# Sphere Earth

This year has seen more than the usual number of references to flat earth conspiracies in the news, including some very fascinating twitter tirades. I think that’s as good a reason as any to talk about a field of engineering and earth science that you may have never heard of before: geodesy. How does your airline pilot know which direction to head when he’s over the ocean with no landmarks? How do we know the exact boundaries between parcels of land and between states and countries? These are questions we answer with geodesy: the science of how we characterize the shape and size of the earth. You see, it’s easy to compare the distance and direction between two locations that are close to one another, but it’s a whole different matter for places that are far apart. Geodesy provides the mathematical framework we need to make calculations about the globe and answer important questions like: How can a GPS satellite guide me to the nearest taco stand? Well, how can it?

You can’t just take a measuring tape between every point on the earth, so to be able to calculate the distance between me and my favorite taco joint, I need to use a coordinate system. For short distances, it’s perfectly fine to assume things are flat and use a Cartesian coordinates. But over long distances, that assumption starts to break down because drawing a straight line between two locations will actually pass through the earth, rather than along its surface. Flat-earthers say the earth’s not a sphere, and I have to agree with them on that. In fact, If the earth were a sphere, our lives would be almost as simple as if it were flat. We could use a spherical coordinate system and define locations using radius, polar angle, and azimuth instead of just X and Y. Well I did say almost as simple.

But, the earth is much bumpier than that, and in fact, because of its rotation, the earth actually bulges along the equator. It’s not a sphere at all. And unfortunately, bumpy bulging coordinate systems make calculating things like distance challenging, if not impossible. So, to bridge the cartographic gap between me and delicious tacos we need an idealized model of the earth. And it turns out that there’s a 3-dimensional shape that matches the earth’s fairly well: the oblate spheroid, also known as an ellipsoid. Geodesists have defined a number of reference ellipsoids over the years to try and match the shape of the earth for use in performing geodetic computations. The reference ellipsoid serves as the basis for a coordinate system we all know and love: latitude and longitude. The math isn’t quite as simple as with Cartesian or spherical systems, but it’s more much accurate. In fact, the satellites that form the Global Positioning System, or GPS, use a reference ellipsoid to calculate a receiver’s location anywhere on earth. Mapping software can take data from GPS satellites and perform computations with very high precision, for example, the distance between me and, well, you know.

Even if the earth were perfectly spherical, the strength of gravity wouldn’t be the same everywhere, because mountain ranges, ocean topography, and distribution of magma create variations in density throughout the planet. Much of the equipment we use for surveying depends on gravity to determine what’s up and down. If you’ve ever used a spirit level, it’s the same concept. But in many places on earth, the gravity vector may not be exactly perpendicular to the reference ellipsoid. You might think your equipment is perfect vertical, when in fact it isn’t. So, we need to be able to make adjustments to our surveying measurements to correct for this. Enter the geoid: Take away the weather, atmosphere, wind, tides, currents, et cetera so the ocean is at rest relative to the earth. The water will bulge up near points of higher gravity and thin out where gravity is weaker, creating a shape we call the geoid. Put more rigorously, it’s the surface to which the force of gravity is everywhere perpendicular. And geodesists have measured the geoid to a high degree of precision so we can have a mathematically defined, standardized model of the earth. That allows GPS satellites and modern surveying equipment to make extremely accurate measurements no matter where they are on earth.

They say that wherever you go, there you are, and no one knows that better than geodesists. They take the irregular, amorphous rock that we live on, and give it structure, form, and definition, providing a framework for a whole host of other sciences and technologies. Geodesy tells us that if it looks like an ellipsoid and spins like an ellipsoid, it might be the earth. Thank you for watching, and let me know what you think.