On January 27, 2008, the US Government announced that a large spy satellite (known as US 193) was out of control and falling back to Earth. After launch, the satellite failed to respond to commands from Earth which would have established it in a final orbit. While many of the details about the satellite are classified, one thing is certain: reentry is inevitable.

Predicting the reentry of a satellite is a classic root finding problem. However, the function describing motion is far from simple. As has been discussed, tracking large asteroids which may potentially hit the Earth is difficult enough. When the asteroid (or satellite in this case) gets close to the Earth, the motion becomes even more complicated. When a satellite (or asteroid) is greater than 800 km from the surface of the Earth, solar radiation pressure is the dominating perturbing force. Because this is caused by the momentum transfer of photons, the forces experienced are quite small. Given enough accurate data, the orbital motion of the object can predicted with some deal of accuracy. Once the object descends below 800 km, the orbital models used above fail to describe the motion accurately. This is due to the atmospheric drag, which becomes the dominating force below 800 km. In theory, given the necessary properties (satellite speed, air density, etc.), the drag force could be calculated. However, the atmospheric properties in the upper atmosphere are far from uniform. According to Sky News the actual crash site of the satellite cannot be predicted until it reaches an altitude of approximately 95 km, at which point the time to impact is only about 30 minutes.

Because of the difficulties of the root finding problem in this case, and due to the large amount (~1,000 lb) of hrydazine on board, the US Government has decided to us a SM-3 missile fired from a Navy ship in the Pacific to shoot down the satellite, claiming that it is safer than allowing the satellite and its carcinogenic fuel to reenter the atmosphere. While this this solves the problem of determining the impact location, it introduces another root finding problem which is necessary to direct the missile towards the satellite. The details of the guidance system are classified; however, the system has been tested before using dummy targets. This is the first test of the missile against a real target, and experts are concerned that the tracking algorithms have only been tested with stable, predictable targets. In a few days time, we will see whether or not this random error and variation will effect the success of the mission.

More discussion of the anti-satellite mission.