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I'm confused about the use of "in the Mercator projection" in #4: > In the Mercator projection, the Earth - which, in reality, is an oblate spheroid - is proje

by schoen 6y ago

I'm confused about the use of "in the Mercator projection" in #4: > In the Mercator projection, the Earth - which, in reality, is an oblate spheroid - is projected as a simple cylinder. This means that "parallel" longitude lines meet at the poles, so the distance between degrees of longitude are much shorter as they get closer to the poles than they are at the equator (~111 km). Latitude and longitude are defined on the globe, not by any particular projection, and the fact that longitude lines meet at the poles is true on the globe. A projection may or may not make them appear to be parallel. No projection is responsible for, or will change, the fact that a degree of longitude as an arc on the Earth's surface varies in length from (Earth's equatorial circumference)/360 at the equator to 0 at the poles.

jcrawfordor 6y ago
The Mercator projection models the earth as a cylinder. I think the association here is just that people are most familiar with the coordinate grid as represented on the Mercator projection, which creates the illusion that lines of longitude are parallel. This illusion is all the stronger because it makes spherical coordinates look like the more familiar cartesian plane, which would tend to be most people's first intuition before remembering that the planet is roughly spherical. The situation is even a bit worse in marine or air navigation because the nautical mile is (or more accurately was) defined by a minute of latitude, which is nearly consistent across the globe and creates the temptation to measure along longitude the same way. In reality nautical and aviation charts have to use a specific conical projection to keep this naive way of measuring distances approximately accurate.
- schoen 6y ago
  Aha, that makes perfect sense. It's not suggesting that the underlying property is only true of the Mercator projection, but that people are most likely to be confused by that property when they think in terms of the Mercator projection. > because the nautical mile is (or more accurately was) defined by a minute of latitude Cool, I've heard that in the past but somehow always forget about it! You have: (arcminute/circle) earthradius * two pi You want: nauticalmile * 1.0006759 / 0.9993246 Thanks!

by schoen 6y ago

jcrawfordor 6y ago

The Mercator projection models the earth as a cylinder. I think the association here is just that people are most familiar with the coordinate grid as represented on the Mercator projection, which creates the illusion that lines of longitude are parallel. This illusion is all the stronger because it makes spherical coordinates look like the more familiar cartesian plane, which would tend to be most people's first intuition before remembering that the planet is roughly spherical. The situation is even a bit worse in marine or air navigation because the nautical mile is (or more accurately was) defined by a minute of latitude, which is nearly consistent across the globe and creates the temptation to measure along longitude the same way. In reality nautical and aviation charts have to use a specific conical projection to keep this naive way of measuring distances approximately accurate.

schoen 6y ago
Aha, that makes perfect sense. It's not suggesting that the underlying property is only true of the Mercator projection, but that people are most likely to be confused by that property when they think in terms of the Mercator projection. > because the nautical mile is (or more accurately was) defined by a minute of latitude Cool, I've heard that in the past but somehow always forget about it! You have: (arcminute/circle) earthradius * two pi You want: nauticalmile * 1.0006759 / 0.9993246 Thanks!