Space Terms 4: What’s your Inclination?

Space Terms 4: What’s your Inclination?

Austin Morris, Director of Engineering

7 minute read

Welcome back to Space Terms, I am your host, A Guy Who Thinks He Understands Things. Today, I will be proving myself wrong.

In previous installments of this series, I have briefly touched on Keplerian elements such as inclination and eccentricity of orbits, but have avoided diving deep into them. The time has now come to rectify that, as we try to begin comprehending the six Keplerian elements (named after Johannes Kepler) and how they define an orbit. Before we begin though, I have a disclaimer.

Take a look at this visualization of the Dunning-Kruger effect from Tim Urban at Wait But Why. Before educating myself more deeply on this subject in order to write this column, I resided firmly at the top of the Child’s Hill. I have since tumbled all the way down into the Insecure Canyon, and have only just begun to climb my way out. If you wish to remain on the Hill, you may feel free to take this exit. Know that there is no judgment from me, and you can go find something else to read, knowing that this will always be here for you if you decide to take the plunge. For the rest of you, stay strong and read on.

The way that I think about the Keplerian elements is as follows: there are two that relate to altitude, two that relate to timing, and two that relate to direction. Each of these pairs can be a little difficult to explain, as the two elements in each pair are interrelated and must be somewhat simultaneously understood, which does not lend itself well to writing about them sequentially.

Let’s take the first pair, which relate to altitude. When most people think of orbiting satellites, they think of an orbit that is a perfect circle. This is an ideal orbit that is not realistically feasible, but most objects in LEO have a fairly circular orbit and vary by only a small margin. This measure is referred to as eccentricity. As explained in a previous installment, an orbit with an eccentricity of 0 is that aforementioned perfect and infeasible circle, while an eccentricity of 1 is a straight line through the center of the planet. This is generally considered to be a bad orbit. An eccentricity of more than 1 is not a sustained orbit, but is instead a hyperbolic escape orbit, swinging by an object (such as a planet) and careening off in another direction. As for negative eccentricity values, don’t. Just don’t.

The other half of the altitude pair is the semimajor axis. In any elliptical orbit, found by an eccentricity above 0 and less than 1, there will be two axes to represent that ellipse: the widest distance between two points on the ellipse is the major axis and the shortest distance is the minor axis. Taking the major axis and dividing it in half results in the semimajor axis, which is the average altitude of this orbit. The reason it is important to understand both of these elements together is that at any average altitude there is a maximum eccentricity that an orbit can reach before it collides with the planet. That is, the orbit can only get so narrow before the narrow part of it is smaller than the Earth is wide.


We have defined the shape and size of the orbit and now we’ll talk about the timing of it. True anomaly is a cool term that has a relatively simple definition: it defines the location of an object along its path at a given time. Essentially, once you have the path identified in your mind, the true anomaly tells you where along that path the object is, and also relates to the time at which the object was in that location. That time is called the epoch, which is another cool yet simple term. This concept is somewhat similar to its pair partner element, the argument of the periapsis.

I have previously defined the periapsis and the apoapsis as the points along your orbit at which you are at your lowest and highest altitudes, respectively. As such, the argument of the periapsis is measured as the point of lowest altitude along your orbital path, measured as a degree measurement up to 360°, with 0° being the point at which you cross the equator. In other words, if your orbit takes, for simplicity, 360 minutes to return to its starting point, this would be a measure of how many minutes it takes from your ascending node (when you pass the equator traveling from south to north) to when you reach your lowest altitude point. The argument of the periapsis, combined with the true anomaly, helps define where along your orbital path your object actually is at any given time.

It is at this point that I will recommend you fasten your seatbelts, because this is about to be a bumpy ride. If you like things that are easy to understand, you should stop reading now, because this next segment broke my brain like Jeremy Bearimy broke Chidi in The Good Place (kudos to those of you who get that reference). Ye be warned.

