Appendices

Table of Contents

Appendix A: Range Definitions and Determination

Negotiating an arms control agreement often involves agreeing how to define the concept of range. The parties need this definition to determine the ranges of both their own delivery systems and those belonging to the other party or parties.

One way to define range is in terms of the maximum distance flown by a weapon during testing. The INF Treaty, for example, defines the “range capability” of a type of ground-launched ballistic missile to be “the maximum range to which it has been tested.”¹ This definition has the considerable virtues of clarity and ease of implementation. By the late Cold War, the United States and the Soviet Union were likely able to collect good data on the launch and impact points of one another’s ballistic missile tests. Based on this information, the range capability of each type of ground-launched ballistic missile could be determined with high confidence.

This approach suffers from some serious flaws, however. States may not always test ballistic missiles as far as they can fly, often because of geographical constraints. For example, China’s only realistic option for testing its ICBMs to anything like their full ranges would be to fire them eastward across the Pacific Ocean—but it has not done so since the 1980s, presumably out of restraint.² As such, its tests are typically conducted across a distance of roughly 2,500 kilometers (1,600 miles), even though its farthest-reaching ICBMs can fly about five times as far.³ (In practical terms, China fires its ICBMs on so-called lofted trajectories—think fly balls in baseball—that reach great heights but do not travel all that far downrange. Firing that same ICBM along a so-called minimum energy trajectory—the equivalent of a line drive—would cause it to travel significantly farther but at lower altitudes.)

The challenges are even greater with cruise and boost-glide weapons. The impact point of a ballistic missile is largely determined by its velocity when its engines burn out.⁴ By contrast, cruise missiles can terminate their flight at any point along their trajectory; the same is basically true for boost-glide missiles once they have reentered the atmosphere. As a result, it is difficult for an observing state to determine whether one of these weapons has been tested to its maximum range. Moreover, unlike ballistic missiles during the unpowered portion of their flight, neither cruise missiles nor boost-glide missiles are constrained to travel along straight lines. As a result, the distance traveled during a test cannot be inferred from the launch and impact points alone.

The range of a cruise missile, therefore, has always been defined in terms of inherent capability rather than testing history. Both the INF Treaty and New START, for example, define it in essentially identical terms as “the maximum distance which can be covered by the missile in its standard design mode flying until fuel exhaustion, determined by projecting its flight path onto the earth’s sphere from the point of launch to the point of impact.”⁵ New START takes a conceptually similar approach for ballistic missiles, defining the range of a given type to be “the maximum distance determined by projecting the flight trajectory onto the Earth’s sphere from the launch point of a missile of that type to the point of impact of a reentry vehicle.”⁶

Such definitions are potentially challenging to operationalize because they require each party to model the other’s delivery systems. Indeed, it is not difficult to imagine disagreement between the parties over whether the range of a given delivery system was just above or just below some threshold. Moreover, resolving such disputes could prove difficult. It stretches credulity to imagine that one state could conduct a demonstration flight of, say, a cruise missile along a totally straight trajectory and allow inspectors to verify that the fuel tank was full before launch and that there was essentially no fuel at the impact site—but, even if it did so, there would be no practical way for inspectors to verify that the missile had flown along the altitude profile that would maximize the distance traveled.

Nonetheless, New START’s definitions for the ranges of cruise and ballistic missiles are the best available option going forward—not least because both parties have considerable experience in applying them. In practice, disagreements between the United States and the Soviet Union or Russia over the range of a missile have been rare. Moreover, the most notable exception—the dispute over the range of the SSC-8 ground-launched cruise missile—was not caused by an ambiguous definition or slight differences between the two states’ physical models of the weapon: Russia claimed that this weapon had a range of 480 kilometers, whereas, according to media reports, the official U.S. estimate was in excess of 2,000 kilometers.⁷ Rather, the United States has (persuasively) argued that Russia has engaged in outright noncompliance, whereas Russia has essentially accused the United States of peddling misinformation.⁸

Defining and Determining the Range of Boost-Glide Missiles

Boost-glide missiles have not been limited under any previous arms control agreement, making it necessary to develop a definition for their range. We propose the following:

The range of a boost-glide missile is the maximum distance that can be flown by a missile of the same type, determined by projecting its flight path onto the Earth’s sphere from the point of launch to the point of impact, assuming that its maximum speed does not exceed the maximum speed reached in any flight test of a missile of the same type.

