A Study of Orbital Debris

 

University of Colorado at Boulder

Department of Aerospace Engineering

 

ASEN 5050 Space Flight Dynamics

December 18, 2003

 

Zach Wilson

 

 

 

Abstract

The near Earth space environment is becoming cluttered with man-made debris and naturally occurring meteoroids.  This region of space is where most satellites, the shuttle, and the International Space Station (ISS) orbit.  When designing structures that will orbit in near Earth orbit, careful analysis and planning must take place to understand the full effect of orbital debris over the mission life.  The safety of the spacecraft and the astronauts from the orbital debris must be insured.  Damage to spacecraft components due to the many collisions with small particles that will occur on orbit must not impair a spacecraft’s ability to complete its mission.  Debris mapping and large object collision detection and avoidance techniques are becoming much more important as the object density in high traffic regions climbs and the probability of a conjunction increases.

Figure 1: Micro-crater in solar array surface.  Repeated impacts of

1mm and smaller particles can cause solar array degradation

.

 

Introduction

Two types of debris populate the near earth space environment, natural and artificial debris.  Natural debris originates from comets and asteroids that cross the path of the Earth and leave small particles for the Earth to encounter.  These particles tend to have small density and mass but very high interplanetary velocities on the order of 19 km/s.  The flux of natural debris is basically constant with some very small deviations corresponding to the solar cycle.  Danger to spacecraft from these naturally occurring meteoroids is relatively low and with adequate shielding, spacecraft can be protected from the vast majority of these predominantly small particles.

Figure 2: Long Duration Exposure Facility (LDEF) natural and artificial micro-

particle impacts over 1 year on orbit.  The results of this LDEF microparticle

experiment revealed that microparticle levels were higher than previously believed.

 

The bulk of the orbital debris in the near Earth space environment is artificial debris.  Artificial debris is material that was put into orbit for a purpose and no longer serves any function.  Artificial debris has many sources and very few sinks.  As time passes and orbital object density increases, artificial debris will become more and more of a factor in the design of spacecraft.  In an orbital debris technical assessment completed by the Committee on Space Debris for the National Research Council, this warning was given in the preface of the 1995 document.

“Over the last 37 years, thousands of spacecraft have been launched into orbit for scientific, commercial, environmental, and national security purposes.  One consequence of this activity has been the creation of a large population of debris—artificial space objects that serve no useful function—in orbit around the Earth.  Much of this debris will remain in orbit for hundreds of years or more, posing a long-term hazard to future space activities.  Currently, the hazard is fairly low; there are no confirmed instances of orbital debris seriously damaging or destroying a spacecraft.  However, continuing space operations and collisions between objects already in orbit are likely to generate additional debris faster than natural forces remove it, potentially increasing the debris hazard in some orbital regions to levels that could seriously jeopardize operations in those regions.” 

Since this document was written there has been several suspected cases of on orbit collisions and in early 2003 a French satellite had its stability boom severed by an old Ariane rocket body.  To begin to alleviate this problem before it poses a more serious risk to spacecraft orbiting the Earth, the sources of the orbital debris must be understood.  Once these sources are identified, methods of reducing the debris introduced to the near Earth orbits can be taken.  Currently, methods of tracking and characterizing the debris already exist and help to define the size and locations of the debris population.  This data has been very useful in creating space debris models that predict the amount of debris that will be encountered over the life of the spacecraft.  These models and data about how orbital debris damages satellites are used by spacecraft designers to determine how best to construct a spacecraft that will survive in the near Earth orbit environment.

 

Debris Production

Orbital debris production starts at the very beginning of the life of a spacecraft being put into Earth orbit.  At launch rocket bodies used to boost satellites into orbit are left orbiting the Earth.  Solid rocket motors create numerous types of debris including motor casings, aluminum oxide exhaust particles, nozzle slag, and solid fuel fragments.  Debris is produced when using pyrotechnics to deploy spacecraft appendages.  This debris joins other items such as launch shrouds, payload shrouds, momentum flywheels, clamp bands, auxiliary motors, and launch vehicle fairings that are all introduced to the debris population early in the spacecraft life.  Over the operational life of the spacecraft more subtle sources of orbital debris become more prominent.  As the spacecraft is subjected to solar heating, solar radiation, and atomic oxygen material degradation begins to free small particles of paint and multi-layer insulation.  Towards the end of the life of the satellite object breakup becomes a possibility.  Object breakup is usually the product of a collision or explosion on the spacecraft.  Explosions occur most frequently when propellant and oxidizer inadvertently mix or when batteries become over-pressurized.  Orbital debris can originate from a wide range of sources, anywhere from tens of thousands of spheres of reactor coolant leaking from Soviet RORSATs to paint chips freed from spacecraft bodies due to atomic oxygen degradation of spacecraft coatings.

