Coulomb’s Law of Colliding Rockets

Imagine two spherical space stations with a limitless supply of rockets. Each space station sends out rockets in straight lines in all directions. The rockets are all of equal size and cruising at constant and equal speeds. The space around the space stations is soon full of rockets moving in straight lines.

Let’s say we want to calculate the total number of collisions happening between these rockets over a period of a year. The way we do this is to first consider the size of the rockets. Big rockets will have more collisions than small rockets. Let’s call the size factor k.

Next thing we have to recognize is that anything related to probability is calculated by multiplications. If the rate at which rockets stream out of space station one is q1, and the rate at which rockets stream out of space station two is q2, then q1 times q2 reflects the number of collisions happening.

We now have k times q1 times q2.

Finally we have to keep in mind that it matters a great deal how far the space stations are from each other. If they are far enough from each other, there are hardly any collisions at all. If they are close together, we get a lot of collisions. The way this tapers off with distance is the inverse square law. We have to take our probability equation and divide it with the square of the distance between the space stations to get the final result. If that distance is r, and the result is called F, we get:

We have arrived at Coulomb’s law of colliding rockets!