This definition is similar to New START’s definition for the range of a cruise missile with the important exception that the former embeds the assumption that, to ensure reliability, a state would want to test a glider at its maximum speed (but not necessarily across its full range).

Estimating the range of a boost-glide missile is likely more difficult than estimating the range of a ballistic missile (though easier than estimating the range of a cruise missile). The flight of a boost-glide missile, before it descends on the target, can be divided into four stages: (1) powered, (2) ballistic, (3) pull-up, and (4) gliding. During the powered and ballistic stages, a boost-glide weapon behaves similarly to a ballistic missile launched on a depressed trajectory. After release, the glider reenters the atmosphere (if it ever leaves it) and executes a pull-up maneuver to enable gliding. The total distance traveled by a boost-glide missile is the sum of the distances covered during each phase of flight.

Estimating the range of a boost-glide missile requires modeling both the rocket booster and the glider. The intelligence community has extensive experience modeling rocket boosters and hence phases 1 and 2 of a boost-glide missile’s flight. The aerodynamic and other relevant properties of gliders can be estimated by observing flight tests. These properties then allow a model of phases 3 and 4 to be constructed.

Phase 4, the glide phase, typically represents both the largest contribution to the distance flown as well as the largest source of uncertainty about range. Although intelligence agencies likely use complex mathematical models to simulate gliding, the following approximation for glide range, l_glide, is useful for understanding which factors are the most important for determining it:

Here, r_e is the radius of the Earth (approximately 6,400 kilometers or 4,000 miles), v_e is the speed of a satellite in low-Earth orbit (approximately 8 kilometers per second or 5 miles per second), v_i is the initial speed of the glider, and L/D is the glider’s lift-to-drag ratio.⁹ The latter two quantities are key for estimating a glider’s range. The lift-to-drag ratio is the relative strength of the lift and drag forces experienced by a glider. The larger this quantity or the initial speed, the farther a reentry vehicle can glide (but the more demanding heat management typically becomes).

There is a trade-off between the range covered in the ballistic portion of a glider’s trajectory and the gliding portion. As a glider reenters the atmosphere, it must pull up to establish gliding. Executing this maneuver slows the glider and hence reduces the potential glide range. The larger the angle through which the glider pulls up, the more it slows. Boost-glide missiles are usually launched on a shallow trajectory that reduces the pull-up angle and thus increases glide range at the expense of reducing the distance traveled during the ballistic phase. Firing the missile on a more lofted trajectory increases the ballistic range but reduces the glide range. So, for a system tested to some maximum v_i, there is an optimal rocket trajectory that maximizes the total range.

As a glider passes through the atmosphere, some of its potential and kinetic energy is turned into heat, which increases the temperature of its skin, leading to the emission of infrared radiation in the same way that a hot stove element glows red. If this infrared signature is sufficiently strong, it could be detected with the space-based infrared sensors that China, Russia, and the United States deploy for ballistic missile early-warning, among other tasks.

There has been considerable debate about whether the United States can detect hypersonic gliders with its existing space-based early-warning architecture, which comprises newer Space-Based Infrared System satellites alongside a few remaining satellites from the legacy Defense Support Program constellation. The capabilities of these systems are classified, but in 2019, Michael Griffin, then undersecretary of defense for research and engineering, stated categorically that “we can’t see these things [hypersonic threats] from a few spacecraft in geostationary orbit.”¹⁰ Other statements by U.S. officials, however, suggest that the newer satellites can, in fact, detect gliders, even if their capabilities are not adequate for all purposes. In 2021, for example, Michael White, the Department of Defense’s principal director for hypersonics, critiqued claims that tracking is currently possible by noting the difficulty of monitoring a glider “precisely and continuously enough to help missile defenses set up an intercept”—a statement that actually appears to concede the premise he was attempting to undermine.¹¹ Statements from U.S. officials that a June 2015 test of a Chinese boost-glide missile involved “extreme maneuvers” also appear to suggest that the United States already has some capability to track a glider in flight.¹² Independent studies have reached this same conclusion.¹³ There is no publicly available information on the capabilities of Chinese and Russian early-warning satellites.

