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Tiangong 1 reentry
by cristiapi 06192017, 11:24 AM
I wrote a program to calculate the Tiangong 1 reentry date.
Starting from a TLE, my prog propagate the initial state down to an altitude of 20 km. The simulation uses the NRLMSISE00 atmospheric model considering the observed and predicted solar activity and geomagnetic levels. As can be seen from the attached graph, while my calculations are in fairly good agreement with this site: http://www.satflare.com/track.asp?q=37820#TOP (“This object is expected to decay around Mon, 16/07/2018 06:20:00 +/ 84 hours UTC (these predictions are provided by Joseph Remis).”), the reentry dates calculated by my program are well beyond the date calculated here: http://www.aerospace.org/cords/reent...ong1reentry/ (“Tiangong1 is predicted to reenter in 2018 January ± 2 months.”). I have 2 questions: 1) has anyone tried to simulate the Tiangong 1 reentry using Orbiter? (Since it’s almost impossible to predict the exact impact location, I’m only interested in the possible reentry date). 2) does anyone know another site where the reentry date is calculated? 
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06192017, 11:26 PM  #2 
Bug Crusher

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Also, I don't think there is any way in Orbiter to input predicted solar activity, is there? On your graph, what am I looking at? It looks like you are predicting mmultiple reentry dates over a wide range of time. Is this the result of Monte Carlo simulations or something? 
06202017, 10:56 AM  #3 
Orbinaut

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But a simulation with the Orbiter's NRLMSISE00 builtin module still would be interesting because I can use my atmospheric model with the default Orbiter's values (excluding the data file) and then I can estimate the differences including the data file for the predicted solar activity and geomagnetic levels. Quote:
I generated the graph using 52 TLE, so the graph shows 52 orbit predictions. From those TLEs, the most probable reentry date range from 20180910 to 20181014. If this topic is of some interest, I can periodically upload (say once a week or twice in a month) the new version of the graph where I use different colors for the plots based on the age of the starting TLE (new TLEs are more "important"). 
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09042017, 12:58 PM  #4 
Orbinaut

Here is the updated result which comes from a vastly improved version of my simulation:
I read the Tiangong1 starting position and velocity from a TLE, then I integrate those vectors down to an altitude of 80 km. Since in that graph I used 103 TLEs, 103 trajectories are showed. The color is for the age of the TLE: new TLEs are vivid blue. In the simulation, the Earth is the ellipsoid WGS 84 which includes the zonal spherical harmonics up to order and degree 20. Then I add: • perturbations from: Sun, Moon and all the planetary systems; • relativistic acceleration; • atmospheric acceleration based on the NRLMSISE00 model along with a data file for the updated geomagnetic and solar activity indices. The initial state of the celestial bodies is read from the DE431 ephemerides. At the end of the simulation, after about 200 days, the differences between the position calculated with my simulation and those calculated with the DE431 are about 1.8 km for the Moon, 600 m for the Earth and a few meters for the other bodies. The integrator is the very good DOPRI853. The step I use is about 144 s; with that step, the simulation speed is about 6.85 days/s. The mathematical model of the Tiangong1 is hard to write and I don’t know its attitude. According to my simulation, it seems that it rotates about the lateral (pitch) axis of about 5 deg/day, but without a visual observation I can only guess that value. Last edited by cristiapi; 09042017 at 02:37 PM. Reason: Typo 
09052017, 03:02 AM  #5 
Bug Crusher

I think you are going about this a little wrong. You need to calibrate the ballistic coefficient of the spacecraft before you have any kind of meaningful simulation. If the trajectory from the 1st TLE is very different from the 103rd TLE, the only thing you know for sure is that you are wrong there. A "correct" model would predict the same trajectory (reentry date) regardless of what TLE you use as your starting point.
Start with the first TLE position, velocity, and time and integrate until the epoch of the 103rd TLE. How close do the positions and velocities agree at that time? If those two don't agree, your model is off. Adjust the ballistic coefficient or whatever parameters you have and integrate again until you can start from the frst TLE and accurately predict the position/velocity of a future TLE. Make sense? Last edited by boogabooga; 09052017 at 03:05 AM. 
09052017, 10:17 PM  #6 
Orbinaut

It makes plenty of sense! And it’s what I’m doing. To calibrate the Tiangong1 parameters I do exactly what you say (I’m currently using 224 TLEs and I calculate several statistical parameters), while for the air density I can just take the result from the NRLMSISE00 model as is (but I use the data file to keep it up to date). But I cannot agree with this:
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The first error comes from the TLE uncertainty which is typically 1 km and when 1 km error is propagated in a perfectly written simulation, the final error will be much bigger. For example, if I propagate one TLE, I obtain the following reentry date: 20180321 21:42 at a location situated on latitude= 17.5623 and longitude= 42.3516. Then, I simply write rj2k[0] += 1 to translate the ECI J2000 x coordinate of the same TLE of 1 km and I obtain: 20180325 06:32, latitude= 0.341365, longitude= 38.7379, a totally different reentry date and location. The second error comes from the conversion from the TEME reference frame (used for the TLEs) to ECI J2000 reference frame and it’s probably bigger than the former (because of the uncertainty in the nutation and precession values). Also, consider that I don’t want to do a correct simulation because if, for example, I switch from WGS 84 gravitational model to the very accurate EGM2008 gravitational model, the time taken to propagate 200 days will be well beyond the actual Tiangong1 reentry date (it will probably take some years). Just consider that to propagate 200 days, the function that calculates the accelerations is called about 1.7 million times (with DOPRI853 integrator). 
09062017, 02:49 PM  #7 
Bug Crusher

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So what are you getting as output, a probability distribution? It is hard to distinguish shades of blue. Is there a systematic relationship between the age of the TLE and the predicted reentry date. 
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09062017, 04:39 PM  #8 
Orbinaut

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If someone is interested in the data files, they can be downloaded from here (216 kB) as a 7z file. 
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09062017, 05:10 PM  #9 
Bug Crusher

Yes, I'd say. Not linear, but you can see a kind of sinewave developing. That might be a clue. Are you using a variable ballistic coefficient?

09062017, 09:30 PM  #10 
Orbinaut

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Cd= 2.05 * .91263 / .55 Cd *= .55 + ((1.4119E8 * ALT + 1.1568E5) * ALT  2.0701E3) * ALT but I need to change 2.05 and .55 when I update the simulation, because the biggest problem with the Tiangong1 model is that I don’t know how to calculate the acceleration about the pitch axis (I don’t know the moment of inertia), so I rotate the station using an empirical angular speed (the angular speed is important because the cross sectional area is variable). 

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