 

Debris Tracking

NASA’s main source of data for debris in the size range of 1 to 30 cm is the Haystack Radar operated by the MIT Lincoln Laboratory.  Haystack has been collecting orbital debris data for ten years under an agreement with the United States Air Force.  Haystack statistically samples the debris population by staring at selected pointing angles and detecting debris that flies through its field of view.  The data are used to characterize debris population size, altitude, and inclination.  Scientists have used the Haystack data to conclude that there are over 100,000 debris fragments in orbit with sizes down to 1 cm.

 

Figure 3: Haystack Radar Dome

 

Radar has relatively poor resolution at high altitudes, so telescopes are also used to observe orbital debris.  A telescope is able to detect high altitude (geosynchronous) orbital debris better than radar and a telescope can see orbital debris that does not reflect radar well as long as it is not in eclipse.  Some electro-optical telescopes are used to actually track objects however the latest technology uses liquid mirror telescopes (LMT) to sample debris populations. 

 

A liquid mirror telescope uses mercury spun at high speeds to give it a parabolic shape as a primary mirror.  Liquid mirror telescopes can only look straight up, but the mirrors are much less expensive to create then conventional telescope mirrors and orbital debris scanning does not require the telescope to move in azimuth and elevation.  NASA currently has a 3-meter liquid mirror telescope that has been able to detect 2 cm diameter objects at altitudes up to 500 km and can easily see 10 cm particles in GEO.  Using optical and radar sensors in concert gives a more complete picture of the orbital debris population. 

 

Ground-based sensors can repeatedly track the largest objects.  A good deal of debris that can be repeatedly tracked is cataloged.  This catalog is used for predicting potential collisions, recognizing space object breakups, and mapping space object density.  United States Space Command using a network of ground-based sensors called the Space Surveillance Network (SSN) maintains one such catalog.  The SSN consists of more than 20 radar and optical sensors.

Figure 4: Space Surveillance Network Site Locations

The radars in the SSN include several phased-array radars that can track a dozen or more satellites simultaneously and scan large volumes of space.  The radars are mostly used to track debris in low Earth orbit (LEO).  There are a few high power deep space radars that are capable of detecting objects in Geosynchronous Earth orbit (GEO).  Optical sensors do most tracking of GEO objects and the network of radar and optical sensors generates up to 80,000 satellite observations each day. 

 

Debris Orbit Determination and Cataloging    

The observations collected by the SSN every day are passed to U.S. Space Command at Cheyenne Mountain in Colorado Springs, Colorado.  The observations are used to perform an orbit determination for each object that was tracked and NORAD mean element sets for each object are generated and put into the catalog.  These NORAD mean element sets are provided to users in the standard two-line mean element set format (TLES) and are tailored for use with the Simplified General Perturbations (SGP4) propagator.  This propagator considers secular and periodic variations due to Earth oblateness, solar and lunar gravitational effects, gravitational resonance effects, and orbital decay using a drag model.  NORAD two-line mean element sets are available on the web for public use at the NASA/Goddard Space Flight Center Orbital Information Group(OIG) site and at www.celestrak.com, which also hosts the SGP4 algorithms. Of the approximately 8,500 objects being tracked today, only about 7 percent are operational satellites, 15 percent are rocket bodies, and the remaining 78 percent are either inactive satellites or assorted other space debris.    The SSN minimum trackable object size is around 10 cm, and the catalog of objects between 10 and 30 cm is not complete however the catalog of objects greater than 20 cm is estimated to be 90 to 95 percent complete for LEO.

Figure 5: SSN cataloged orbital debris in LEO.