If a glider can indeed be tracked with space-based infrared sensors for a significant portion of its flight, then its properties—including the initial glide speed and lift-to-drag ratio—can be inferred, allowing the glide range to be estimated.

Appendix B: Chase Maneuvers in Geostationary Orbit

Satellites are typically repositioned in a way that minimizes fuel consumption in order to maximize their service lives. For a co-orbital anti-satellite attack, however, minimizing the time-to-interception would likely be a more important goal to reduce the chance that the targeted satellite’s owner would detect the attack while it was ongoing and instruct its satellite to take evasive action. So-called chase maneuvers enable an attacking satellite to directly approach a target satellite in a short amount of time at the cost of a large amount of fuel. The time needed for a chase maneuver in the case of a co-orbital anti-satellite weapon initially situated on the edge of a geostationary satellite’s keep-out zone helps determine the requirements for verifying such zones (see chapter 6).

Consider an attacking satellite and a target satellite in the same initial orbit at time t₀ separated by some angle (see figure 1). The attacker aims for its satellite to intercept the target satellite at some future time, t_i. At t₀, the attacking satellite moves from its initial orbit to the interception trajectory by applying thrust that results in a speed change, Δv. The satellite must apply the same thrust (in the opposite direction) at t_i to move back onto the initial orbit ahead of the rendezvous.¹⁴ There are an infinite number of potential interception trajectories, each taking a different amount of time Δt=t_i-t₀ and requiring a different Δv. Faster intercepts require a greater Δv and hence more fuel. The total amount of fuel the attacking satellite has available is set by some “Δv budget” (in other words, the total speed change it can effect over its remaining lifetime). For medium to large satellites, this budget is typically in the range of 1–4 kilometers per second (0.62–2.5 miles per second) at the start of their service lives.¹⁵

In practice, it would be unlikely that a co-orbital anti-satellite weapon could or would expend this entire budget in a single attack. Such a weapon would have to be launched before the attack—perhaps a considerable time in advance—and would likely have already expended some fuel on maneuvering. If the weapon were capable of being used more than once, the attacker might want to conserve sufficient fuel for follow-on attacks. Even if it were not, the attacker would still probably not want to use up all its fuel in the initial approach in case the target satellite undertook evasive maneuvering.

If two satellites in geostationary orbit are separated by 1 degree in true anomaly (720 kilometers or 450 miles), the fuel required, expressed as Δv, for the lagging satellite to execute a chase maneuver and catch up with the other is shown as a function of the maneuver time, Δt, in figure 2 (which is obtained by solving Lambert’s problem).¹⁶ Very fast maneuvers—less than an hour or so—require a prohibitive quantity of fuel. Maneuvers potentially fast enough to catch the target before being detected by a space situational awareness system making observations every 2–3 hours would require a speed change of approximately 0.2 kilometers per second (0.12 miles per second), representing the approximate amount of fuel expected to be used for station keeping in a geostationary orbit in a year.

Appendix C: An Open-Source Assessment of Chinese, Russian, and U.S. Space Situational Awareness Capabilities

The “refresh rate” of a space situational awareness system—how often it views each satellite—helps determine the minimum warning time that a state would receive of an attack on one of its satellites and is thus an important factor in determining the verifiability of keep-out zones (see chapter 6). Space situational awareness capabilities would also contribute to verifying the prohibition on space-based missile defenses (see chapter 7), though in this case would be only one of several verification tools.

The frequency at which the Chinese, Russian, and U.S. space situational awareness systems can detect satellites cannot easily be estimated with open-source information because of the opacity around the relevant capabilities. Because some (perhaps many) modern satellites can transmit continuously to their owners, states presumably receive constant updates from those spacecraft. (So-called cross links between satellites enable communications from any that are not within range of the owner’s downlinks.) However, many satellites do not keep track of their own positions, which must be measured by the satellites’ owners. Moreover, effective space situational awareness requires monitoring other states’ satellites—not least those that could pose a potential threat to a state’s own satellites.

The following description of space situational awareness capabilities—although qualitative and based only on the limited information that is publicly available—is hopefully helpful in understanding their possible attributes and limitations and in identifying needed improvements, which Beijing, Moscow, and Washington have strong incentives to undertake regardless of their participation in arms control. This account focuses on monitoring geostationary satellites. The more straightforward case of monitoring satellites in Molniya orbits is discussed briefly at the end.

Ground-Based Optical and Infrared Telescopes

A fixed ground-based telescope can image at most 45 percent of the geostationary belt. (Unlike low-Earth orbit satellites, which are in constant motion relative to the Earth’s surface, geostationary satellites remain fixed above the same point on the ground.) Achieving full coverage of the geostationary belt with ground-based sensors therefore requires at least three sites spread around the Earth’s equator. 

Ground-based optical telescopes are widely used to track satellites in geostationary orbit. Their inability to detect satellites during the day, however, creates significant gaps in coverage that co-orbital anti-satellite weapons could exploit. The duration of this gap, which is twelve hours on average, varies with latitude and season, so hemispheric diversity can mitigate this problem—but only to some extent. Moreover, because an individual optical measurement cannot determine the altitude of a satellite, it cannot be used to infer the relative speeds of two satellites (although it could determine whether one satellite had entered the keep-out zone of another). Estimating a satellite’s altitude requires extended observations, observations from multiple locations, or the illumination of the satellite with a laser (which requires more complex and expensive equipment).

The ongoing development of shortwave infrared telescopes has made it possible to observe geostationary satellites during daylight.¹⁷ There likely remains, however, some portion of the day when a satellite is too close to the sun to be imaged in this way. Moreover, no ground-based telescopes (visible or infrared) can operate when the weather is overcast, as clouds are opaque to the relevant wavelengths (though spacing telescopes geographically, even at similar longitudes, creates some resilience to weather effects).

Russia has access to the most extensive network of optical telescopes, including dedicated military facilities in the North Caucasus, the Altai Republic, and Tajikistan.¹⁸ The U.S. Ground-Based Electro-Optical Deep Space Surveillance system includes optical telescopes located in the continental United States, Hawaii, and the British Indian Ocean Territory.¹⁹ China operates optical sensors at its Purple Mountain Observatory and has negotiated a number of international partnerships, including with Chile, Mexico, and South Africa, to improve the latitudinal diversity of the telescopes at its disposal.²⁰ In addition, commercial actors have developed ground-based telescope networks that rival those of governments.²¹ It is possible that governments have plans to use such capabilities to supplement their own in a crisis or conflict.

Space-Based Optical Sensors

Optical sensors on satellites avoid some of the weaknesses of ground-based sensors, though require significantly more investment. Space-based sensors are not affected by terrestrial weather. Moreover, a single satellite can survey, over time, the whole of the geostationary belt from an orbit in which it moves relative to that belt.

Some optical imaging sensors—such as the U.S. Space-Based Visible sensor aboard the Midcourse Space Experiment satellite and its successor, the Space Based Space Surveillance satellite—are located in low-Earth orbit.²² Every geostationary satellite is within the line-of-sight of such sensors at least once during each sensor’s orbital period (approximately ninety minutes). Geostationary satellites cannot be observed from low-Earth orbit, however, during periods when they are too close to the sun. Canada’s NEOSSat satellite, for example, cannot observe objects located within 45 degrees of the sun, creating a six-hour period each day when it cannot image a given geostationary satellite.²³

Optical sensors can also be placed on high-altitude satellites. The U.S. Geosynchronous Space Situational Awareness Program constellation, for example, comprises four satellites—two just above and two just below geostationary orbit—which rotate in opposite directions relative to the geostationary belt.²⁴ Optical sensors in near-geostationary orbits still have exclusion zones, but they generally occur at different times from those for sensors on the ground or in low-Earth orbit. They also survey the geostationary belt at a lower cadence than low-Earth orbit satellites since their orbital periods are closer to the geostationary orbital period. Increasing the number of high-altitude optical sensors ameliorates both exclusion and cadence issues.

Russian inspector satellites, located in both low-Earth and geostationary orbits, may have surveillance capability, though perhaps of quite limited range.²⁵ The Tundra early-warning satellites may also have some space surveillance capability.²⁶

Ground-Based Radio Telescopes

Radio telescopes can be used to intercept downlink or broadcast radio-frequency signals from a high-altitude satellite, allowing for its position to be calculated through triangulation. (States also have dedicated downlinks to receive signals from their own satellites, but, in general, these are poorly located for detecting signals from foreign satellites in geostationary orbit.) The operations of radio telescopes are not significantly affected by terrestrial weather and are entirely unaffected by the day-night cycle. Radio telescopes can only detect satellites that are actually broadcasting—but especially in a crisis or conflict, the high-altitude satellites involved in nuclear command-and-control would almost certainly transmit continuously (though if any of these satellites rely exclusively on laser communications, they could not be monitored at all with radio telescopes). As with other ground-based assets, a number of suitably spaced radio telescopes are needed to provide coverage of the whole of the geostationary belt.

