1. A common misconception about lines of latitude is that they were simply defined as the intersection of different angles with the surface of the Earth, as measured relative to the equator: 10° 20° 30° 40° 50° 60° 70° 80° 90°

2. 10° 20° 30° 40° 50° 60° 70° 80° 90° A common misconception about lines of latitude is that they were simply defined as the intersection of different angles with the surface of the Earth, as measured relative to the equator: 10° 20° 30° 40° 60° 50° 70° 80° Equator 90°

3. In reality, lines of latitude were defined as angles of given size relative to the position of the North Star Polaris above the horizon. Currently, the axis of the Earth’s rotation, by geological coincidence, points nearly directly at Polaris.

4. At the North Pole, Polaris is directly overhead, at the equator it is directly on the horizon. As an observer moves from equator to the North Pole, Polaris will ‘move’ from horizon to zenith. For centuries, Earth-bound observers measured the angle between the horizon and Polaris to find their latitude.

5. Here is how latitude was actually determined and defined: Zenith Various devices have historically been used to measure the angle between the horizon and Polaris – the Sextant is still standard equipment on all ships today (just in case all electronic equipment fails) Horizon Zenith POLARIS Equator

6. Here is how latitude was actually determined and defined: Zenith Horizon Various devices have historically been used to measure the angle between the horizon and Polaris – the Sextant is still standard equipment on all ships today Horizon Zenith POLARIS 30° Equator

7. Here is how latitude was actually determined and defined: Zenith Horizon Various devices have historically been used to measure the angle between the horizon and Polaris – the Sextant is still standard equipment on all ships today Horizon Zenith POLARIS 60° 30° Equator

8. Here is how latitude was actually determined and defined: Zenith Horizon Various devices have historically been used to measure the angle between the horizon and Polaris – the Sextant is still standard equipment on all ships today POLARIS 90° Horizon 60° 30° Equator

9. INTERLUDE: Did you notice something odd about the arrow pointing to Polaris? Yes, the Polaris arrow always points in the same direction despite the different positions of the observer. This might seem odd but is actually simple: Polaris is so far away from Earth that its light hits ANY and all latitudes of the Northern Hemisphere from the same direction. Essentially, all of its incoming light is parallel by the time it reaches Earth.

10. At this point you might be wondering, why is the way that latitude is recognized and defined, important? After all, the two methods, simple geometry versus angle-to-Polaris-measurement yield the same exact results. 30° 60° 90° Equator 60° 30° Indeed, they do. HOWEVER, the fact that latitude was actually defined by direct measurement, is the cause of an interesting peculiarity we find in our latitude’s position today. vs.

11. When latitudes were measured, it was assumed that the Earth was a perfect sphere. Now we know that the Earth is actually an oblate spheroid (flattened at the poles) with an elliptical cross-section. Turns out this subtle shape difference creates an important difference in the location of measured latitude versus geometric latitude.

12. Here is how: 10° 20° 30° 40° 50° 60° 70° 80° 90° This is where geometrically determined latitudes are on a perfect sphere 10° 20° 30° 40° 50° 60° 70° 80° 90° And here is where they fall on an oblate spheroid. The difference is subtle…can you see it?

13. Let’s make it more obvious… 45° This is where geometrically determined latitudes are on a perfect sphere Let’s just mark 45° to make our graphic less busy to behold. Let’s also mark the arc length distance between 0-45° and 45-90º 90° On a sphere they are of identical lengths (makes sense)

14. Let’s make it more obvious… Now let’s change the Earth’s shape to a spheroid. Watch what happens to our arc lengths. 90° 45° Let’s exaggerate this so it is REALLY obvious! As the Earth becomes more elliptical, the arc length between 0- 45º becomes LONGER, whereas the arc length between 45º-90º becomes SHORTER. In terms of the Earth, the distance on the rounded surface of the Earth would be FARTHER from 0- 45º than it would be from 45º-90º. ~5006km ~4995km

15. How does that match what you got for these distances by measuring them in Google Earth? EQUATOR to HALFWAY (45º) = 5006km (~3110 miles) HALFWAY (45º) to North Pole = 4995km (~3104 miles) Hm, that’s odd. Your equator- halfway distance is actually SHORTER than the halfway-North Pole distance! (and the numbers probably don’t match either) What’s going on here? Hm, that’s odd. Your equator- halfway distance is actually SHORTER than the halfway-North Pole distance! (and the numbers probably don’t match either) What’s going on here?

16. Well, let’s see what happens when we assign latitude using observational measurements made from the surface of the Earth (or its ocean surface). Let’s compare, a spherical and an oblate spheroidal Earth. Spherical EarthOblate Spheroidal Earth 45° POLARIS 45° Horizon 45° Horizon POLARIS 45°

17. Interesting, isn’t it? Because of the difference in the oblate Earth’s elliptical curvature, a 45° degree angle between horizon and Polaris is reached sooner as an observer moves towards the North Pole. Spherical EarthOblate Spheroidal Earth

18. This is why, on the real Earth, the arc length distance between equator and 45º is SHORTER than the arc length between 45º and the North Pole. Oblate Spheroidal Earth Because the diagram here greatly exaggerates the oblate shape of the Earth, the differences in the arc lengths are also greatly exaggerated. EQUATOR to HALFWAY (45º) = 3097 miles HALFWAY (45º) to North Pole = 3117 miles The actual distances are approximately: