by Anilkumar, A K

Abstract (Summary)
In the space surrounding the earth there are two major regions where orbital debris causes

concern. They are the Low Earth Orbits (LEO) up to about 2000 km, and Geosynchronous Orbits (GEO) at an altitude of around 36000 km. The impact of the debris accumulations are in principle the same in the two regions; nevertheless they require different approaches and solutions, due to the fact that the perturbations in the orbital decay due to atmospheric drag effects predominates in LEO, gravitational forces including earth’s oblateness and luni solar

effects dominating in GEO are different in these two regions. In LEO it is generally known

that the debris population dominates even the natural meteoroid population for object sizes 1

mm and larger. This thesis focuses the study mainly in the LEO region.

Since the first satellite breakup in 1961 up to 01 January 2003 more than 180 spacecraft and

rocket bodies have been known to fragment in orbit. The resulting debris fragments

constitute nearly 40% of the 9000 or more of the presently tracked and catalogued objects by

USSPACECOM. The catalogued fragment count does not include the much more numerous fragments, which are too small to be detected from ground. Hence in order to describe the trackable orbital debris environment, it is important to develop mathematical models to simulate the trackable fragments and later expand it to untrackable objects. Apart from the need to better characterize the orbital debris environment down to sub millimeter particles, there is also a pressing necessity of simulation tools able to model in a realistic way the long term evolution of space debris, to highlight areas, which require further investigations, and to

study the actual mitigation effects of space policy measures.

The present thesis has provided newer perspectives for five major issues in space debris

modeling studies. The issues are (i) breakup modeling, (ii) environment modeling, (iii)

evolution of the debris environment, (iv) collision probability analysis and (v) reentry


The Chapter 1 briefly describes an overview of space debris environment and the issues

associated with the growing space debris populations. A literature survey of important earlier work carried out regarding the above mentioned five issues are provided in the Chapter 2.

The new contributions of the thesis commence from Chapter 3. The Chapter 3 proposes a new breakup model to simulate the creation of debris objects by explosion in LEO named “A Semi Stochastic Environment Modeling for Breakup in LEO” (ASSEMBLE). This model is based on a study of the characteristics of the fragments from on orbit breakups as provided in the TLE sets for the INDIAN PSLV-TES mission spent upper stage breakup. It turned out that based on the physical mechanisms in the breakup process the apogee, perigee heights (limited by the breakup altitude) closely fit suitable Laplace distributions and the eccentricity follows a lognormal distribution. The location parameters of these depend on the orbit of the parent body at the time of breakup and their scale parameters on the intensity of explosion.

The distribution of the ballistic coefficient in the catalogue was also found to follow a

lognormal distribution. These observations were used to arrive at the proper physical,

aerodynamic, and orbital characteristics of the fragments. Subsequently it has been applied as

an inverse problem to simulate and further validate it based on some more typical well

known historical on orbit fragmentation events. All the simulated results compare quite well

with the observations both at the time of breakup and at a later epoch. This model is called

semi stochastic in nature since the size and mass characteristics have to be obtained from

empirical relations and is capable of simulating the complete scenario of the breakup.

A new stochastic environment model of the debris scenario in LEO that is simple and

impressionistic in nature named SIMPLE is proposed in Chapter 4. Firstly among the

orbital debris, the distribution of the orbital elements namely altitude, perigee height,

eccentricity and the ballistic coefficient values for TLE sets of data in each of the years were

analyzed to arrive at their characteristic probability distributions. It is observed that the

altitude distribution for the number of fragments exhibits peaks and it turned out that such a

feature can be best modeled with a tertiary mixture of Laplace distributions with eight

parameters. It was noticed that no statistically significant variations could be observed for the

parameters across the years. Hence it is concluded that the probability density function of the altitude distribution of the debris objects has some kind of equilibrium and it follows a three

component mixture of Laplace distributions. For the eccentricity ‘e’ and the ballistic

parameter ‘B’ values the present analysis showed that they could be acceptably quite well

fitted by Lognormal distributions with two parameters. In the case of eccentricity also the

describing parameter values do not vary much across the years. But for the parameters of the