The final two Keplerian elements are those that define the direction of an orbit, with the first of these two simply called the inclination. Inclination is a measure of the degree difference between your orbit and the equator, measured at your ascending node, which again is when you pass the equator traveling from the Southern Hemisphere to the Northern Hemisphere. Traveling directly along the equator, in the same direction as the Earth’s rotation, constitutes a 0° inclination. If your orbit is traveling directly in a northeastern direction, that would be considered a 45° inclination. If your orbit travels directly north and south, over the poles, that would quantify a 90° inclination. Northwest, therefore, is a 135° inclination, while traveling directly along the equator in the opposite direction of the Earth’s rotation is thus a 180° inclination.

Where things start to get a little spicy is when we talk about what happens past a 180° inclination. Most sensible people, like I like to consider myself, would imagine it continues counting upward, eventually circling around to 359° and then starting back at 0° where 360° would be. Instead, inclination is best thought of as counting up to 180° and then counting back down to 0° as we return to matching the equator. This is the exact moment that my mind shattered. If this is the case, then wouldn’t there be two orbits of 179° inclination that are actually 2° apart? Yes and no. Here is where I need to introduce the final Keplerian Element, in the hopes that it will make more sense of this mess that I’ve left behind in explaining inclination, thanks to the aforementioned unfortunate situation that both terms must be understood simultaneously in order to understand either.

I have now mentioned the ascending node a few times in the hopes that it will make this final element easier to understand. The longitude of the ascending node is the longitude point at which you cross the equator traveling from south to north. When talking about Earth orbits, this term is essentially interchangeable with right ascension of the ascending node. I mention this because it is a term that you may come across in reading other space things, but for simplicity I will be sticking with longitude of the ascending node. Every orbit has this point except for a perfect 0° inclination along the equator, which has no ascending node. Longitude of the ascending node is important in understanding the reason that inclination is measured only up to 180° in that once the inclination passes 180°, the ascending node has now flipped to the opposite side of the planet as it previously was. As such, an orbit with 179° inclination and longitude of the ascending node that crosses somewhere in the middle of the United States would not be equivalent to an orbit with 179° inclination and a longitude of the ascending node that crosses somewhere in the middle of Russia, on the opposite side of the world. These inclinations would instead be 2° apart, because their ascending and descending nodes are roughly opposite each other.

Another way of thinking about this example is to consider an orbit with 179° inclination and longitude of the ascending node that crosses somewhere in the middle of the United States. If this orbit were to progress another 2° degrees and pass the equator, it would now be traveling from north to south over the United States, meaning that its ascending node would flip to the other side of the world, crossing the equator from south to north somewhere in line with the middle of Russia. This orbit would still be considered a 179° inclination, but with respect to that new longitude of the ascending node.

Just in case I have actually explained this all in a way that makes some coherent sense to you, I’d like to throw you for one final loop. The final brain-breaking bit of fun to mention is that these elements are interchangeable for all planetary bodies in our solar system, with two notable exceptions. Uranus, as some of you may know, is notable in the fact that it has an extreme axial tilt (basically it’s tipped on its side). Venus, on the other hand, rotates retrograde, counter to its orbit around the sun. This means that it rotates in the opposite direction of all the other planets in the solar system. If somehow the rest of this column hasn’t hurt you enough, feel free to do your own independent research into the identification and characterization of orbits around Venus and Uranus.

As mentioned before, driving on a road is an activity that generally occurs in two dimensions. Flying is an activity that adds one more to become three dimensions. Orbit is a complicated thing, and defining a specific orbit even more so. That is why orbits have no chill and immediately jump to six-dimensional thinking in order to navigate. This definition of orbit is a definition which has been done for thousands of orbital objects, to determine where they will be placed into orbit, and will be done for tens of thousands more in the coming years. Managing the crossing of these many objects requires equally complex calculation and preparedness, and inevitably leads to collisions and crowding of orbit. Stay tuned with KMI as we work to determine where our spacecraft will fit into the whole messy situation, and tag along on our mission of keeping space clear for all.

 

Recommended column to read next: Space Terms 3: An Intermediate Guide to Jargon