Russia has an extensive network of large radio telescopes, while China has recently built one in Argentina to expand its coverage.²⁷ Official U.S. descriptions of its space surveillance network do not mention radio telescopes, but some U.S. observatories could be used for space situational awareness.²⁸

Ground-Based Radars

Ground-based radars illuminate satellites with radio, or microwave, frequency radiation to measure their direction and range. Radars capable of detecting satellites in high-altitude orbits have small fields of view (generally a fraction of a degree) and relatively long measurement times (on the order of minutes).²⁹ As a result, they are poorly suited for wide-area monitoring but can accurately locate objects whose positions are known approximately (such as a satellite that has not conducted a repositioning maneuver since it was last observed). Like ground-based radio telescopes, they are not affected by either the day-night cycle or terrestrial weather.

There is uncertainty about the extent of Russia’s and particularly China’s deep-space radar capabilities. Russia’s Deep Space Network radio telescopes have been used in experiments as radar receivers for detecting space debris in high-altitude orbits, suggesting that Russia has at least some capability to monitor satellites in those orbits with ground-based radars.³⁰ China, meanwhile, possesses radars capable of observing low-Earth orbit satellites, but it is not known whether it also has radars capable of imaging satellites in high-altitude orbits.³¹

The United States possesses at least three radars capable of detecting high-altitude satellites: ALTAIR in the Marshall Islands, Millstone Hill in Massachusetts, and Globus II in Norway. If the field of view for each radar extends 60 degrees either side of the local vertical, this network should cover the entire geostationary belt, except for a gap between 70 degrees east to 110 degrees east—very roughly from India to Vietnam. This gap is home to about thirty of the one hundred Chinese, Russian, and U.S. satellites in geostationary orbits. (It is possible that, because of power limitations, the field of view for each radar is smaller than 120 degrees, which would increase the size of the coverage gap.)

Gaps in Coverage for a Space-Situational Awareness System

If a high-altitude satellite and any nearby objects belonging to other states cannot be monitored by any remote sensing system, violations of the satellite’s keep-out zone could not be detected. Such a situation can occur if the satellite is located outside of the fields of view of all of a state’s sensors. There are also temporal gaps—when a satellite is located too close to the sun, for example—during which even suitably located sensors cannot function effectively.

These challenges are particularly acute for geostationary satellites, which do not move much relative to the Earth’s surface. Ground-based visible telescopes cannot observe any satellites during daytime. Moreover, around local noon, a geostationary satellite may be too close to the sun to be observable by ground-based infrared telescopes or by optical sensors in low-Earth orbit. How long these exclusion periods last depends, in part, on the design of each individual sensor, which is generally classified—though, if NEOSSat is anything to go by, the periods may last for several hours.³² An aggressor could conduct an attack during a gap without risk of detection. The duration of these gaps may be reduced by adding additional optical or infrared sensors on the ground or on satellites in low-Earth orbit. Depending on the size of each sensor’s exclusion zone, however, it may not be possible to eliminate them entirely.

Closing gaps requires substantially more sophisticated and expensive technology than ground-based telescopes or sensors in low-Earth orbit. Optical sensors in high-altitude orbits (particularly orbits above the geostationary belt) are useful, as a given satellite is generally back-lit at different times from when it is observed from low-Earth orbit or the ground. Ground-based radars and radio telescopes are other options. Although the latter can only detect a satellite while it is transmitting and a co-orbital weapon might not transmit during an attack, radio telescopes could still be useful in verifying that a potentially hostile satellite has not moved.

