4. 2003-003B's A/m Compared with that of Shuttle's TPS
Introduction
On Flight Day 2 of STS 107, an object came loose from Columbia; three days later it decayed from orbit. It was only discovered after the loss of Columbia and her crew, through an unprecedented search of archived radar observation logs. It quickly became one of the focal points of the accident investigation. In this report, I refer to the object by its International Designation, 2003-003B. It also has the catalogue number 27713.
1. Summary
Area to Mass Ratio
The greater an object's area to mass ratio (A/m), the greater its atmospheric drag, and the faster its decay from orbit. This physical characteristic is useful in discriminating among the various candidates for the mystery object.
Based upon 2003-003B's published orbital elements (Section 2), I found that its A/m was about 0.049 m^{2}/kg (Section 3). This result is within the margin of uncertainty of the 0.040 m^{2}/kg value I derived originally, from my estimate of the orbital elements.
I gained confidence in my results when Thierry Marais kindly shared the results of his independent analysis, which agreed with mine to within a few percent.
At the CAIB's public hearing of 2003 May 6, the experts conducting the investigation into 2003-003B revealed that their value of A/m was about 0.045 m^{2}/kg +/- 15%, which encompasses both of our results.
Comparison With Thermal Protection System
In Section 4, I evaluate the possibility of 2003-003B having been an element of Columbia's TPS (Thermal Protection System) - tiles, blankets, RCC panels and carrier panels. This cannot be done with complete confidence because the attitude of 2003-003B is unknown. Its attitude would have determined its effective area subject to drag. A tile orientated face into the direction of orbital motion would experience far greater drag than one oriented edge-on.
2003-003B's reported slow rotation would have averaged out its effective area, but there is still a large uncertainty due to the lack of information on the orientation of its axis of rotation; therefore, I evaluated A/m over the range of possible orientations.
I found 2003-003B's A/m to have been most consistent with the physical properties of the densest elements of a shuttle's TPC, primarily its RCC (Reinforced Carbon-Carbon) panels, as reported on Mar 18 by James Oberg, writing for MSNBC News.
At the CAIB's public hearing of 2003 May 6, investigators reported that the only remaining candidates not excluded either on the basis of A/m or radar signature were certain fragments of either an RCC panel or an RCC T-seal. The former would have to have been about 0.33 in. (0.00838 m) thick, which is close to the value that I found.
I found that High Density HRSI (High Temperature Reusable Surface Insulation) also could have matched 2003-003B's A/m, but only in the range between average and maximum values of effective area. Ultimately, investigators excluded all types of tiles, on the basis of radar signature tests.
In the CAIB press briefing of 2003 Mar 11, Maj. Gen. Barry listed carrier panels among the items to undergo radar signature tests. They are removable access panels that carry tiles or thermal blanket. In the CAIB press briefing of 2003 Mar 18, board member Dr. James Hallock speculated that 2003-003B could have been a carrier panel.
This prompted me to consider the aluminium carrier panels. I found that without any tiles, they could have closely matched the A/m of 2003-003B. Carrier panels that retained a 1/8" or 1/4" densified layer of High Density HRSI tile, could also have matched. Carrier panels that retained 3" thick High Density HRSI tile would not have been a good match. Ultimately, carrier panels were excluded on the basis of radar signature tests.
Under certain circumstances, FRCI (Fibrous Refractory Composite Insulation Tiles) and Low Density HRSI could also have matched 2003-003B's A/m - mainly if in sheets of several tiles, which seemed an unlikely scenario. In any case, all tiles were excluded on the basis of radar signature..
I found that AFRSI (Advanced Flexible Reusable Surface Insulation Blankets) would have been excluded on the basis of A/m.
A Unique Debris Shedding Event?
A check of the satellite catalog reveals that no previous shuttle mission that did not conduct an EVA or satellite deployment resulted in the cataloguing of unaccounted debris.
Most of the catalogued debris were items confirmed lost by astronauts during EVAs: a screwdriver on STS 51I, a wire carrier and a socket on STS 88, a pad on STS 102.
Two pieces of debris were catalogued subsequent to the EVA of STS 106. I am unaware of any reports from NASA linking them to the EVA. Their orbital elements are not sufficiently accurate to confirm that separation occurred during the EVA.
