International Guidelines for the Preservation of
Space as a Unique Resource

Phillip D. Anz-Meador, Ph.D., Dept. of Physics
Embry-Riddle Aeronautical University

(Continued)

Yet another means of characterizing the environment is by the spatial density S, i.e. the number of equivalent objects per cubic kilometer. This quantity, derived in a manner analogous to that in the classical theory of gasses, is of great utility as it may be related to both the flux F and the expected collision rate C:

F = S*v [impacts/m2/year]

and

C = F*A = S*v*A [impacts/year],

where v is the relative velocity between an object (the “target”) and the impactor (the “projectile”) and A is the area (cross-sectional or surface area) of the target object. The incident flux represents the number of particles striking a surface within a given time; the flux is usually expressed in units of [impacts/m2/yr], but may appear in other units. An excellent analogue for the flux is the amount of water falling on the windshield of a vehicle driving through a rainstorm. The final amount will depend upon the size of the raindrops, or the distribution in size, the velocity of the drops, and the velocity of the vehicle as it drives through the storm.
The following figures (after Ref. X5) depict the spatial density of cataloged (> 10 cm in LEO, > approximately 1 m in Geosynchronous Earth orbit, or GEO) objects in LEO and deep space. The reader may mentally multiply the LEO figures by a factor of 300, and the GEO figure by a factor of 50, to obtain the flux at these altitudes.

Fig. 2. The spatial density of equivalent satellite objects in LEO. Altitude divided into 10 km wide altitude bins. Spatial density portrayed on a linear vertical axis to emphasize altitudes of high absolute concentration.

In Figure 2, perhaps the most prominent features are the “spikes” event just below 800 km altitude, and just above 1400 km altitude. These result from the relatively dense packing of specific spacecraft in the Iridium and Globalstar commercial communication satellite constellations, respectively.

Fig. 3. The spatial density of equivalent satellite objects in LEO. Altitude divided into 10 km wide altitude bins. Spatial density portrayed on a logarithmic vertical axis to emphasize distribution by type, altitude, and concentration. Concentration of anomalous debris around 1300 km altitude due to the SNAPSHOT satellite.

Fig. 4. The spatial density of equivalent objects in deep space (here, defined as altitudes above LEO and below GEO). Altitude in 100 km bins. Readily evident are the US and Russian navigation satellite constellations in middle Earth orbit.

Fig. 5. The spatial density of equivalent objects near GEO. Altitude in 100 km bins. “High” and “Low” boundaries define a nominal GEO operational region.

Because these figures only portray those objects capable of being cataloged (with certain exclusions for national security), it is important to recall that these are larger than approximately 10 cm in LEO and larger than 1 m in GEO. Whereas the LEO region is believed to be reasonably complete, this is not the case in deep space, and GEO in particular. Recent measurements (Ref. X6) indicate that a significant population of objects larger than 10 cm reside in the GEO belt. One reason for this may lie in a historical undercounting of objects (primarily operational debris) released in the GEO belt. For example, objects such as solar array retention straps have not been cataloged for many historical payloads.

Unrecognized fragmentations may also have contributed to the GEO local environment. Thus, the GEO environment portrayed in Fig. 5 may substantially be undercounting the actual spatial density/flux.

While these charts depict the distribution of cataloged objects, they are not directly translatable to either a “high quality” flux or a collision rate. In the case of a flux, this is because the relative velocity between two objects depends on the actual orbital properties of the pair of objects involved in any prospective collision. For objects whose orbital planes are randomly distributed with respect to each other and the remainder of the population, these are:

• the apogee (maximum altitude) and perigee (minimum altitude) of each object in the pair; and
• the inclination (the angle between the orbit plane and the Earth’s equator) of each object.

Apogee/perigee altitudes determine the velocity, as a function of altitude, of each of the individual objects. For circular orbits, as are the majority in LEO, MEO, and GEO, the orbital velocities of both objects are roughly equal, and collisions on the front and sides surfaces of the “target” object are prevalent. However, if one object is in an elliptical orbit (i.e. a large difference in perigee and apogee altitudes), then (a) the elliptical orbit, at perigee, may be traveling up to 3 km/s faster than the other object, and (b) the object in the elliptical orbit may therefore “catch up” with the other object and strike it from “behind”. This is observed on-orbit, as shuttles and other spacecraft flying at 28∞ inclinations commonly return with a multitude on craters on their rearward-oriented surfaces. The inclination is also an important determinant of the outcome of any collision, as certain inclination allow for “head on” collisions at up to 14-15 km/s. Conversely, the uniformly low inclinations found in GEO, along with the coordinated motion of the objects there, tends to lower the relative velocities possible.

Another factor contributing to the calculation of collision rate is the relative cross-sectional area of projectiles and targets. While Figures 2 and 3 indicate two roughly equivalent peaks in spatial density at around 800-1000 km and 1400-1500 km altitude, more collisions are expected to take place at the lower altitude. This is because the objects resident at and about that altitude are significantly larger (many being derelict SL-16 R/B), and hence present more “target area”, than are the spacecraft around 1400-1500 km altitude. This has been confirmed by high fidelity long-term computer modeling of the evolution of the environment.

Computer models, based on measurements of the environment (including the analysis of objects returned from space), are used to project an “average” environment due to objects smaller than those depicted in Figures 2-5.

Fig. 6: The modeled environment for 1 mm-1 m impactors; target orbit is 400 km circular, 51.6∞ inclination (similar to the ISS nominal orbit).

Figure 6 depicts the output of the NASA ORDEM2000 computer model (Ref. X7). As may be seen, the cumulative flux due to the debris population 1 mm and larger in size is five (5) orders of magnitude larger than the cataloged population.

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