#### Title

On the Average Probability of Hitting a Satellite during a Laser Counterartillery Engagement

#### Contributing USMA Research Unit(s)

Systems Engineering

#### Publication Date

Winter 2014

#### Publication Title

Journal of Directed Energy

#### Document Type

Article

#### Abstract

This paper investigates the probability that a high-energy laser fired at an incoming projectile will inadvertently hit (not necessarily damage) a background satellite. This is called the C-RAM mission, for counter rocket, artillery, and mortar. We show how such an engagement can be defined by parameters describing projectile trajectory, laser characteristics, laser firing, and spacecraft orbit parameters, so that a probability of hit can be accurately calculated from the geometry of the situation. The model takes into account laser location, laser pointing and angular sweep, laser beam angular divergence, and orbit height, inclination, and ascending node. It does not take into account atmospheric refraction or absorption, it assumes that the laser beam propagates beyond the intended target into space, and it does not address the probability of damage given a hit. Based on the single-engagement probability calculation, Monte Carlo sampling is then used to find a general probability of hit. For each replication, the threat launcher is placed at a random distance and azimuth, the impact point randomly placed within 1 km of the laser, and the engagement placed randomly in the trajectory. The spacecraft parameters are selected randomly from a comprehensive set of 1417 orbital elements for actual operational or formerly operational spacecraft. A simulation constructed to represent defense against mortar in a near-term counterinsurgency conflict gives a probability of hit of about 15.5 ´ 10^{-9} per engagement per satellite, or 15.5 nanohits, for satellites in sun-synchronous orbits. Another simulation constructed to represent a hypothetical major combat operation with long-range rocket and artillery threats in addition to mortars. This simulation yields 27.5 nanohits for the same set of satellites. An extensive sensitivity analysis explores how these results vary as the parameters describing spacecraft, projectile, laser, and engagement are changed, giving results from 0 to 549 nanohits. Hits increased as the laser site moved north, as the distance to the threat launch point increased, as the engagement moved away from the midpoint of the projectile trajectory, as laser beam quality deteriorated, as engagement duration increased, and as satellite altitude increased. Over all cases, the statistical 95% confidence interval was ±3-10%. Accumulating the scenario results over a notional three-year counterinsurgency conflict and 20 sun-synchronous spacecraft of interest, we get a total of 0.0034 expected spacecraft hits during the conflict. Accumulating over a notional two-week major combat operation and the same spacecraft, we get 0.015 expected hits.

#### First Page

181

#### Recommended Citation

Burk, Roger, "On the Average Probability of Hitting a Satellite during a Laser Counterartillery Engagement" (2014). *West Point Research Papers*. 423.

https://digitalcommons.usmalibrary.org/usma_research_papers/423

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