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The following description and methodology describes the satellite constellation coverage model developed by Thomas G. Roberts and featured in “Why a Space-Based Missile Interceptor System is Not Viable” in the Bulletin of the Atomic Scientists and “What Can 24 Satellites Do for U.S. Missile Defense?” a brief CSIS Aerospace Security Project report.
Although satellites can be organized into constellations using infinitely many orientations, the most frequently cited models are those by Walker, Ballard, and Rider.1 Some of the most common types of constellations—used by GPS, Iridium, and Globalstar communications systems—are Walker’s star and delta constellations.2
A star constellation features satellites in equally spaced, polar or near-polar orbital planes, which together can offer full Earth coverage. Satellites in polar orbits pass over the north and south poles. Star constellations offer their densest coverage at the Earth’s poles and their sparsest coverage at the Earth’s equator. The Iridium satellite constellation—a commercial network of 66 communication satellites—utilizes this orientation to achieve full-Earth coverage.3
A delta constellation features satellites in equally spaced, inclined orbits. Inclined orbits do not pass over the Earth’s poles, covering only lower latitudes. Therefore, unlike star constellations, delta constellations leave the Earth’s poles with little to no coverage. Delta constellations can more easily provide regional focus, covering a band of the Earth’s surface, centered on the equator. The Globalstar constellation—another network of commercial communication satellites—uses this type of design to cover 80 percent of the Earth’s surface.4 Figure 1 depicts the orbital paths of 720 satellites in 24 equally-spaced orbital planes oriented in a 65° Walker delta constellation.
The 2018 National Defense Authorization Act, which outlined a plan for the development of a space-based interceptor layer, required such a system to be “regionally focused.”5 Since star constellations can only focus on the poles, the delta constellation would likely be a more appropriate choice for an SBI layer.
Computational SBI Model
A computational model can be developed to study the effectiveness of a space-based missile interceptor (SBI) system oriented in a delta constellation by using the assumptions outlined in a 2004 American Physical Society (APS) study on SBIs.6 In the APS study, each hypothetical interceptor is capable of intercepting a missile inside a spherical region surrounding the interceptor. The size of the region—known as the kill radius—is dependent on the acceleration profile of the interceptor, its terminal velocity, and the response time between the interceptor firing and the moment it reaches its target. The kill radius is depicted in Figure 2.
For a missile to be intercepted in boost phase, it must pass within an interceptor’s kill radius before the booster burns out and the warhead is jettisoned. If multiple missiles are launched at once from the same location, then each warhead must pass within a unique interceptor’s kill radius in order to be destroyed.
Although the 2004 APS study referenced a variety of hypothetical parameters for an interceptor’s maximum acceleration, terminal velocity, and response time, its most generous values were 10g, 6 km/s, and 170 seconds respectively. With those variables, a kill radius () can be calculated:
With a kill radius of this size, a low-altitude, space-based missile defense system would need hundreds or thousands of interceptors in orbit to effectively defend against missile attacks in their boost phase from threat regions across the globe.
A constellation of SBIs designed for midcourse-phase missile defense, on the other hand, would require fewer satellites on orbit, but more advanced tracking and discrimination data to avoid being fooled by decoys. In “What Can 24 Satellites Do for U.S. Missile Defense?” the midcourse SBI model used the same parameters for maximum acceleration and terminal velocity as the boost-phase model, but a 12-minute response time (the approximate length of time before a hypothetical ICBM from North Korea entered its terminal phase over Guam) and an interception altitude of 500 km. Accordingly, the kill radius for an SBI designed for midcourse intercepts is significantly larger than it would be if it were designed for boost-phase intercepts.
For any given Walker delta constellation of space-based interceptors, some latitudes will receive more missile defense than others. The interactive map on the top of this webpage describes the minimum number of interceptors within range of a missile launched from any location on Earth. This particular model assumes an intercept point at 200 km above the Earth’s surface.
Users can toggle the size of the constellation (choosing between roughly 100, 500, 1000, 1500, or 2000 interceptors) and its inclination (30, 45, 60, or 90 degrees).7 Regions of the map not covered by any interceptors may still experience some coverage, but an interceptor cannot be guaranteed to be within range at all times. Similarly, a region labeled as having one interceptor within range will at times be covered by many more than one interceptor.
Computational SBS Model
The space-based missile sensor (SBS) model featured in “What Can 24 Satellites Do for U.S. Missile Defense?” makes several assumptions to simplify the coverage calculations for a constellation of space-based sensors, including:
- Assuming Earth’s gravity is constant;
- Ignoring the gravitational pull from the Moon and Sun;
- Ignoring drag and degradation of satellites’ orbits;
- Using the WGS 84 Earth Gravitational Model8 for calculating horizon-limited coverage;
- Ignoring other field of view limitations, including signal fade and distortion from the Earth’s atmosphere;
- Ignoring lag time for slewing sensors; and
- Ignoring time delays for tracking association.