Can (and if so how) a planetary ring form around the earth?

Answer

In principle, it certainly can, and it already exists in a sense, with all the junk that astronauts have deposited in orbits around the Earth.

The giant planets of our solar system (Jupiter, Saturn, Uranus, and Neptune) all have extended satellite systems around them, which are, in a sense, planetary systems in miniature. The rings are usually explained as dust particles that have arisen as a result of the collision and mutual pulverization of small satellites, or of a small satellite with an object that came from elsewhere. These dust particles can get into fairly stable orbits, but infinite life doesn’t have those orbits.

The fact that the smaller planets do not have them may have to do with their smaller mass and greater proximity to the sun. For example, the relative disturbing influence of the sun is quite large compared to the attraction of the Earth, and smaller bodies are very sensitive to it. If two asteroids had the good idea to collide near Earth, a planetary ring would form, but it might not last long. The Earth itself has too few (only 1…) satellites to make a ring by colliding with each other, and there are no asteroids large enough to pulverize the Moon.

The satellite systems of the major planets are thought to have been around since the early history of the solar system, with those planets retaining some debris in their orbit around them. The small planets had too little mass to accomplish that feat. For example, you need more ‘ad hoc’ events to get satellites around the minor planets. Mercury and Venus have none, Earth’s is probably the result of a rather curious collision, and Mars’s are trapped asteroids. There is little chance of such an event happening now, the solar system has become much calmer.