The update of ORDEM2000, the NASA Orbital Debris Engineering Model, to its new version ORDEM2010, is nearly complete. As a part of the ORDEM upgrade, this paper addresses the simulation of micro-debris (greater than 10 m and smaller than 1 mm in size) populations in low Earth orbit. The principal data used in the modeling of the micron-sized debris populations are in-situ hypervelocity impact records, accumulated in post-flight damage surveys on the space-exposed surfaces of returned spacecrafts. The development of the micro-debris model populations follows the general approach to deriving other ORDEM2010-required input populations for various components and types of debris. This paper describes the key elements and major steps in the statistical inference of the ORDEM2010 micro-debris populations. A crucial step is the construction of a degradation/ejecta source model to provide prior information on the micron-sized objects (such as orbital and object-size distributions). Another critical step is to link model populations with data, which is rather involved. It demands detailed information on area-time/directionality for all the space-exposed elements of a shuttle orbiter and damage laws, which relate impact damage with the physical properties of a projectile and impact conditions such as impact angle and velocity. Also needed are model-predicted debris fluxes as a function of object size and impact velocity from all possible directions. In spite of the very limited quantity of the available shuttle impact data, the population-derivation process is satisfactorily stable. Final modeling results obtained from shuttle window and radiator impact data are reasonably convergent and consistent, especially for the debris populations with object-size thresholds at 10 and 100 m

Hyde, J. L.

Liou, J.-C.

Matney, M.

Prior, T. G.

Xu, Y.-L.

Matney, Mark

Prior, T.

NASA Technical Reports Server

Simulation of Micron-Sized Debris Populations in Low Earth Orbit

The update of ORDEM2000, the NASA Orbital Debris Engineering Model, to its new version . ORDEM2010, is nearly complete. As a part of the ORDEM upgrade, this paper addresses the simulation of micro-debris (greater than 10 micron and smaller than 1 mm in size) populations in low Earth orbit. The principal data used in the modeling of the micron-sized debris populations are in-situ hypervelocity impact records, accumulated in post-flight damage surveys on the space-exposed surfaces of returned spacecrafts. The development of the micro-debris model populations follows the general approach to deriving other ORDEM2010-required input populations for various components and types of debris. This paper describes the key elements and major steps in the statistical inference of the ORDEM2010 micro-debris populations. A crucial step is the construction of a degradation/ejecta source model to provide prior information on the micron-sized objects (such as orbital and object-size distributions). Another critical step is to link model populations with data, which is rather involved. It demands detailed information on area-time/directionality for all the space-exposed elements of a shuttle orbiter and damage laws, which relate impact damage with the physical properties of a projectile and impact conditions such as impact angle and velocity. Also needed are model-predicted debris fluxes as a function of object size and impact velocity from all possible directions. In spite of the very limited quantity of the available shuttle impact data, the population-derivation process is satisfactorily stable. Final modeling results obtained from shuttle window and radiator impact data are reasonably convergent and consistent, especially for the debris populations with object-size thresholds at 10 and 100 micron

 1 
 Simulation of Micron-Sized Debris Populations in Low Earth Orbit 
 
Y.-L. Xu1∗
 
, M. Matney2, J.-C. Liou2, J. L. Hyde1, T. G. Prior1 
1ESCG, Mail Code JE104, 2224 Bay Area Blvd., Houston, TX 77058, USA 
2Orbital Debris Program Office, NASA Johnson Space Center, NASA, 2101 NASA Parkway, 
Houston, TX 77058, USA 
 
Abstract 
  
The update of ORDEM2000, the NASA Or
                                                          
∗ Corresponding author, E-mail: yu-lin.xu-1@nasa.gov 
bital Debris Engineering Model, to its new 
version – ORDEM2010, is nearly complete. As a part of the ORDEM upgrade, this paper 
addresses the simulation of micro-debris (greater than 10 µm and smaller than 1 mm in 
size) populations in low Earth orbit. The principal data used in the modeling of the 
micron-sized debris populations are in-situ hypervelocity impact records, accumulated in 
post-flight damage surveys on the space-exposed surfaces of returned spacecrafts. The 
development of the micro-debris model populations follows the general approach to 
deriving other ORDEM2010-required input populations for various components and types 
of debris. This paper describes the key elements and major steps in the statistical inference 
of the ORDEM2010 micro-debris populations. A crucial step is the construction of a 
degradation/ejecta source model to provide prior information on the micron-sized objects 
(such as orbital and object-size distributions). Another critical step is to link model 
populations with data, which is rather involved. It demands detailed information on area-
time/directionality for all the space-exposed elements of a shuttle orbiter and damage 
laws, which relate impact damage with the physical properties of a projectile and impact 
conditions such as impact angle and velocity. Also needed are model-predicted debris 
fluxes as a function of object size and impact velocity from all possible directions. In spite 
of the very limited quantity of the available shuttle impact data, the population-derivation 
process is satisfactorily stable. Final modeling results obtained from shuttle window and 
radiator impact data are reasonably convergent and consistent, especially for the debris 
populations with object-size thresholds at 10 and 100 µm. 
https://ntrs.nasa.gov/search.jsp?R=20100026028 2019-08-30T10:25:18+00:00Z
 2 
Paper Outline 
 