 

One problem with the LEO catalog is that the accuracy of predictions of the future location of objects in LEO is not always good.  Because of this, the use of the LEO catalog as a collision avoidance tool is not always practical.  This predicted position uncertainty is due to the variability of the density in the upper atmosphere and the uncertainty of the objects orbital attitude.  In other words, the cross-sectional area that the atmosphere imparts drag on is unknown.  These uncertainties are significant (on the order of hundreds of kilometers for some objects) compared to any observation errors over the course of a day.  As altitude increases the necessary cross section needed to track an object increases.  Above 5000 km the smallest objects detectable by radar are about 1 meter in diameter.  Above 5000 km optical telescopes are the primary sensors and can track meter-sized objects in GEO, however, not all meter-sized objects are cataloged in GEO.  Unfortunately, tracking of smaller debris is very difficult and only statistical estimates can be made of the number of smaller debris items especially at high altitudes.

                     Figure 6: The distribution of objects in the Space Command catalog by inclination.  Notice                                 Figure 7: The distribution of objects in the Space Command catalog by mean motion.

                   areas of high object density at the critical inclination and in the sun-synchronous inclination.                             Notice regions of high density in the geosynchronous orbits and the low Earth orbits.

 

One other possible means of tracking orbital debris from orbit is spaced based sensors.  Although none currently exists, there have been many studies completed that explore the use of all kinds of sensor technology deployed on a spacecraft with the main goal of detecting orbital debris.  The Department of Energy’s national laboratories have proposed everything from infrared and optical to radar and LIDAR spaced based orbital debris detection sensors.

 

Orbital Debris Modeling

To fill in the gaps of current orbital debris catalogs and to project orbital debris growth in the future, orbital debris models have been created.  There are two main types of models currently being used to understand the orbital debris environment, population characterization models and debris growth characterization models. 

 

Population characterization models convert data on the orbital elements of debris and output data on the orbital debris flux or orbital debris collision probability.  The population characterization model currently used by NASA when designing their spacecraft is the Orbital Debris Environment Model (ORDEM).  ORDEM breaks the orbital debris environment down into many regions and uses data from the United States Space Command catalog to model the flux of objects larger than 10 cm.  For objects smaller than 10 cm, sampling data from ground telescopes and the Haystack radar as well as flux measurements from the Long Duration Exposure Facility (LDEF) satellite and the space shuttles are used to model small orbital debris populations in the different model regions.  ORDEM calculates the flux and velocity distribution for a given size debris relative to an orbiting spacecraft using information provided about the spacecraft and its orbit.  The current engineering version of the ORDEM model is ORDEM96, however an ORDEM2000 has been created to take into account new measurements from the Haystack radar and shuttle flights since 1996 that may reflect changes in the small orbital debris environment.  One reason it is important to update ORDEM is because the orbital debris population in near Earth orbit is growing and the model needs to reflect this increase.  Growth of orbital debris in near Earth orbit is studied using debris growth characterization models.  Most of the debris growth characterization models combine three types of modeling to create a picture of what future orbital debris populations will look like.  Traffic models, breakup models, and orbit propagation models. 

 

A traffic model keeps track of debris launched into orbit by recording when the objects are placed in orbit, size and mass of the object, and the objects initial orbital elements.  A traffic model used for studying orbital debris growth must also include information on objects launched in the future.  When inputting information about future debris, the current trends in debris introduction and launch rate must be considered as well as trends in spacecraft material and design improvement that could lower the possibility of accidental explosions on orbit and material breakdown on orbit. 

 

The traffic model builds a baseline for what will be in orbit in the future, some of these objects will degrade and release smaller debris, this process is described using a breakup model.  The breakup model takes into account all of the inputs of the traffic model and provides a means of simulating the number of fragments released by all traffic model orbital debris due to collisions, explosions, and material degradation. The breakup model also calculates changes in velocity that may place these fragments into different orbits.  All of this information is then passed into an orbit propagation model that determines how the orbits of the larger traffic model objects and the smaller breakup model objects change as a function of time.