Two pieces catalogued from STS 51, appear to be from the anomalous deployment of the ACTS satellite, which resulted in the shedding of debris into orbit.
2003-003B may well be unique; however, it was only found after it had decayed, as a result of an unprecedented post-flight search of archived radar observation logs, motivated by the loss of Columbia and her crew.
Would a similar retrospective of previous shuttle missions have turned up other unaccounted debris? What would have been their physical properties? If the archival data exists, it might be worth the effort to find out just how unique 2003-003B may have been.
In the introduction to the original version of this report, I expressed the hope that the mystery object that separated from Columbia in orbit would be catalogued, and its orbital elements published. That happened on 2003 Apr 09, when USSTRATCOM (U.S. Strategic Command) issued a single set of 2-line orbital elements with the International Designation 2003-003B, and the catalogue number 27713.
The orbital elements are required to estimate the object's area to mass ratio - one of the physical characteristics useful in discriminating among the various candidates for the mystery object. In my original analysis, it was necessary to estimate the object's orbital elements based upon the somewhat sketchy information made public in February 2003. Using the published orbital elements, shown below, simplified the analysis and increased confidence in the results.
STS 107 debris 1 27713U 03003B 03018.89361124 .04158089 28060-1 63330-2 0 15 2 27713 39.0177 214.2209 0013015 7.8234 352.0943 16.06862990 17
The 2-line elements include two different decay terms: ndot/2, used by the SGP orbit propagation model, and B*, used by the newer SGP4 model.
The method used to compute the object's area to mass ratio, described in Section 3, requires the ndot/2, and it is important that it correspond to the epoch of the elements. Using a formula which relates B* and ndot/2, I found that the B* value of 0.63330*10^{-2} corresponds to an ndot/2 value of 0.0522 rev/d^{2}, which I used to compute the area to mass ratio.
For a circular orbit, area to mass ratio is given by the following formula:
A/m = 5.0237*10^{-9} * ndot/2 / ( Cd * rho * n^{(4/3)} )
where:^{ } | A/m^{ } | = area / mass, m^{2}/kg |
ndot/2^{ } | = one half rate of decay = 0.0522 rev/d^{2}, Section 2. | |
Cd | = drag coefficient, assumed = 2.2 | |
rho^{ } | = atmospheric density = 6.0*10^{-11} kg/m^{3}, explained below | |
n | = mean motion = 16.06863 rev/d, Section 2 |
I estimated the atmospheric density experienced by 2003-003B using the National Space Science Data Center's web-based MSIS-E-90 Atmosphere Model. The period covered by the model ended 2002 July, so I ran it against six historical proxy dates with 10.7 cm solar flux^{1} and geomagnetic Ap index similar to those of 2003 Jan 17-20 UTC.
Those dates were 1972 Jan 21, 1978 Jan 3, 1983 Jan 19, 1993 Jan 14, 1994 Jan 6, 1999 Jan 14. I chose January dates to ensure that solar illumination was similar to that experienced by 2003-003B.
For all six proxy dates, I computed the mean atmospheric density during 2003-003B's first revolution after the epoch of its orbital elements (Section 2). The mean values ranged between 4.9*10^{-11} kg/m^{3} and 6.9*10^{-11} kg/m^{3}, with an overall mean of 6.0*10^{-11} kg/m^{3}, used to compute A/m:
A/m^{ } | = 5.0237*10^{-9} * 0.0522 / ( 2.2 * 6.0*10^{-11} * 16.06863^{(4/3)} ) |
= 0.049 m^{2}/kg |
To accurately estimate the A/m of the TPS requires knowledge of their effective area for drag, which in turn requires knowledge of the attitude of 2003-003B. All that has been reported by the CAIB is that it rotated slowly. It is reasonable to assume that it rotated about a transverse axis. The CAIB may eventually determine the orientation of the axis of rotation, but for now, the best that can be done is to evaluate A/m over the range of possible orientations.
The minimum effective area occurs when the axis of rotation is parallel to the direction of orbital motion. It is equal to length x thickness.
The maximum effective area occurs when the axis of rotation is perpendicular to the direction of orbital motion. It is equal to (length + thickness) * width * 2 / PI.
In this section, A/m has been computed for the minimum effective area, the maximum effective area, and the arithmetic average of the two.
