Basics of datums

By this point, you know that the earth can be modeled as a spheroid or (less accurately) as a sphere. You also know that different dimensions have been used for these models. This story goes all the way back to the ancient Greeks and their various estimates of the earth's circumference. It takes us through Newton's hypothesis that the earth bulges at the equator and is flattened at the poles, and all the way up to present-day satellite technology with its highly accurate measurements of the earth's shape and size.

While a spheroid is a good model, it doesn't describe the earth's shape exactly. Is that surprising? Not really—a spheroid is a perfectly regular mathematical form and the earth is just a big hunk of rock. Strictly speaking, we shouldn't say that the earth's shape is an spheroid. We should say that a spheroid is the shape that best describes the earth while still being practical to work with.

What is the earth's shape really like? Well, for one thing, it has mountains and valleys. Okay, suppose we take some giant-sized sandpaper and a huge can of putty and we sand down the bumps and fill in the cracks so that we have a perfectly smooth, even surface. Actually, that's what surveyors and geodesists do, except that they use math instead of sandpaper and putty. For the purpose of determining horizontal reference points (latitude and longitude), they level their measurements down to a surface called a geoid. The geoid is the shape that the earth would have if all its topography were removed—or, more accurately, if every point on the earth's surface had the value of mean sea level.

It would be great if the geoid were a spheroid, but it's not. The geoid is irregular because the force of gravity isn't constant over the earth's surface. Gravity is stronger in some areas—where dense material, like iron, is concentrated under the earth's crust—and weaker in others. These changes are fairly gentle, but they're significant, as you'll see in the concepts that follow.

Latitude-longitude values are measured on the earth and mathematically leveled to the geoid. This process does not affect the horizontal positions of points. From the geoid, points are then calculated to corresponding positions on the surface of a spheroid. This process does affect horizontal positions.