that deorbits often happen right after an orbit perigee, not after an equatorial transit. And, while the altitude might change 10km when transiting the equator, it's unclear what effect that has on the atmospheric density or drag the sat sees at its current (and expected, before divebomb reentry) altitude, in light of all the other effects (including solar wind, etc.).
So, in the interest of keeping it simple, and using an alternative less rigorous method (cause Marco has the more rigorous method in hand), I think we may get pretty close to the more rigorous method by generating a plot of the orbital perigee positions over the earth for the next two weeks, even assuming a lot of things that aren't necessarily good to assume as this thing dives into the atmosphere. I'm interested in seeing how close we do get, or how far off we are.
Anyway, once we have that plot, we can highlight perigees that are closer to the equatorial crossings as more likely deorbit spots in the Orbital-Perigee-First Model. Also, it will be clear from that plot whether the perigee is leading into or out of an orbital transit (see Meithan's plot, for example).
Also, see:
Generally, depth and thickness of the atmosphere are measured in terms of its lowest layer, the troposphere. The troposphere extends from the Earth’s surface upward to between about 6 and 20 kilometers (4 and 12 miles). The exact extent depends on location. The troposphere is shallowest -- or narrowest -- at the poles, and deepest -- or thickest -- at the equator. At the geographic North and South Poles, the troposphere reaches only 6 kilometers (4 miles) high, while at the equator, it extends nearly 20 kilometers (12 miles) high. Depths and degree of thickness gradually shift between these two extremes in the middle latitudes. For instance, at 50 degrees latitude, roughly the latitude of Seattle, Washington, the atmosphere is just under 10 kilometers (6 miles) thick.
23/3/18 01:17
Hi Kevin: you wrote "Marco mentioned that deorbits often happen right after an orbit perigee, not after an equatorial transit" -- what isn't captured in that historical analysis is the most relevant factor: NOT the latitude of perigee, but rather the latitude of lowest altitude in the orbits leading up to reentry. Based on Tiangong's orbit right now, propagating forward, I will say the odds of reentry over the northern hemisphere are greater than over the southern hemisphere. This is not so much a consequence of the projected latitude of minimum altitude; rather, it is that the minimum altitude is likely to occur within +/- 15 degrees latitude, combined with the fact that perigee is occurring on the ascending node. Reentry will happen in less than two weeks. It is unlikely in that short window that perigee (and minimum altitude) will transition from occurring during the ascending node to during the descending node. This increases the odds of a reentry over land.
23/3/18 06:33
@Meithan - I've seen your updated Tiangong 1 page - nice plots!
The thing I don't understand from the plot of reentry is how you determined/selected the time of reentry on the bottom plot - I don't see any data points, just a curve. The perigee of the orbital path is moving continuously, but it only intersects with the actual position of the satellite at specific times - is that point one of the times, and you chose March 31 as linked in with Marco's work?
Also, I'm just curious - did you need that many variables to fit a cos to the data? I also note that due to dwell time, the +- peaks are weighted much more heavily than the transits... and you can see the curve misses the transits pretty regularly as a result. There might be a better way to weight the fit so that it follows the transits better.
23/3/18 19:54
@Rob Matson: Very good remarks. I was just starting to look at elevation data, as opposed to simply using the orbital elements, and indeed there are some differences in computed latitudes. In fact, this explains the discrepancy that Mark White spotted in latitude values I quoted earlier: one of the values was obtained by looking at the latitude of minimum elevation while the other was the latitude of orbital perigee proper; they differ substantially.
I think I do agree with Rob in that any attempt of predicting the latitude of reentry should be based on *elevation* data, since atmospheric density scales with it, and that is what ultimately causes reentry. But I don't want to get too deep into atmospheric details, as Dr. Langbroek's models already do so and it would be futile to try and re-create those models "by hand".
I've already produced a simple prediction (which I can update effortlessly as the predicted time of reentry is updated) based on the latitude of the orbital perigee. Let's see now what comes out using elevation data instead, i.e., by determining the latitude of the point of lowest elevation in each orbit. I have all the required data; it's just a matter of crunching it.
@Kevin White: Your second guess is correct: I'm taking the time of reentry directly from Dr. Langbroek's predictions.