For physical data on the Shuttle TPS (Thermal Protection System) I relied mainly on NASA's News Reference Manual.
I learned their approximate physical characteristics in the USENET sci.space.shuttle discussion that began here.
They are removable access panels that carry tiles or thermal blanket. The ones in question are located between the wing leading-edge RCC panels and the rest of the wing. Their approximate dimensions are 0.00318 m x 0.102 m x 0.584 m (1/8" x 4" x 23"), and they are made of aluminium, of density about 2,700 kg/m^{3}.
Attached to the carrier panels on the under-side of the wings are High Density HRSI (High Temperature Reusable Surface Insulation Tiles), of thickness approximately 0.0762 m (3 inches). and density about 352 kg/m^{3}.
The following table shows the effective A/m of a carrier panel with areal dimensions 0.102 m x 0.584 m, with and without the 0.0762 m HD HRSI tiles:
Thickness | Mass | Min Effective Area | Max Effective Area | Ave Effective Area | ||||
Carrier - m | HRSI - m | kg | m^{2} | m^{2}/kg | m^{2} | m^{2}/kg | m^{2} | m^{2}/kg |
0.00318 | 0.00000 | 0.509 | 0.0019 | 0.0036 | 0.0380 | 0.0747 | 0.0199 | 0.0392 |
0.00318 | 0.07620 | 2.101 | 0.0464 | 0.0221 | 0.0429 | 0.0204 | 0.0446 | 0.0213 |
In the sci.space.shuttle discussion cited earlier, it was suggested that if a carrier panel became separated from the shuttle, only the densified layer of the tiles would be likely to remain attached. Below is the A/m that would result from 0.00318 m (1/8") or 0.00635 m (1/4") densified layers, of density assumed to be 50 percent greater than the bulk density of a whole tile:
Thickness | Mass | Min Effective Area | Max Effective Area | Ave Effective Area | ||||
Carrier - m | HRSI - m | kg | m^{2} | m^{2}/kg | m^{2} | m^{2}/kg | m^{2} | m^{2}/kg |
0.00318 | 0.00318 | 0.608 | 0.0037 | 0.0061 | 0.0382 | 0.0628 | 0.0210 | 0.0344 |
0.00318 | 0.00635 | 0.708 | 0.0056 | 0.0079 | 0.0384 | 0.0543 | 0.0220 | 0.0311 |
RCC
RCC (reinforced carbon-carbon) panels have a density of about 1600 kg/m^{3}, and range in thickness from 0.00635 m to 0.0127 m.
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.00635 1.219 0.0025 0.0021 0.0776 0.0637 0.0401 0.0329
0.00828 1.590 0.0033 0.0021 0.0780 0.0490 0.0406 0.0256
0.01270 2.438 0.0051 0.0021 0.0788 0.0323 0.0419 0.0172
At the maximum effective area, a 0.00828 m thick piece of 0.3 m x 0.4 m RCC closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3)^{}. This is nearly identical to the thickness of candidate RCC fragments reported in the CAIB public hearing of 2003 May 6, to have matched both the A/m and radar signature of the object. Thinner pieces having effective areas intermediate between the maximum and the average would also match.
High Density HRSI
High Density HRSI (High Temperature Reusable Surface Insulation Tiles) have a density of about 352 kg/m^{3}. Typically, they are 0.15 m squares, ranging in thickness from 0.0254 m to 0.127 m.
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 0.201 0.0038 0.0189 0.0167 0.0833 0.0103 0.0511
0.02700 0.214 0.0041 0.0189 0.0169 0.0790 0.0105 0.0490
0.04900 0.388 0.0074 0.0189 0.0190 0.0490 0.0132 0.0340
0.12700 1.006 0.0191 0.0189 0.0265 0.0263 0.0228 0.0226
At the average effective area, a 0.027 m thick piece of 0.3 m x 0.4 m High Density HRSI closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3)^{}. At the maximum effective area, a 0.049 m thick piece matches.
