Publications

Kinetic energy at the small can be very big

To envision the potential damage that a piece of debris could cause in a direct hit, consider the kinetic energy (potential to do damage on impact) of a car just before it hits the wall in one of the by now familiar auto safety commercials on television. The kinetic energy of a cube of aluminum 10 cm on a side moving at even 5 km/s relative to a satellite is 25 times greater than that of the car. The principal advantage for the satellite is that the cross section of debris/satellite impact is considerably smaller than that of the car and the wall.

Lab Notes

You're driving along a proverbial springtime road in New England trying to avoid the potholes. You jerk the steering wheel right, then left, but eventually you still hit the deepest one because you can't quite figure exactly where your passenger-side tire is and the potholes come in very quick succession.

Now project yourself upward into the region of orbiting satellites travelling over 5 km/s. How do you avoid the oncoming "potholes" of other satellites and space debris? Arthur Lue and his associates in the Space Situational Awareness Group are concerned with the ever-increasing number of objects to avoid and how close they come to active satellites on a daily basis. They consider two issues—how many potholes there are and how accurately can they locate the passenger-side tire. If they can determine the precise location of every object in a satellite's orbit, it may not be necessary to jerk its steering wheel too often.

A snapshot of the environment surrounding the Earth shows the conjunctions that occurred in a 144-minute (less than two and a half hours!) time frame on 20 May 2009. Green dots mark the more than 2,500 conjunctions of less than 10 km, while the red dots mark the 31 conjunctions of less than 1 km.

Lue worries about the expanding collection of space debris and satellites in orbit around the Earth. According to Lue, the current Spacetrack Catalog lists almost 15,000 objects greater than 10 cm in size. These include objects ranging from active and dead satellites and rocket bodies to misplaced tools from manned space flights to the myriad pieces of scrap metal resulting from the Chinese anti-satellite missile test of 2007 (about 2,500 objects) and the Iridium/Cosmos collision in 2009 (about 1,400 objects). "We’re already near the Kessler Syndrome limit (the point at which there will be a runaway chain-reaction increase in the number of objects in orbit, [1]),"
Lue says.

Recalling the asteroid-Earth scenario of the movies Armageddon and Space Cowboys, Lue offers two alternatives. "Either you go out and destroy the asteroid or you predict its path accurately and move the people out of the city where it is going to hit." For satellites and debris, he offers the same two alternatives: get rid of all the debris or shift the position of the satellite to avoid the collision. A recent commercial on television shows the Air Force Space Command shifting the position of a satellite to avoid a collision with a piece of space debris. Although this is definitely a positive result (the satellite survives), the procedure leaves the satellite with less fuel to make future orbit corrections, potentially reducing its active lifetime. In fact, shifting position only extends the satellite's safety margin for about six hours before another conjunction of less than 10 km will occur, according to Lue.

For Lue, close is 10 km. If you set a sphere of 10 km radius around each object in space, these spheres will overlap with other objects every six hours or so. Extending this safety margin is the main thrust of Lue's work. Can all the objects that might cause damage be identified and characterized, and how accurately can their paths along their individual orbits be described?

Although spherical conjunction, shown as light blue circles, might indicate that one or both of these objects should alter its path to avoid collision, the ellipsoids show that no corrections are necessary for this pass of these objects. In the figure, v1 and v2 are the (three-dimensional) velocities of the two objects, and Δx is the current separation.

Newer and more sensitive satellite-tracking telescopes are helping to solve the first problem of locating objects down to less than 10 cm in size. Once each object is located, it needs to be continuously tracked to define its orbit. Now, Lue's analysis comes into play. The six-hour frequency conjunction mentioned above is for a simple sphere. Lue proposes that if the orbits can be defined more accurately, elongated ellipsoids of potential future locations of objects will not overlap as often and the "ellipsoidal time between conjunctions" can be extended to 15 days—a significant improvement over six hours. With these tools—more accurate measurements of orbiting objects and improved algorithms for defining future locations of the objects—only those very close conjunctions will require a notification to satellite owners to suggest that they move the satellite to avoid the collision. As an added bonus to the collision avoidance, "there shouldn't be as many additional influxes of debris into the Space Catalog," Lue says.

Lue has one final suggestion. "Don't put any more nonessential junk up there until we clean out some of the stuff that is already there." Backing off from the Kessler limit requires cleaning up what already exists in orbit and creating a policy of minimal invasive actions when new satellites are deployed.

1. D.J. Kessler and B.G. Cour-Palais, "Collision Frequency of Artificial Satellites: The Creation of a Debris Belt," Journal of Geophysical Research, vol. 83, no. A6, 1978, pp. 2637–2646.