A common misconception about lines of latitude is that they were simply defined as the - PowerPoint Presentation

Slide1

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°Slide2

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°Slide3

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. Slide4

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. Slide5

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

Horizon

Zenith

POLARIS

EquatorSlide6

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°

30°

EquatorSlide7

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°

60°

30°

EquatorSlide8

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°

EquatorSlide9

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.Slide10

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.Slide11

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.Slide12

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?Slide13

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)Slide14

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 Slide15

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?Slide16

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 Earth

Oblate Spheroidal Earth

45°

45°

POLARIS

45°

Horizon

45°

Horizon

POLARIS

45°

45°Slide17

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 Earth

Oblate Spheroidal EarthSlide18

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: