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Chapter 3, Mapping Your World
#22 Digging to China
HACK
HACK
#22
Digging to China Hack #22
Impale the planet and debunk urban myths with some basic arithmetic.
If you started digging straight down and didn’t stop, according to a popular
phrase you’d be “digging to China.” Is this really true? You might think that
calculating this requires some awesome spherical trigonometry, but we can
work this out from latitude and longitude values with a simple transformation.
Imagine that the Earth is an orange, and slice it into four quarters, demi-
hemispheres. Slice the Earth in half along the equator, and the halves in half
along the prime meridian. Looking at the quartered Earth along the prime
meridian, with London facing you:
Top-right quarter is from 0° to 90° N latitude, 0° to 180° E longitude.
Top-left quarter is from 0° to 90° N latitude, 180° W to 0° longitude.
Bottom-right quarter is from 90° S to 0° latitude, 0° to 180° E longitude.
Bottom-left quarter is from 90° S to 0° latitude, 180° W to 0° longitude.
It can help to examine a physical globe of the Earth that shows the lines of
latitude and longitude.
A line going through the center of the sphere from one point comes out at
another point in the opposite quadrant—its antipode. (This is why English
people call the Australian continent the Antipodes.) So the latitude of the
second point is the inverse, the negative mirror image of the first one, ...