B distribution there is some trend across the years which perhaps may be attributed to causes

such as decay effect, miniaturization of space systems and even the uncertainty in the

measurement data of B. However in the absence of definitive cause that can be attributed for

the variation across the years, it turns out to be best to have the most recent value as the

model value. Lastly the same kind of analysis has also been carried out with respect to the

various inclination bands. Here the orbital parameters are analyzed with respect to the

inclination bands as is done in ORDEM (Kessler et al 1997, Liou et al 2001) for near circular

orbits in LEO. The five inclination bands considered here are 0-36 deg (in ORDEM they consider 19-36 deg, and did not consider 0-19 deg), 36-61 deg, 61-73 deg, 73-91 deg and 91-

180 deg, and corresponding to each band, the altitude, eccentricity and B values were

modeled. It is found that the third band shows the models with single Laplace distribution for

altitude and Lognormal for eccentricity and B fit quite well. The altitude of other bands is

modeled using tertiary mixture of Laplace distributions, with the ‘e’ and ‘B’ following once

again a Lognormal distribution. The number of parameter values in SIMPLE is, in general,

just 8 for each description of altitude or perigee distributions whereas in ORDEM96 it is

more. The present SIMPLE model captures closely all the peak densities without losing the

accuracy at other altitudes.

The Chapter 5 treats the evolution of the debris objects generated by on orbit breakup. A

novel innovative approach based on the propagation of an equivalent fragment in a three

dimensional bin of semi major axis, eccentricity, and the ballistic coefficient (a, e, B)

together with a constant gain Kalman filter technique is described in this chapter. This new

approach propagates the number density in a bin of ‘a’ and ‘e’ rapidly and accurately without

propagating each and every of the space debris objects in the above bin. It is able to

assimilate the information from other breakups as well with the passage of time. Further this approach expands the scenario to provide suitable equivalent ballistic coefficient values for

the conglomeration of the fragments in the various bins. The heart of the technique is to use a

constant Kalman gain filter, which is optimal to track the dynamically evolving fragment

scenario and further expand the scenario to provide time varying equivalent ballistic

coefficients for the various bins.

In the next chapter 6 a new approach for the collision probability assessment utilizing the

closed form solution of Wiesel (1989) by the way of a three dimensional look up table, which

takes only air drag effect and an exponential model of the atmosphere, is presented. This

approach can serve as a reference collision probability assessment tool for LEO debris cloud

environment. This approach takes into account the dynamical behavior of the debris objects

propagation and the model utilizes a simple propagation for quick assessment of collision

probability. This chapter also brings out a comparison of presently available collision

probability assessment algorithms based on their complexities, application areas and sample

space on which they operate. Further the quantitative assessment of the collision probability estimates between different presently available methods is carried out and the obtained

collision probabilities are match qualitatively.

The Chapter 7 utilizes once again the efficient and robust constant Kalman gain filter

approach that is able to handle the many uncertain, variable, and complex features existing in

the scenario to predict the reentry time of the risk objects. The constant gain obtained by

using only a simple orbit propagator by considering drag alone is capable of handling the

other modeling errors in a real life situation. A detailed validation of the approach was

carried out based on a few recently reentered objects and comparison of the results with the

predictions of other agencies during IADC reentry campaigns are also presented.

The final Chapter 8 provides the conclusions based on the present work carried together with

suggestions for future efforts needed in the study of space debris. Also the application of the

techniques evolved in the present work to other areas such as atmospheric data assimilation and forecasting have also been suggested.

Bibliographical Information:

Advisor:Ananthasayanam, M R; Rao, P V Subba

School:Indian Institute of Science

School Location:India

Source Type:Master's Thesis

Keywords:aerospace engineering space debris modelling on orbit breakup clouds evolution collision risk re entry kalman filter assemble model simple orbital elements propagation probability semi major axis


Date of Publication:02/01/2004

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