 

NASA currently uses the EVOLVE model for studying the evolution of the orbital debris environment.  EVOLVE uses a fast orbit propagator which accounts for J2 and lunar-solar gravitation perturbations and aerodynamic drag.  This fast orbit propagator allows EVOLVE to not only keep track of the orbital changes of the debris but also to model loss of LEO debris into the Earth’s atmosphere.  Using Evolve to model the orbital debris environment is a two-step process.  The first step is to have EVOVLE calculate the current environment using historical records of launches and breakup events.  Once this current environment baseline is established, it is used as the initial environment for debris environment projections.  EVOLVE simulates the processes contributing to the evolution of the orbital debris and for that reason it is able run many different scenarios varying a wide range of parameters to look at future space debris environments.  EVOVLE also has the capability to model the effectiveness of new orbital debris mitigation techniques.  The major uncertainties for EVOLVE and other models like EVOLVE all hinge upon future debris population and orbital conditions.  The number, characteristics and initial distribution of objects that will be launched in the future, and the number of explosions and collisions that will occur in the future is difficult to predict.  Future levels of solar activity and the corresponding effects on atmospheric drag also are hard to predict but must be quantified for the models to give estimates of future debris population.  Current orbital debris models predict that the orbital debris population is going to continue to grow unless deliberate actions are taken to minimize the creation of new debris.  Spacecraft and rocket manufacturers are taking some steps to minimize space debris, but in most cases this is only done when it does not cost any more to take these steps.  It probably will take some spacecraft losses before industry begins to take more aggressive, more expensive measures to reduce debris creation.

 

Debris Prevention

As the debris population grows in near Earth orbit, techniques and policies for limiting the new orbital debris that are introduced to the existing debris population are starting to be discussed.  There are many ideas about how to not only reduce the amount of debris added to the environment but also to get rid of debris that already exists.  Some suggestions are more cost effective then others, and some probably are not realistic in the near term.  Ideas such as orbiting vehicles that autonomously clean up debris, space based laser platforms that would “shoot down” orbital debris, and large low mass high density pieces of foam that would orbit the Earth and collect the smaller debris are all intriguing but will probably not be possible any time soon.  There are many simpler and more cost-effective methods of at least reducing the amount of new debris introduced into Earth orbit.  Some of these methods can and are being employed in the near term and should make an impact on the Earth’s orbital debris environment.

 

A very easy way to begin to reduce the amount of new orbital debris is to limit the amount of mission related objects being released from spacecraft.  Mission related debris includes objects released in spacecraft deployment and operation, refuse from crewed missions, and rocket exhaust products.  These objects make up roughly 13% of the total cataloged space debris population, a large percentage of the un-cataloged space debris.  Because human activity in space is extremely limited, debris from crewed mission is a minor portion of the total mission related debris.  Exhaust products of solid rocket motors, while a relatively large source of small orbital debris, does not pose a great deal of risk to operational spacecraft.  The debris is very small (less then 10 microns) and the orbital lifetime of the debris is short.  Solar radiation and atmospheric drag remove 95% of these particles from orbit within one year of their insertion.  The area where significant improvement can be made in reducing mission related space orbit debris is with objects released from spacecraft during deployment and operations.  Deployment items such as clamps, covers for lenses or sensors, de-spin devices, pyrotechnic release hardware and wraparound cables make up the majority of the cataloged mission related debris population.  Normally these objects are released in orbits that are used by many other spacecraft.  Technology has already been and continues to be developed that avoids simply jettisoning these objects.  Using tethers to retain objects that would have been released is now a fairly standard practice wherever possible in spacecraft deployment.  Explosive bolts that release much less debris have been developed along with non-explosive technologies for separating objects in space without releasing any debris.

 

Fragmentation debris from collisions and explosions makes up 42% of the cataloged space objects currently orbiting the Earth.  Since collisions are believed to be very infrequent, the vast majority of this debris is created when spacecraft and rocket bodies explode.  These explosions are most frequently caused by propulsion system accidents or battery overcharge accidents.  Because of the large number of new particles introduced to the debris population in high use orbits each time an explosion occurs, this area of debris reduction has received significant attention.  To reduce the chance of explosions on rocket bodies and spacecraft after their useful life, efforts are being made to reduce the amount of stored energy left in the vehicles.  This means that when the vehicles are being designed all of the possible sources of energy that might remain at the end of a vehicles life are identified and methods for dissipating that energy at the end of the vehicles functional lifetime are implemented.  These methods include venting of unspent liquid propellant and other pressurized gasses from used rocket bodies and spacecraft, and completely discharging batteries and preventing recharging.  In some cases excess propellant is used to perform retrograde burns that degrade the orbit of the rocket body or used spacecraft so that atmospheric drag will burn the vehicle in faster.  These lifetime reduction maneuvers provide a method for disposing of excess propellant and reducing the amount of time that the vehicles will be orbital debris.  Improved propellant tank design and electrical power system design has also reduced the number of operational vehicle explosions. 