1. Introduction 
2. STS impact data 
a. Window data 
b. Radiator data 
3. The construction of a reference degradation/ejecta source model 
a. Major assumptions 
b. Orbital elements and the surface area of a large-size space-resident object 
c. A reference degradation/ejecta source model 
4. Prediction of STS impacts from the reference degradation/ejecta model 
a. Damage laws 
b. Mark-files 
c. Butterfly-type directional debris fluxes 
5. Statistical inference of the new ORDEM micro-debris populations 
a. Definition of model parameters 
b. A detailed analysis of STS data 
c. Population modeling for debris objects of MD (medium-density) material type 
d. Population modeling for debris objects of HD (high-density) material type 
e. Consistency analysis for models based on different types of data 
6. Discussions on the modeling results 
7. Concluding remarks and future work 
National Aeronautics and Space Administration
Simulation of Micron-Sized Debris 
Populations in Low Earth Orbit
Y.-L. Xu1, M. Matney2, J.-C. Liou2, J.L. Hyde1, T. Prior1
1 ESCG/Jacobs, NASA/JSC 
2 Orbital Debris Program Office, NASA/JSC
38th COSPAR Scientific Assembly
18-25 July 2010, Bremen, Germany
National Aeronautics and Space Administration
2
STS impact data and the development of 
ORDEM2010 sub-millimeter populations (in LEO)
• To use newly collected OD data and to take advantage of newly developed 
analytical techniques and supporting models, NASA has recently updated the 
Orbital Debris Engineering Model, ORDEM2000, to its new version, 
ORDEM2010.
• ORDEM2010 micro-debris (greater than 10 μm and smaller than 1 mm in size) 
populations are statistically estimated from space shuttle (window and 
radiator) impact data that are collected from post-flight visual damage 
inspections of space-exposed shuttle orbiter surfaces.
• The development of the model micro-debris populations follows the general 
procedure of statistical inference used in ORDEM2010. It takes the following 
key steps:
– Data analysis, 
– Construction of reference populations,
– Definition of model parameters in terms of the reference populations,
– Linking model parameters with data, 
– Searching for best estimates of the model parameters based on data; updating reference 
populations using the best estimated parameters, and
– Assessment of the modeling results and repeating the above two steps until satisfactory 
results are obtained. 
National Aeronautics and Space Administration
3
Example window data with a material-type 
breakdown
Xu
• Cumulative crater depth and size (diameter) distributions of STS window impacts 
from medium-density (MD)  and high-density (HD) OD impactors as identified in 
post-flight surveys of 34 mission flights (STS-71, 72, 75-77, 79, 80, 84-104, 106, 
108-112).  Steel, Cu, and Ag are considered to be HD and all others MD. (Note that 
MD includes two impacts from low-density plastic impactors.)
• MD and HD data are used separately to derive respective MD & HD populations.
234 
impacts
35 
impacts
(0.25 mm)
National Aeronautics and Space Administration
4
Window data: crater diameter and depth 
distributions of paint, Al, & steel impacts
Xu
• Note the close resemblance between the total numbers and cumulative crater 
depth and size (diameter) distributions of window impacts from Paint and Al 
(Aluminum) objects. This is a useful information on the abundance of Paint and 
Al particles in the debris environment.
National Aeronautics and Space Administration
5
Radiator data with a material-type breakdown
Xu
• Cumulative tape-hole diameter 
distributions of STS radiator impacts 
from medium-density (MD) and high-
density (HD) impactors  as identified 
in post-flight surveys of 38 mission 
flights (STS-71-73, 75-77, 79-104, 106, 
108-112).
There is an aluminum-
on-aluminum issue for 
the radiator impacts. 
Some unknowns are 
assumed to be missing 
Al impacts.
25 impacts
35 impacts
National Aeronautics and Space Administration
6
Extraction of missing Al impacts from unknowns
• Missing Al impacts are picked up from unknowns using the “rejection 
method” (with a minor modification) based on the known distributions 
of unknowns, paint, and Al impacts
– A description of the “rejection method” can be found in “Numerical Recipe” 
Xu
National Aeronautics and Space Administration
7
A degradation/ejecta model: general 
considerations and assumptions
Xu
• An ORDEM2010 model debris population consists of a large group of 
representative orbits. It is practically infeasible to obtain micron-sized debris 
populations from the STS impact data directly without providing adequate 
prior information on the debris populations (i.e., reference populations).
 Small objects in the debris environment are believed to generate mostly due to some 
