What happens when two satellites collide head-on in orbit?

Partly settled. Some of it is understood, some is still argued about.

Kapitza's problem #200 asks students to describe qualitatively what happens in a head-on satellite collision. Donald Kessler and Burton Cour-Palais formalized the long-term hazard implied by such collisions in 1978, predicting that above a critical debris density, collisions could cascade exponentially (the 'Kessler syndrome'). Real collisions -- notably the 2009 Iridium 33/Cosmos 2251 crash and China's 2007 anti-satellite test -- have generated thousands of tracked fragments, and as of the mid-2020s, models like NASA's LEGEND and newer cascade simulators still cannot say with confidence whether a runaway cascade is already underway or how close low-Earth orbit is to the critical threshold, making the long-term debris trajectory a genuinely open, actively modeled problem.

An entrance-exam thought experiment about two satellites colliding anticipated, by more than a decade, one of the defining unresolved engineering-physics problems of the modern space age.

Explanations that circulated

• A single satellite collision is a minor, self-contained event with no wider consequences (Kessler's 1978 analysis, since repeatedly borne out by real collisions such as the 2009 Iridium-Cosmos event, shows fragments can trigger a self-sustaining cascade of further collisions)

References

• Collision Frequency of Artificial Satellites: The Creation of a Debris Belt, Donald J. Kessler, Burton G. Cour-Palais, Journal of Geophysical Research, 1978
• Kessler's syndrome: a challenge to humanity, Various authors, Frontiers in Space Technologies, 2023