A model of space debris populations around Earth.

What kinds of problems could debris in space cause? They travel at speeds on the order of tens of thousands of miles per hour, which means that debris of any shape, size, and form will be destructive if it collides with a satellite or space shuttle. Collisions with space debris isn’t unheard of. Also, they could delay space launches if it is known that a large cloud of debris is hovering directly over the launch pad.

Space debris comes from a variety of sources. Nuts and bolts could become loose and float away from spacecraft during normal operation. When rocket stages (or segments) separate in space, they release debris. Also, in-space collisions between satellites, while rare, will create large-sized debris – the same goes for intentional spacecraft destruction, such as the Chinese anti-satellite test that was conducted a few years ago. Some of these events unleashes several thousand pieces of debris, most of which are tiny (less than an inch in size) and are much more difficult to track than larger-sized debris.

Over the past few decades, scientists and engineers have brainstormed possible solutions to decreasing space litter. However, all of the ideas have been technologically and/or economically infeasible. This could change as time goes on, especially as technology advances and/or the cost of launching a vehicle into space decreases. One possible solution is launching a garbage-collecting spacecraft to do just that, but what to do with the collected garbage is a problem. Another solution is somehow colliding objects with the orbiting debris in an effort to reduce their energy enough so that they fall into the Earth’s atmosphere (due to gravity) and burn up, but no one has thought of a feasible means to do that.

(Image from Wikipedia)

The basic gist of how Monte Carlo simulations work is that you randomly select inputs, perform calculations on the randomly-selected inputs, and collect the outputs. This process is repeated several times (perhaps thousands, tens of thousands, or even more! As with any statistical sample, the more, the better), and in the end, all the outputs are gathered together and analyzed. To randomly select inputs, you’ll need to specify boundaries for which inputs can be selected from. A statistical model can help with this, such as a Gaussian distribution, which is a fancy term for the familiar “bell curve.” As for the aggregated outputs, statistical analysis would make sense in order to make sense of thousands of data sets. Basically, statistics is a useful tool that compliments the Monte Carlo technique. Also, generally computers are used to perform a Monte Carlo simulation due to the large number of repetitive calculations required.

This is what a bell curve looks like.

Monte Carlo simulations can be used in space sciences. For example, if one wants to analyze the risk of failure of a spacecraft in orbit, one can perform a Monte Carlo simulation with random inputs for how the spacecraft begins its orbit (speed, physical orientation, etc.), since that state cannot be predetermined accurately and instead can be modeled statistically. Then, the laws of orbital mechanics can be applied to the inputs to produce outputs that can be analyzed later. A more simple example of where the Monte Carlo method is used is the classic game of Battleship. Initially, a player would randomly guess locations for where a battleship is located. After the player scores a hit, the player would follow an algorithm (guess points that are in line with the hit) to sink the battleship (the outcome).

(Image from Wikipedia)