regular, non-violent processes of surface material degradation.
 A degradation/ejecta source model is constructed to provide the desired reference 
populations for the micro-debris population derivations.
 Catalog (>10 cm) objects are taken as parent bodies of the small micron-sized particles.
• Two major assumptions in the construction of the degradation/ejecta model.
 Number of micro-debris objects created by a surface degradation process is proportional 
to the surface area of a parent body. (Note that the production rates for different 
material types are to be determined by the data of different material types during 
the population derivation process.)
 Micro-debris objects created in a surface degradation process share the same orbit with 
its parent body at the creation time. Every orbit of the degradation/ejecta particles is 
propagated independently under the influence of solar radiation pressure and 
atmospheric drag, in addition to gravitational perturbations.
National Aeronautics and Space Administration
8
A degradation/ejecta model: orbital parameters 
and surface area of parent bodies
Xu
• The building of a degradation/ejecta source model requires detailed 
information on the orbital parameters and surface areas of parent bodies.
• The SSN catalog maintains a historical record of orbital parameters for every 
tracked object, known as Two Line Element (TLE) set data. Orbital elements of 
an individual SSN cataloged object can be conveniently extracted from the 
TLE sets for any reference time as long as the object is in orbit at that time.
• SSN products do not explicitly provide a surface area for a cataloged object, 
though an area-to-mass ratio could be estimated from the information 
contained in the SSN catalog. There are different sources to obtain 
approximate surface areas for SSN catalog objects.
• The detailed dimensions of some intact satellites are known. For these objects, their 
surface area may be computed from the physical dimensions measured before launch.
• For objects with known mass, an approximate surface area may be obtained from the 
area-to-mass ratio estimated from the TLE records.
• However, both physical dimensions and mass of the majority of the catalog objects, 
breakup fragments in particular, cannot be directly measured.  In general, the information 
on the physical and geometrical properties of such an SSN cataloged object is 
embedded in its radar cross section (RCS) measurements. 
National Aeronautics and Space Administration
9
Observed RCSs of SSN cataloged objects: 
two examples 
Xu
• The “size” (or “characteristic length”) of an OD object is usually estimated from the 
mean (or median) of the measured RCSs. 
• The conversion from RCS to object size is an intricate inverse problem in fundamental 
radiative scattering theories, requiring an accurate interpretation of returned radar 
signals originating from the complicated interaction of electromagnetic radiation with 
an object of arbitrary morphology. NASA uses SEM (Size Estimation Model) to convert 
RCS to object size. SEM is developed using static laboratory RCS measurements of a 
representative set of debris objects.
• The probability 
density distributions 
of RCS shown left 
are based on 320 
measured RCSs for 
#00159 and 284 
values for #00657 
National Aeronautics and Space Administration
10
Linking model populations with data
Xu
• When data and reference model populations are available, the next 
critical step is to link data with model populations. 
• The model prediction of STS impacts demands three major elements
1) Damage equations (or damage laws) to predict impact damage 
characteristics, given physical size and material density of a projectile and 
impact conditions, 
2) Detailed information on STS flight timeline and space-exposed area-
time/directionality of each window and radiator element of a shuttle orbiter 
(i.e., the so-called Mark-files) for every altitude session of each involved 
space mission, and 
3) Detailed information on directional debris fluxes (of “butterfly” type) on 
every orbit of involved space missions, calculated using the reference and 
updated model populations. 
National Aeronautics and Space Administration
11
STS impacts predicted from reference 
populations in the degradation/ejecta model 
Window impacts 
predicted from 
MD objects in 
reference 
populations   
Window impacts 
predicted from HD 
objects in 
reference 
populations   
• A Bayesian statistical process refines reference populations based 
on data!
National Aeronautics and Space Administration
12
Estimation of model populations from data
Xu
• When data and reference populations are available and the connection 
between data and model populations is established (i.e., the model matrix 