 

Debris produced from collisions, although not a huge concern right now, will become a larger problem in the future.  The amount of debris that is building up in heavily trafficked orbits continues to climb.  Because the development of an effective collision avoidance system would be very costly, other options are being explored.  Moving spent vehicles into disposal orbits or de-orbiting vehicles altogether are both options that would require extra fuel to complete.  This extra fuel budget gets translated into a shorter mission lifetime for many vehicles and therefore it is not a widely used method.  Some work has been done, especially in GEO where space is limited, to establish disposal orbits for old vehicles so that GEO slots can be used by another vehicle.  Although this solves the immediate space problem, the amount of debris continues to increase and existing debris is just being shifted around in Earth orbit not removed.  In LEO, the use of long tethers is being tested out as a means to provide extra drag to accelerate the rate of descent of some objects.  Tethers have also been used to power low thrust electric propulsion engines that push dead or crippled satellites and rocket bodies out of orbit much faster then gravity alone would. 

Figure 8: Example of Tether Deorbit Concept

 

The amount of debris due to degradation of spacecraft surfaces such as paint and thermal blankets has been reduced somewhat by the development of better materials.  Spacecraft designers rarely have to make sure that these coatings hold up any longer then the functional life of the spacecraft but these coatings are in orbit for much longer periods of time.  Surface degradation is one of the main sources for very small artificial debris, and some reduction in the amount produced could be achieved by developing coatings that would last for the orbital life of the vehicle and not just the functional life.

Figure 9: Windshield of the space shuttle damaged by a paint chip hurtling through space.

 

Close Approach Detection and Collision Probability

As the LEO and GEO debris population becomes larger the importance of having tools available to detect and warn of possible collisions with operational vehicles with enough lead-time to take preventive action is becoming evident.  These tools need to have the capability to check a satellite against the entire catalog for several days in the future to detect possible collisions, do a more detailed analysis of the potential collision incidents with a more complete set of data, and perform calculations to determine the probability of a collision actually occurring.

 

Because the catalog of tracked objects continues to grow, fast algorithms to do the initial collision detection analysis are gaining popularity.  One such algorithm is presented in Vallado’s book.  The algorithm begins by eliminating as much of the catalog as possible by weeding out any object whose periapse radius is greater than the apoapse radius of the satellite that is being protected within a certain threshold.

Once any obvious objects are eliminated from the analysis ephemerides are generated for the primary spacecraft and all secondary objects that remain as possible collision candidates.  These ephemerides will most likely be initially produced using a SGP4 propagator and the most recent TLES for each object.  Each secondary objects set of positions, velocities, and accelerations are then differenced with the primary object.

Next a distance function is defined along with its time derivatives using dot products.  The distance function is defined to be the square of the distance so it is not necessary to evaluate a square root.

These distance equations are evaluated for a sequence of times until two adjoining times that contain a minimum are found.  Close approaches occur whenever  is at a local minimum ( = 0 and  > 0).  To determine the times of closest approach the coefficients () of the derivative function for the range-rate cubic polynomial equation  that corresponds to  are computed using a cubic spline.  If the derivatives of the distance function are used a cubic spline still applies except the first and second derivatives are used instead of the function and the first derivative.

Where  varies from 0 to 1.  Extract the real, distinct root(s)  of  on the interval 0.0 to 1.0.  If

then a local minimum range exists.  The time and range corresponding to  still needs to be determined.  A quintic spline is used to capture the contribution of acceleration and to keep the solution accurate.  The quintic polynomial uses  and does not require that the root be found.  The minimum distance is:

and the associated time of close approach is

where  is an endpoint of the time interval containing the minima and .

