RE: Reentry of 14052B / 40142

I have completed propagating USSTRATCOM's epoch 14361.97334517 TLE through final descent using GMAT 2013a.

As is, the TLE requires an unrealistically high value of Cd A / m in order to re-enter at the observed time and place,
but this is highly sensitive to perigee height, which appears to be about 10 km too high. Increasing the eccentricity
value of the TLE about 1.7 percent to 0.0850669, reduced the altitude of the first perigee crossing after epoch from
109.85 km to 99.85 km. This yielded a reasonable trajectory using a reasonable value of Cd A / m (0.132 m^2/kg).

The resulting trajectory was late by ~55 s. This could have been eliminated by further increasing the eccentricity and
decreasing Cd A / m, but the resulting trajectory altitude would have been significantly too low, and the Cd A / m would
have been unrealistic. Instead, I simply reduced the epoch of the TLE by 0.000635400 d.

The propagated trajectory agrees fairly closely with the track on the image from the MASCOT camera at Cerro Paranal,
Chile, as reduced by Cees Bassa. Proceeding chronologically, for a given R.A., the declination error varies from ~+0.385
deg to ~+0.23 deg. Culmination was about 76 deg above the horizon, so the data is highly sensitive to trajectory error.

Re-entering objects typically become self-luminous when they descend to about 96 km. During the time span of the image,
the trajectory descended from about 94 km to 93 km, so would have been expected to be self-luminous.

Via the ReentryWatch mailing list, I received an all sky camera image from the observatory operated by Alain Maury at
San Pedro de Atacama, Chile (said to have appeared on his Facebook page). Culmination was about 34 deg above the
horizon, so not as sensitive to track error as the MASCOT data. I have not precisely reduced any data from the image,
but comparison against a star chart and spot checks at several locations reveals good agreement between photo and
propagated trajectory.

The re-entry trajectory passed 5.9 km south of Santa Rita do Pardo, Brazil, where the large COPV tank was found. It
passed 7.8 km SSE of Andradina, Brazil, where the small annular metal object was found. Re-entry fragments greatest in
areal density typically fall within about 10 km either side of the track, depending on wind speed and direction.

In response to my request for information on high altitude wind data, Nico Janssen suggested the following site:

http://earth.nullschool.net/about.html

The data closest in time and position to the debris locations reveals moderate wind above ~5 km altitude, mainly from
the east or south east. Below 5 km, the wind was generally lighter, and predominantly from the northeast quadrant. I
have not attempted to estimate the effects of the wind on the approximately vertically descending debris, but I suspect
that their net effect may be sufficient to explain why the debris fell several km north of the ground track.

To facilitate use of the trajectory, I have created the following Excel spreadsheet, which will compute an ephemeris for
site coordinates entered by the user:

http://satobs.org/seesat_ref/misc/14052B_re-entry_ephemeris.xlsm

The file opens to sheet "Compute Ephemeris", which contains the trajectory state vector from 100 km altitude to below
20 km, at ~5 s intervals. Simply enter the site coordinates in the clearly marked cells, and the ephemeris will be
computed automatically. The ephemeris data will be familiar to astronomers and satellite observers. Ephemeris data above
the horizon is displayed in red font. Scroll vertically to see all of the data.

The next two sheets contain ephemerides for the above mentioned camera sites, spanning the visible range of the images.
The time resolution on these sheets is as computed by GMAT's numerical integrator, typically less than 1 s. This should
make it easier to compare the trajectory with the photos.

The sheets labelled Santa Rita do Pardo and Andradina contain the ephemerides for those locations at 0.5 s intervals,
near the time of closest approach. Column 14 contains the distance along the ground between the site and the trajectory
ground track.

Sheet "Pre-computed" contains trajectory data from the two sites that account for a significant fraction of the
published videos of the re-entry.

The final two sheets summarize the aforementioned wind data.

Below is the GMAT script used to compute the trajectory:

http://satobs.org/seesat_ref/misc/14052B_v6h.script

I used the GMAT script generator in TLE Analyzer V2.12 to convert the modified TLE to the format required by GMAT. I
copied the orbital elements section of the script produced by TLE Analyzer into my customized version. The above script
differs slightly from the one I used, in that the default propagator accuracy has been set to 1e-009. I used 1e-010 in
order to obtain a finer time resolution, at the expense of much longer execution time. The greater accuracy setting did
not materially affect the accuracy of the estimated trajectory.

Ted Molczan


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