Donald J. Kessler

Derivation of the collision probability between orbiting objects The lifetimes of Jupiter's outer moons

Abstract Equations are derived which relate orbital parameters to the probability of collision between orbiting objects. These equations follow from a new conceptual approach, and are in a form to be easily applied to a variety of orbital collision problems. The equations are used in this paper to calculate the collision lifetime of Jupiters eight outer satelites. The average time between collisions for any of the four retrograde moons was calculated to be 270 billion years, while the corresponding time for the four posigrade moons was 0.9 billion years. This relatively short time for the posigrade moons is strongly suggestive of a past collision history. The consequences of these collisions and the possible relationship to the Pioneer 10 and 11 penetration data is discussed.

Collisional cascading - The limits of population growth in low earth orbit

Abstract Predictions have been made by several authors that random collisions between made-made objects in Earth orbit will lead to a significant source of new orbital debris, possibly within the next century. The authors have also concluded that there are a number of uncertainties in these models, and additional analysis and data are required to fully characterize the future environment. However, the nature of these uncertainties are such that while the future environment is uncertain, the fact that collisions will control the future environment is less uncertain. The data that already exist is sufficient to show that cascading collisions will control the future debris environment with no, or very minor increases in the current low Earth orbit population. Two populations control this process: Explosion fragments and expended rocket bodies and payloads. Practices are already changing to limit explosions in low Earth orbit; it is now necessary to begin limiting the number of expended rocket bodies and payloads in orbit.

Contribution of explosion and future collision fragments to the orbital debris environment

Abstract The time evolution of the near-Earth man-made orbital debris environment modeled by numerical simulation is presented in this paper. The model starts with a data base of orbital debris objects which are tracked by the NORAD ground radar system. The current untrackable small objects are assumed to result from explosions and are predicted from data collected from a ground explosion experiment. Future collisions between Earth orbiting objects are handled by the Monte Carlo method to simulate the range of collision possibilities that may occur in the real world. The collision fragmentation process between debris objects is calculated using an empirical formula derived from a laboratory spacecraft impact experiment to obtain the number versus size distribution of the newly generated debris population. The evolution of the future space debris environment is compared with the natural meteoroid background for the relative spacecraft penetration hazard.

Sources of Orbital Debris and the Projected Environment for Future Spacecraft

The major source of the nearly 5000 objects currently observed orbiting the earth is from rocket explosions. These explosions have almost certainly produced an even larger unobserved population. If the current trend continues, collisions between orbiting fragments and other space objects could be frequent. By the year 2000 satellite fragmentation by hypervelocity collisions could become the major source of earth orbiting objects, resulting in a self propagating debris belt. The flux within this belt could exceed the meteoroid flux, affecting future spacecraft design.

The effects of particulates from solid rocket motors fired in space

Abstract Solid rocket motors are currently used to transfer satellites from low Earth to geosynchronous orbit. Since the apogee kick burn is directed out of the orbital plane, most of the aluminum oxide particles making up the plume will not immediately de-orbit. Studies show that the flux (number of impacts/m2/yr) resulting from just one burn can exceed the natural meteoroid flux for particles of like size (1–10 μm). Furthermore, this man-made flux is distributed evenly from low Earth to geosynchronous altitudes. Solar radiation pressure is the dominate perturbation causing the orbital eccentricity to oscillate with a phase dependent on the initial orbital orientation to the Sun. A semi-analytical technique which includes the effects of the J2, solar, and lunar gravitational accelerations as well as radiation pressure and atmospheric drag is developed to analyze the stability of the wide range of particle orbits. A statistically significant random sample of particles are propagated forward in time with the results indicating that less than 5% of all the particles will remain in orbit over one year.

Meteoroid impacts on the Gemini windows

Abstract Fourteen windows of the Gemini spacecraft were closely examined after return from space flight for evidence of meteoroid impact. Although a number of microscopic pits were found on each window, only one of these pits appears to have been caused by a meteoroid impact. A meteoroid flux-mass relation calculated from this single hit is found to be in close agreement with Naumanns (1966) analysis of the Explorer and Pegasus meteoroid penetration experiments. Particle, mass, and area distribution curves are derived from the flux-mass relation and are presented in graphical form. Problems in interpreting the data because of contaminants on the windows are also discussed.

Orbital debris issues

Abstract Orbital debris issues fall into three major topics: Environment Definition, Spacecraft Hazard, and Space Object Management. The major issue under Environment Definition is defining the debris flux for sizes smaller (10 cm in diameter) than those tracked by the North American Aerospace Defense Command (NORAD). Sources for this size debris are fragmentation of larger objects, either by explosion or collision, and solid rocket motor products. Modeling of these sources can predict fluxes in low Earth orbit which are greater than the meteoroid environment. Techniques to measure the environment in the size interval between 1 mm and 10 cm are being developed, including the use of telescopes and radar both on the ground and in space. Some impact sensors designed to detect meteoroids may have detected solid rocket motor products. Once the environment is defined, it can be combined with hypervelocity impact data and damage criteria to evaluate the Spacecraft Hazard. Shielding may be required to obtain an acceptable damage level. Space Object Management includes techniques to control the environment and the desired policy to effectively minimize the hazard to spacecraft. One control technique — reducing the likelihood of future explosions in space — has already been implemented by NASA. The effectiveness of other techniques has yet to be evaluated.

Orbital debris environment for spacecraft in low earth orbit

The results of measurements and modeling have been combined to describe an orbital debris environment model that can be used to evaluate spacecraft reliability vs shielding issues. Recent measurements by ground radars and telescopes, combined with analysis of recovered spacecraft surfaces, have provided some measurements of the environment over most of the size spectrum from micron size to the size of spacecraft. These measurements are consistent with models that assumed that smaller debris resulted from the breakup of satellites. Recent efforts to minimize satellite breakups will reduce the projected environment and delay the time period when satellite breakups from random collisions become important. However, there still remains a significant uncertainty in the current environment, and an even larger uncertainty in the projected environment. Uncertainties in the current environment will be reduced as a result of planned measurements. The future environment will mostly depend on future debris control measures taken and, to a lesser extent, on the amount of traffic to orbit.

Collision probability at low altitudes resulting from elliptical orbits

Abstract The collision probability between a spacecraft and another object in Earth orbit can be expressed as a function of the orbital perigee, apogee, and inclination of the object. Usually, the probability is not a sensitive function of inclination. Collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object. The probability per unit time is largest when the perigee and apogee are nearly equal (i.e., the orbit is nearly circular). Therefore, it is usually concluded that objects in circular orbits represent the greatest hazard to other spacecraft. However, at low altitudes, atmospheric drag causes perigee and apogee to change with time, such that circular orbits have a much shorter lifetime than many of the elliptical orbits which pass through the lower altitudes. Consequently, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have a much higher total collision probability than circular orbits. Objects in these elliptical orbits could represent the greater source of hazardous objects to spacecraft operating in low Earth orbit. Some common objects in these elliptical orbits are rocket bodies used to boost payloads from low Earth orbit to geosynchronous orbit.

Average relative velocity of sporadic meteoroids in interplanetary space

Meteoroids average velocity relative to spacecraft determined using sporadic meteors orbital elements data in interplanetary space