The goal was converting the time-of-reentry prediction, with its uncertainty, into a prediction for the latitude of reentry, which is something Dr. Langbroek doesn't report (probably because it's impossible to predict at the moment, and we're simply having fun with data here ;) ). In that plot, the red curve is the fitted model, and the blue curve is the extrapolation into the future using that model. I realize that the model is not perfect, in part because I used the last 6 cycles to fit it, so in a sense it's an "average model". Perhaps I could use only the last few weeks to get a more "local" model?
About the cosine fit: well, generally a simple cosine fit requires 3 parameters already (amplitude, frequency/period and phase constant). Since the cycle is not exactly periodic, I added a fourth parameter to account for time-varying period (by making the simplest assumption, i.e. that it changes linearly, if at all). That fourth parameter (T1) turned out to be small, so a constant-period model would also do.
24/3/18 00:34
Thanks for your reply, Meithan -- I'm pleased that you agree (or at least recognize the potential) that the most relevant parameter for predicting reentry latitude is the evolving latitude of minimum geodetic altitude. I look forward to seeing your analysis based on that metric. In parallel with our efforts, I'm writing a little bit of code to spit out that predicted progression of that latitude from a given TLE.
24/3/18 00:56
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25/3/18 18:47
We must remind ourselves that the atmosphere of Earth has the approximate form of a rectangle, because at higher latitudes, the atmosphere rises further from the surface of earth than in the equator; the atmosphere at the equator is denser than a pont at same height closer to the poles. So maybe that is one contributing factor as to why higher probabilities of reentry at higher latitudes.
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/ \ |=>> Polar jets
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25/3/18 18:47
I just found that throughout all of 2018 the perigee has occurred around 1pm local time at the longitude of perigee. Does that mean we can predict a re-entry between 2pm and 6pm local time?
Does this mean there will be no night-time fireball?
27/3/18 16:04
I'd post more but it's 1am here. Check my plot on twitter at @chiefpad
27/3/18 16:06
Hi Paul: I don't think perigee for Tiangong-1 can maintain a constant 1 pm local time at perigee longitude since the satellite is not in a sunsynchronous orbit. For instance, we have local, low elevation, predawn sunlit passes of the station on its ascending node visible from southern California this morning and tomorrow morning. I believe those passes were each not that long after perigee (or at least not long after minimum geodetic altitude), so that's quite far from 1 pm local time.
27/3/18 21:19
OK, here's finally an updated latitude prediction based on two models:
https://meithan.net/tiangong1/
The two models (red and orange data/lines) are:
1) The latitude at each perigee
2) The latitude at which minimum geodetic elevation occurs along each orbit
Both models (cosines of the form A*cos(2*pi*t/T + phi) + B) were fitted with recent data starting 1 March. The data sets -one data point per orbit- were generated from the TLEs using PyEphem.
The blue curves are meant to show how elevation at perigee is not always the minimum elevation in the orbit because the Earth is wider at the equator. When the perigee occurs at high northern/southern latitudes the point of minimum elevation along the orbit does not occur at perigee (but closer to the equator instead).
However, coincidentally the perigee if the currently predicted reentry date will be close to the equator, so the two models produce very similar predictions for the reentry latitude.
And, as said before, these predictions are probably completely wrong as the final latitude of reentry will depend on exactly when the station reenters (and not just on the projected latitude of perigee/min. elev.). But we're having fun here ;).
28/3/18 18:03
Now for Long! (now that we know the time of perigee(s), we can plot the projected longs at those same times, stretch them out along the orbital path about 2 minutes?, and those streaks are the most likely spots of deorbit.)
so, instead of a full set of ground tracks over the full reentry window, plot just the points along those ground tracks that correspond to perigee positions (or min elevation positions, i guess).
again, just fun with numbers!
29/3/18 21:52
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31/3/18 16:40
I hope we have an opportunity to view some of the re-entry over the Chicagoland area.
Does anyone know what the chances of this are?
John
Personalized t-shirt printing
31/3/18 16:46
Thanks everyone for participating in this comment thread. I enjoyed it immensely. And thank YOU Marco for continuing to put up with us and to regularly update this blog entry with your thoughts and work. The tie-in with Humanity Star was excellent science.
It'll be interesting to see if anyone adjusts their models based on the last few hours of telemetry. I love those graphs.
2/4/18 20:41