 

Next, the minimum distances from each secondary object to the primary object are examined and any close approach miss distance below a user set threshold is marked for more thorough inspection.  If this threshold is broken by any of the secondary object approaches then the next step in the process starts.  Once a conjunction is deemed close enough to be concerned an attempt is made to gather more precise data for both the threatening object and the primary spacecraft.  Additional data could include the most recent TLES for the secondary object and position, velocity, acceleration and covariance data from a high precision orbit propagator for the primary and secondary spacecraft if available.  The covariance provides data that describes a 1-sigma volume around the predicted position that the spacecraft is most likely contained in.  Normally the largest covariance error is in the intrack direction with smaller errors in the radial and crosstrack directions that result in an elliptical volume with the long axis aligned with the velocity vector.  A well-tuned, high precision propagator should provide accurate estimates of ephemeris error.  If precise covariance data is not available for one or both objects involved in the conjunction then large, conservative estimates for ephemeris error must be used.  To be on the safe side, the 1-sigma error ellipsoid is often inflated to a 3-sigma error ellipsoid that will contain the spacecraft or object 97 percent of the time. 

Figure 10: STK Conjunction Analysis Tool (CAT) showing intersecting error ellipsoids.

With each object surrounded by an error ellipsoid the conjunction analysis continues.  Legitimate collision opportunities will have the error ellipsoids for the two objects intersecting.  Using very small time steps over the time range of the close approach the distance between the surfaces of the two error ellipsoids can be calculated.  There is many other mathematical methods for determining if the two surfaces are intersecting including taking the error ellipsoids from both objects, combining them around one of the objects and then determining if both objects are contained in the error ellipsoid volume.  Probably the easiest way to see if the two error ellipsoids are intersecting is graphically.  There are a number of graphical 3D software packages available that will allow a user to plot two error ellipsoids for inspection.

 

If after a detailed inspection of the object positions, velocities, and position and velocity uncertainties it is determined that there is a legitimate chance of a collision occurring, the last step in the process is to try and quantify that chance.  Once again there are several methods for coming up with collision probability numbers.  One such method would be to do a Monte Carlo analysis at the time of closest approach.  A random number generator can be used to vary the positions of the two objects within their error ellipsoid volumes and data can be collected for each case.  The data can be binned in terms of miss distance, for instance, there were three instances in one million cases where the miss distance was under ten meters and seven instances in one million cases where the miss distance was under fifty meters.  A histogram can be created showing all of the bins side by side with a bell curve showing the most likely miss distance range.  Figure 8 shows a case where the average miss distance was around 65 meters.  In this particular case there was a two in a million chance that the miss distance would be less than twenty meters and zero instances in one million cases that the miss distance was less than ten meters.

Figure 11: Results of a Monte Carlo analysis of Collision Miss Distance.

 

Conclusion

The ISS mission planners assumed in their design that the ISS would have to be moved twice a year to avoid orbital debris and that estimate has proven to be fairly accurate.  As the debris population has increased, the techniques for tracking debris and detecting possible collisions have become faster and more dependable.  Despite having reliable technology to detect close approaches, the debris population is still growing at rates much faster than is necessary.  Launch vehicle and satellite manufacturers need to start thinking about debris mitigation more actively.  While steps that don’t cost these manufacturers any money are being taken, there are still many design decisions that could be made to slow debris production without affecting performance.  While these extra steps may cost additional money, they could go a long way towards preventing costly collisions and keeping high traffic orbits usable in the future.  If measures like the ones mentioned in the Debris Prevention section above are taken, the growth of the near Earth orbital debris population will probably continue to increase in a linear manner.  Although it is difficult to predict the launch rate and the exact rate of orbital debris growth one thing is for sure, as the population grows the threat of collision grows.  Collisions could potentially set off a chain reaction in near Earth orbit that could cause the exponential growth of the orbital debris population.  When an orbital region has such a dense population of orbital debris objects with sufficient mass that the rate of fragment production because of collisions is greater than the rate at which objects are removed the region is said to have reached “critical density”.  This means that fragments from collisions will cause an increasing number of new collisions.  This chain reaction would need no additional mass to occur, once it starts it feeds itself and could potentially create a near Earth orbit environment with a collision hazard that is too high for space operations.  Though the time frame over which such an event would occur over is not agreed on, many long-term models do agree that it will occur unless something changes.  To preserve near Earth orbit for generations to come, steps need to be taken that prevent the orbital debris problem from spiraling out of control.

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