Relativity and Perspective
Adam Kall, Director of Science
6 minute read
It should come as no surprise, given my current position as Director of Technology for an aerospace company, that I was a bit of a nerd growing up. One moment of note defining my level of nerdiness was my senior year of high school when I took a public speaking class. This was a class everyone had to take, and everyone had to give a final talk where they could speak on any topic for between 15 and 20 minutes. Most people would choose to talk about their hobbies, or maybe what degree they wanted to get in college. Many of my classmates chose those topics. I, on the other hand, decided to explain to the class the concept of time dilation, how an observer's time moves slower the faster they are traveling, and a brief introduction to the concept of relativity. After 25 minutes my teacher told me I was out of time, and that “I should have been moving faster if I wanted to talk longer.” The concepts of relativity and time dilation are not simple topics that can be explained fully in a 20-minute speech or a single blog post. These concepts also require a very different education than mine in order to understand them at a deeper level than I do. That doesn’t mean the initial concepts are out of reach, or that we can’t learn something by changing the perspective from which we view a problem.
A common way to explain these concepts is to consider two passenger trains. The Hogwarts Express transports students to and from the school of Hogwarts at a regular speed of 40 miles per hour (mph), but the Polar Express is much more variable, needing to pick up those who don’t believe in Santa Claus and take them to the North Pole. If a student attempted to jump from the moving Hogwarts Express to a stationary Polar Express, the experience would be similar to having a steel wall hit them at 40 mph, because from the perspective of the non-believing student, that is exactly what happened. However, if the Polar Express were to pull alongside the Hogwarts Express and travel in the same direction at 30 mph, then the leap across might actually be survivable, since from the perspective of the student, the difference in speed is only 10 mph. If the Polar Express decided it would have safety standards slightly higher than that of Hogwarts, it could move at precisely the same speed as the Hogwarts Express, so that the student’s perspective would become a leap between two relatively stationary objects.
This becomes extremely relevant when talking about objects orbiting in space since a satellite can’t orbit unless it is going very fast, and with everything going very fast there are a lot of relative speeds to figure out and understand. A core concept of the KMI mission design is acknowledging that we can’t “catch” an object if its relative speed is high, as the “catch” would quickly just become a collision. What we need to do instead is bring our satellite into the same orbit and at the same place as our target, so we are both traveling in the same direction, at the same time, and with the same speed. Just like in the situation with the trains, the KMI spacecraft and the target piece of debris will be stationary relative to each other, while still traveling at 17,000 mph relative to an observer on the ground. This way, when the KMI spacecraft moves to make contact with the debris piece, it will be more analogous to a train passenger sitting down in their chair, rather than leaping from the train station platform to a passing hypersonic train and hoping they land in a doorway.
Perspective can also help with understanding how space debris has become an issue even though space is so big. The statement “space is big” really feels like a redundant statement, but it is worth reminding everyone. As Douglas Adams put it, “Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.” So if space is so big, it seems unbelievable that we could somehow “fill” it with debris. If the perspective is of a landfill, where objects pile on top of each other, then space is certainly not filled and there is still plenty of space in which to pile more. But unlike a landfill, all of the objects in space have to be moving at orbital velocities, or else they won’t stay in space. That means instead of sitting stationary in a pile, every piece of space debris carves out an ellipse that it travels through and in which it could collide with other objects that share the same space. When viewed as dangerous ellipses instead of dangerous objects, space starts to feel very full.
6 minute read
In this image, red dots represent debris objects from the 2009 Iridium/Kosmos collision. The blue lines trace the ellipses that make up the orbital paths of those objects. This represents fewer than 10% of the objects in orbit around Earth.
The next perspective change is to recognize that humans aren’t dealing with a debris problem in all of space, but just in the volume of space around Earth. For the space defined as Low Earth Orbit (LEO), that ranges from 62 miles above the ground to 1,250 miles high (100km to 2,000km). For perspective, the moon orbits 238,900 miles away. Even within the limited LEO space, the area of concern is further reduced. Objects below 400 miles tend to deorbit due to friction with the atmosphere, and most satellite missions want to be lower than 800 miles to minimize how strong their communications and radiation shielding need to be. These factors turn the volume from being an unbelievably big number to a number I can calculate and write out (300 quadrillion m3 or 300 million billion m3). This is still a large volume, and if we were to fill it with satellites it could fit significantly more than the 6,000 or so that have ever been made. However, this is still thinking about the satellites as stationary. If they are moving, then we need to carve out a range of safety around them, say 1,500 feet, to make sure no two objects come too close. As this sphere moves in an ellipse it forms a shape called a Torus, but the less technical term is “doughnut-like shape.” However, this shape would only have an average volume of 3,000 m3 so several trillion objects could supposedly fit. The reason this isn’t true is due to one final perspective shift when thinking about things in orbit.
An orbit is not a freely-drawn ellipse, but instead has to follow very specific laws discovered by Johannes Kepler. One of those is that the orbit travels along a flat plane, meaning you can imagine a large piece of paper cutting through the Earth so that the object is always touching the surface as it travels, and that this orbital plane has to pass through the center of the Earth. This means it is impossible to just orbit the northern hemisphere, and any orbit that reaches a large latitude in the north will also reach a large latitude in the south. This leads to the unique problem that as soon as a second orbital plane is introduced, representing a new object in orbit, it has to intersect the original orbital plane somewhere. So if the goal is maximum safety, then the range from 400 miles to 800 miles can fit 1,408 satellites in a single orbital plane. From that point on, any additional object brings a risk of crossing an existing orbital plane, and every additional object increases the risk exponentially. Suddenly, even with all the space in space, the 34,000 trackable objects feel like an excessively dangerous number.
Understanding relativity and perspective is a means to a very important end. Problems that appear insurmountable sometimes are, but the vast majority of the time a bit of perspective will reframe the problem in just the right way to make it solvable. The current problem is that there are a lot of figurative trains constantly zipping around in orbit and crossing over other tracks, and even worse is the fact that most of the trains don’t have any controls. However, this impossible challenge becomes more probable if KMI is able to match up with the trains and have a relative speed of 0, enabling the jump or connection between them.
As I said in the beginning, relativity and perspective is not a topic that is succinctly summed up in a few hundred words. This was just the beginning, but it is my hope that it triggers the important first step, of learning to tackle challenges by changing the perspective from which they are viewed. KMI was initially created because the co-founders and I wanted to pursue our dreams of a futuristic space, but space debris felt like an insurmountable challenge to that dream. It was only once we changed our perspective and looked at solving space debris as the starting point for our dream that we realized what we faced was not just a problem, but also an opportunity to create a futuristic space by keeping space clear for all.
Recommended column to read next: Speed is King