Molniya Orbits

Satellites in Molniya orbits spend most of their time high above the Northern Hemisphere, before quickly traversing the Southern Hemisphere at low altitudes. Observing such satellites is largely similar to observing satellites in geostationary orbit with three major exceptions. First, because satellites in Molniya orbits move relative to the ground, their trajectories can be more easily measured by a single sensor without the need for triangulation. Second, Molniya orbits are inclined by 63 degrees, so satellites in such orbits appear to be more distant from the sun than geostationary satellites, facilitating their monitoring with optical sensors based on the ground and in low-Earth orbit. Third, Chinese, Russian, and U.S. ground-based space situational awareness assets appear to be sparser in the Southern Hemisphere, through which satellites in Molniya orbits transit. However, because such satellites are traveling at high speeds during this part of their trajectory, they are probably more difficult to attack than when they are moving through the Northern Hemisphere and can be more easily observed from the ground.

Notes

¹ Shaddix et al., “Daytime GEO Tracking With ‘Aquila.’”

² Russia leads the nongovernmental International Scientific Optical Network, which comprises almost one hundred ground-based optical sensors in forty observatories across sixteen countries. See Igor Molotov et al., “International Scientific Optical Network for Space Debris Research,” Advances in Space Research 41, no. 7 (2008): 1022–1028. Separately, Russia maintains the Russian Space Surveillance System. Bhavya Lal et al., “Global Trends in Space Situational Awareness (SSA) and Space Traffic Management (STM),” D-9074, IDA Science & Technology Policy Institute, April 2018, 28, https://www.ida.org/idamedia/Corporate/Files/Publications/STPIPubs/2018/D-9074.pdf.

³ Robert F. Bruck and Robert H. Copley, “GEODSS Present Configuration and Potential,” 2014 Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, September 9–12, 2014, 1, https://amostech.com/TechnicalPapers/2014/Poster/BRUCK.pdf.

⁴ Lal et al., “Global Trends in Space Situational Awareness (SSA) and Space Traffic Management (STM),” 29, 50.

⁵ Brian Weeden, “Trends in Commercial Space Situational Awareness,” Space Situational Awareness: Strategic Challenges for India, Bengaluru, India, June 14–15, 2018, https://swfound.org/media/206218/weeden_commercial_ssa_jun2018.pdf.

⁶ Stokes et al., “The Space-Based Visible Program,” 213; and Air Force Space Command, “Space Based Space Surveillance,” fact sheet, March 22, 2017, https://www.afspc.af.mil/About-Us/Fact-Sheets/Article/249017/space-based-space-surveillance-sbss/.

⁷ Since a NEOSSat satellite must be pointed more than 45 degrees away from the sun, its exclusion zone is a roughly 90 degree arc, which is traversed by a geostationary satellite in about six hours. Robert Scott and Stefan Thorsteinson, “Key Findings From the NEOSSat Space-Based SSA Microsatellite Mission,” 2018 Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, September 11–14, 2018, 4, https://amostech.com/TechnicalPapers/2018/Space-Based_Assets/Scott.pdf.

⁸ Weeden and Samson, eds., “Global Counterspace Capabilities,” 3–8. The satellites in higher altitude orbits travel at a lower angular velocity than the geostationary belt and so move backward relative to it, whereas the satellites in lower altitude orbits move forward.

⁹ Weeden and Samson, eds., “Global Counterspace Capabilities,” 2–7, 2-13–2-14.

¹⁰ Future satellites may be placed in geostationary orbit. Podvig, “Fourth Tundra Early-Warning Satellite Is in Orbit.”

¹¹ Cassandra Garrison, “China’s Military-Run Space Station in Argentina Is a ‘Black Box,’” Reuters, January 31, 2019, https://www.reuters.com/article/us-space-argentina-china-insight/chinas-military-run-space-station-in-argentina-is-a-black-box-idUSKCN1PP0I2.

¹² Galen Watts, John M. Ford, and H. Alyson Ford, “Space Situational Awareness Applications for Radio Astronomy Assets” in Proceedings of Society of Photo-Optical Instrumentation Engineers 9469, Sensors and Systems for Space Applications VIII (May 22, 2015), 94690N.

¹³ Livingstone, “Radar Systems for Monitoring Objects in Geosynchronous Orbit,” 13.

¹⁴ I. Molotov, “Status and Plans of the Russian Deep Space Network With Emphasis on the VLBI/Delta-DOR Techniques,” 18th International Symposium on Space Flight Dynamics, Munich, Germany, October 11–15, 2004, 443.

