# The Kessler Syndrome

The Kessler syndrome is a play on "China Syndrome", and describes an exponential increase in fragments of space debris, as orbiting objects smash each other and create millions of small objects capable of crippling most active satellites.

Donald Kessler's scenario starts with the accumulation of derelict objects in low earth orbit. Those collide with each other, making smaller fragments in more orbits. These bullets can disable active satellites, creating more derelicts. This can grow exponentially. The accumulation of penetrating debris is the problem, in orbits with high relative inclination (hence high closing rates) at intensely populated altitudes. The number of collisions is proportional to the square of the density.

The reason the collisions happen is because most satellite orbits are in many different orbital planes, most highly inclined to the equator. Where two of these orbits intersect, the closing velocity between the satellites is approximately proportional to the angle between the planes. Because of the oblateness of the earth, inclined orbits precess, at different rates for different inclinations and altitudes and ellipsicities; two orbits that do not originally intersect may precess until they do. Even then, a collision will only happen if the orbiting objects arrive at the same point simultaneously.

The number of collisions is proportional to the cross sections of the objects and the square of their number. If all satellites are broken into eight equal pieces, the cross section goes down by a factor of four, but the square of the number goes up by a factor of 64. The result of these breakups is 16 times the collision rate, or double the collision rate per object. At some point, all orbiting objects are broken into tiny bits, and space becomes unsurvivable for active satellites.

The situation is not quite that dire because of a complication. The colliding objects will expend energy, and change orbital parameters. Chances are good that the perigee of many of the new orbits will lower, possibly low enough to increase drag significantly, or even directly reenter. The average inclination of the remaining material will be lower. So collisions will increase, and mass in orbit will decrease. Eventually there will be a ring of very small objects. Given the earth's massive moon, this ring will eventually be perturbed into reentry.

However, that ring will last a *long* time, and interdict space for many uses, perhaps for hundreds of years. It will certainly make the region of low earth orbit unusable for new satellites in inclined orbits.