International Guidelines for the Preservation of Space as a Unique Resource
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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.
3. Effects Upon Spacecraft
As of this writing (November 2003), there has been only one (1) recognized accidental collision between cataloged objects: the French Cerise satellite's gravity gradient stabilization boom was cut by a piece of French debris produced by the 1986 fragmentation of an Ariane R/B third stage. All other historical (alleged) collisions were conducted as military anti-satellite or ballistic missile defense tests. The vast majority of fragmentations have been accidental explosions.
These explosions range in severity from mission survivable (e.g. a battery box explosion aboard the NOAA 8 spacecraft) to the catastrophic, in which a body is totally destroyed in the blast. Therefore, this section will concentrate on the effects of impacts on spacecraft.
A qualitative assessment of impact effects is provided in the following table, after Ref. X1.
|Diameter of Impactor [cm]||Effect|
|< 0.01||Surface erosion|
|< 0.1||Potentially serious damage to spacecraft|
|0.3 at 10 km/s relative velocity (typical in low Earth orbit)||Equivalent to being struck by a bowling ball traveling at 60 mph (88 ft/s)|
|1.0 at 10 km/s relative velocity||Equivalent to being struck by a 400 lb safe traveling at 60 mph|
It is illustrative in a quantitative sense to examine the dependency of the probability of impact or penetration upon environmental and physical variables. Environmental variables are those dependent upon the orbital characteristics of the target (and projectile) objects, such as the relative velocity between the two; physical variables include the mass densities of the materials constituting the two objects.
The effect of the incident flux may be characterized by the Poisson probability of one or more (n ≥ 1) impacts of size 'd' and larger is:
Where F(d, v) is the size and velocity-dependent flux, dA is the differential unit of surface area, n is the number of impacts, and integrals are performed over both surface area and the velocity distribution.
A common figure of merit for estimating the hazard to spacecraft (for example, in calculations performed for the International Space Station [ISS] and the space shuttle fleet) is the probability of no penetration, or PNP. The PNP may be expressed using the Poisson statistic P0 = exp(-N), where:
The variable T is the surface thickness, ø is the impact angle measured from surface normal, v is the relative velocity, f(v) is the fraction of velocities between v and v + dv, p is a mass density, A is the area of the exposed surface, and t is the elapsed time of exposure. The subscripts 't' and 'p' refer to target and projectile, respectively, and the set () are, in general, non-integer rational numbers. Additional dependencies relating to target yield and tensile strengths or other material characteristics may be manifest. Multi-layer shielding and body self-shielding can modify these relations.
Impacts in MEO and GEO occur at correspondingly lower velocities. However, even in GEO, the average relative velocity is on the order of 500 m/s, with a maximum around 1.5 km/s. As such, and to apply a terrestrial measure, these are commensurate with being struck by either "standard" or "high velocity" ammunition.
While the debris population accounts for roughly half of all objects tracked and cataloged by the US, simple calculations reveal that the impact rate of these cataloged objects onto a one m2 target, per year, is minuscule. However, small untracked debris do present a meaningful hazard to spacecraft because of accelerated aging of spacecraft components, degradation of sensitive surfaces such as mirrors, optical surfaces, radiators, and solar panels, and the potential for a 'mission kill' should a single-point failure mode be susceptible to impact by small debris. The STS-50 mission provides an example of component degradation, as segments of the radiator assembly were required to be replaced following approximately 10 days of flight with the payload bay facing in the direction of the velocity vector (the so-called "ram" direction). Shuttle flight deck windows are also replace with a frequency of (on average) one outer pane per mission. High pressure propellant lines, pressurized storage vessels, and exposed cable bundles provide additional examples of single-point failure mode elements on small spacecraft.
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