¹⁵ Brian Weeden, Paul Cefola, and Jaganath Sankaran, “Global Space Situational Awareness Sensors,” 2010 Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, September 14–17, 2010, 6–7, https://amostech.com/TechnicalPapers/2010/Integrating_Diverse_Data/Weeden.pdf.

¹⁶ The duration also depends on the latitude of the sensor, the time of year, and the brightness of the satellite. The exclusion period will be longest at the vernal and autumnal equinoxes and shortest at the solstices.

¹⁷ James M. Acton, “Hypersonic Boost-Glide Weapons,” Science & Global Security 23, no. 3 (2015): 193.

¹⁸ “Ensuring U.S. Technological Superiority: An Update From Under Secretary Michael D. Griffin,” Hudson Institute, Washington, DC, August 23, 2019, https://www.hudson.org/research/15273-transcript-ensuring-u-s-technological-superiority-an-update-from-under-secretary-michael-d-griffin.

¹⁹ Sydney J. Freedberg Jr., “Pentagon Hypersonics Director Rebuts Critics, Step by Step,” Breaking Defense, February 2, 2021, https://breakingdefense.com/2021/02/pentagon-hypersonics-director-rebuts-the-critics-point-by-point/.

²⁰ Franz-Stefan Gady, “China Tests New Weapon Capable of Breaching US Missile Defense Systems,” The Diplomat, April 28, 2016, https://thediplomat.com/2016/04/china-tests-new-weapon-capable-of-breaching-u-s-missile-defense-systems/.

²¹ David K. Barton et al., “Report of the American Physical Society Study Group on Boost-Phase Intercept Systems for National Missile Defense: Scientific and Technical Issues,” Reviews of Modern Physics 76, no. 3 (2004): S159–S169; and Cameron L. Tracy and David Wright, “Modeling the Performance of Hypersonic Boost-Glide Missiles,” Science & Global Security 28, no. 3 (2020): 15–20.

²² There are scenarios where the second burn may not be required—for example, if the attacking satellite had a very agile and accurate standoff weapon or produced a very large explosion. Such technologies would be extremely challenging and would leave little room for error, so they seem unrealistic for the foreseeable future.

²³ Rebecca Reesman and James R. Wilson, “The Physics of Space War: How Orbital Dynamics Constrain Space-to-Space Engagements,” Center for Space Policy and Strategy, The Aerospace Corporation, October 16, 2020, 5, https://aerospace.org/sites/default/files/2020-10/Reesman_PhysicsWarSpace_20201001.pdf.

²⁴ David de la Torre Sangrà and Elena Fantino, “Review of Lambert’s Problem,” 25³³ International Symposium on Space Flight Dynamics, Munich, Germany, October 19–23, 2015, https://issfd.org/2015/files/downloads/papers/028_Sangra.pdf. A helpful worked example following the universal variables solution can be found in Howard D. Curtis, Orbital Mechanics for Engineering Students, third edition (Oxford: Butterworth-Heinemann, 2014), 328.

²⁵ INF Treaty, article VII.4.

²⁶ Jay Mathews, “China’s ICBMs Seen Deterring Soviet Attacks,” Washington Post, May 22, 1980, https://www.washingtonpost.com/archive/politics/1980/05/22/chinas-icbms-seen-deterring-soviet-attacks/11e35feb-b28a-4814-b6a0-477623feb191/.

²⁷ “The Chinese ICBM Test of August 7 [UPDATED],” SatTrackCam Leiden (b)log (blog), August 17, 2019, https://sattrackcam.blogspot.com/2019/08/the-chinese-icbm-test-of-august-7.html.

²⁸ ICBMs equipped with a post-boost vehicle can modify their trajectory slightly after burnout. A terminally guided reentry vehicle could also allow for maneuverability after reentry.

²⁹ INF Treaty, article VII.4. Almost identical language can be found in Protocol to New START, part 1, article 59(a).

³⁰ Protocol to New START, part 1, article 59(b).

³¹ Trevithick, “Russia Shows Off Parts of Its Controversial Cruise Missile System”; and Ankit Panda, “U.S. Intelligence: Russia Tried to Con the World With Bogus Missile,” Daily Beast, February 18, 2019, https://www.thedailybeast.com/us-intelligence-russia-tried-to-con-the-world-with-bogus-missile. 

³² Coats, “Russia’s Intermediate-Range Nuclear Forces (INF) Treaty Violation.”