It would take several HRSI tiles to account for the area of 2003-003B. I do not know whether or not several could detach together as a sheet, but for the sake of argument, the following table shows the effective A/m spanning the known range of thicknesses of HRSI, for a sheet having the reported areal dimensions of 2003-003B, 0.3 m x 0.4 m:
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 1.073 0.0102 0.0095 0.0812 0.0757 0.0457 0.0426
0.04070 1.719 0.0163 0.0095 0.0842 0.0490 0.0502 0.0292
0.12700 5.364 0.0508 0.0095 0.1006 0.0188 0.0757 0.0141
At the maximum effective area, a 0.0407 m thick, 0.3 m x 0.4 m sheet of High Density HRSI closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3).
FRCI
FRCI (Fibrous Refractory Composite Insulation Tiles) have a density of about 192 kg/m^{3}. Typically, they are 0.15 m squares, ranging in thickness from 0.0254 m to 0.127 m.
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 0.110 0.0038 0.0347 0.0167 0.1526 0.0103 0.0937
0.08050 0.348 0.0121 0.0347 0.0220 0.0633 0.0170 0.0490
0.12350 0.534 0.0185 0.0347 0.0261 0.0490 0.0223 0.0418
0.12700 0.549 0.0191 0.0347 0.0265 0.0482 0.0228 0.0415
At the average effective area, a 0.0805 m thick, 0.3 x 0.4 m sheet of FRCI closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3)^{}. At the maximum effective area, a 0.1235 m thick sheet matches.
It would take several FRCI tiles to account for the area of 2003-003B. I do not know whether or not several could detach together as a sheet, but for the sake of argument, the following table shows the effective A/m spanning the known range of thicknesses of FRCI, for a sheet having the reported areal dimensions of 2003-003B, 0.3 m x 0.4 m:
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 0.585 0.0102 0.0174 0.0812 0.1388 0.0457 0.0781
0.04580 1.055 0.0183 0.0174 0.0851 0.0807 0.0517 0.0490
0.08150 1.878 0.0326 0.0174 0.0920 0.0490 0.0623 0.0332
0.12700 2.926 0.0508 0.0174 0.1006 0.0344 0.0757 0.0259
At the average effective area, a 0.0458 m thick, 0.3 x 0.4 m sheet of FRCI closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3). At the maximum effective area, a 0.0815 m thick sheet matches.
Low Density HRSI
Low Density HRSI (High Temperature Reusable Surface Insulation Tiles) have a density of about 144 kg/m^{3}. Typically, they are 0.15 m squares, ranging in thickness from 0.0254 m to 0.127 m.
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 0.082 0.0038 0.0463 0.0167 0.2035 0.0103 0.1249
0.12700 0.411 0.0191 0.0463 0.0265 0.0643 0.0228 0.0553
A single 0.15 x 0.15 m Low Density HRSI does not closely match the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3)^{}.
It would take several HRSI tiles to account for the area of 2003-003B. I do not know whether or not several could detach together as a sheet, but for the sake of argument, the following table shows the effective A/m spanning the known range of thicknesses of HRSI, for a sheet having the reported areal dimensions of 2003-003B, 0.3 m x 0.4 m:
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.02540 0.439 0.0102 0.0231 0.0812 0.1851 0.0457 0.1041
0.06920 1.196 0.0277 0.0231 0.0896 0.0749 0.0586 0.0490
0.12700 2.195 0.0508 0.0231 0.1006 0.0459 0.0757 0.0345
At the average effective area, a 0.0692 m thick, 0.3 x 0.4 m sheet of Low Density HRSI closely matches the A/m of 2003-003B, 0.049 m^{2}/kg (Section 3)^{}.
AFRSI
AFRSI (Advanced Flexible Reusable Surface Insulation Blankets) have a density of 128 to 144 kg/m^{3}, and range in thickness from 0.0114 m to 0.0241 m. They are manufactured as 0.91 x 0.91 m squares of the required thickness, much larger than the area of 2003-003B.
Thickness Mass Min Effective Area Max Effective Area Ave Effective Area
m kg m^{2} m^{2}/kg m^{2} m^{2}/kg m^{2} m^{2}/kg
0.01140 0.197 0.0046 0.0231 0.0786 0.3989 0.0416 0.2110
0.02410 0.416 0.0096 0.0231 0.0810 0.1945 0.0453 0.1088
AFRSI does not closely match the A/m of 2003-003B, 0.049 m^{2}/kg. (Section 3)^{ }.