How Big is a Degree?

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2023-09-17 16:00:05

You may have seen the new Apple Watch ad where the watch auto-dials 911 to relay the message that its owner has “taken a hard fall and is not responding.” The message goes on to say that “The emergency location is latitude 47.7, longitude -117.5 with an estimated search radius of 41 meters.” As a geospatial professional, do you see anything faulty in this ad?

Let’s do some rough calculations using rounded values for ease of reading. If we assume Earth is a sphere, its circumference is about 25,000 miles or 40,000 kilometers (km). (A better model of Earth’s shape is an “oblate spheroid” — an ellipsoid that slightly bulges at the equator and is slightly flattened at the poles.)

To compute the length of one degree of latitude or longitude, we need to know how many degrees there are on Earth. The answer is simple, but also a bit confusing because of the way we measure latitude and longitude.

Let’s start with latitude. There are 90 degrees of latitude between the Equator and each of the Poles. If we were to circumnavigate Earth, starting at the North Pole, then heading directly south to the South Pole, then heading north again to the North Pole, we would cover 360 degrees of latitude. This is not surprising, since the circumnavigation path would be a circle.

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