calculated), model populations (more strictly speaking, model parameters) are 
estimated from data through an appropriate statistical approach.
• STS data are in the form of counts (i.e., number of impacts). The Poisson 
distribution is the nominal distribution for discrete data in much the same 
way that the Gaussian distribution is the bench-mark for continuous data.
• Since we have only one single data set (i.e., we are unable to repeat the 
random sampling process for the OD impacts), it is impossible to investigate 
the “actual” frequency distribution of the impacts. It simply assumes that the 
OD impacts follow a Poisson-like distribution. This means that the random 
mechanism of the OD impacts is assumed to be known to us, which is 
approximately Poisson.
National Aeronautics and Space Administration
13
First-step best-estimated model parameters
Orbital Group            Model Estimates
adjust. factor   sigma (%)
-------------------------- ---------------------------------------------
MD, 10-31.6 um            0.18               7
MD, 31.6-100 um          0.45             15
MD, 100-316 um           1.15             21
MD, 316um-1mm          3.69 19
Orbital Group              Model Estimates
adjust. factor     sigma (%)
-------------------------- -------------------------------------------------
HD, 10-31.6 um            0.10               18
HD, 31.6-100 um          0.32               36
HD, 100-316 um           0.45               40
HD, 316um-1mm          0.00 38
(MD)
Power law (cumulative) 
size distribution in initial 
reference populations:
~ (object-size)-2.6
(HD)
Power law (cumulative) 
size distribution in initial 
reference populations:
~ (object-size)-2.8
National Aeronautics and Space Administration
14
Update of reference populations: first iteration
• The adjustment factors used to update 
reference populations are obtained 
from model parameters through a 
simple numerical scheme as shown.
• Note the important difference between 
model parameters and adjustment 
factors applied to update reference 
populations. Only for a single 
parameter model, the model parameter 
will be identical to the  single 
adjustment factor.
• The updated reference populations are 
to be used to recalculate model 
matrices and to re-derive a new set of 
model parameters. Such a procedure 
is repeated until all model parameters 
become sufficiently close to 1.
Note that other numerical schemes can also 
be used to construct adjustment factors from 
model parameters as a function of object 
size.  As practical calculation results show, 
what scheme to use is not critical since all 
final adjustment factors will converge to ~1. 
National Aeronautics and Space Administration
15
An issue with data fitting
Window crater depth  (mm)
Window crater size (mm)
2007, ISS
good data fitting  bad results?
• Though the “overemphasized” data fitting (left) 
looks good, it generally causes the “dip” at >31.6 µm 
and “hump” at >316 µm cumulative fluxes  (as 
shown in the above example) estimated from such 
derived model populations. See the next two slides
for more discussions.
National Aeronautics and Space Administration
16
Final modeling results: MD+HD
Xu
• Note the saddle-like shape and upward-turned tails of the window 
data curve (left panel)
• How is the data-matching in the final modeling results shown above 
compared with that shown in the last chart? 
National Aeronautics and Space Administration
17
Derivation of ORDEM2010 model populations 
Xu
SSN
Haystack
HAX
Haystack
G
O
L
D
S
T
O
N
ESTS impact data
(LEGEND & SSN)
(Degradation Model)
?
National Aeronautics and Space Administration
18
Spatial density distributions (≥10 and ≥100 µm)
Xu
≥10 μm ≥100 µm
National Aeronautics and Space Administration
19
Summary
Xu
• ORDEM2010 micro-debris populations are estimated from STS impact 
data. 
 The principal data used in the modeling of the sub-millimeter debris populations 
are in-situ hypervelocity impact records, accumulated in post-flight damage 
surveys on the space-exposed surfaces of returned spacecrafts.
 Besides data, the modeling process requires adequate prior information on the 
small-sized debris populations (i.e., reference populations from a source model).
 The general statistical approach used in the population inference is stable and 
effective.
• In spite of the very limited quantity of the available shuttle impact data, 
the population-derivation process is satisfactorily stable. Final 
modeling results obtained from shuttle window and radiator impact 
data are reasonably convergent and consistent, especially for the 
debris populations with object-size thresholds at 10 and 100 µm.


Simulation of Micron-Sized Debris Populations in Low Earth Orbit

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server

NASA Technical Reports Server