## Thursday 4 February 2016

40) “From near Cape Horn, Chile to Port Philip in Melbourne, Australia the distance is 10,500 miles, or 143 degrees of longitude away. Factoring in the remaining degrees to 360 makes for a total distance of 26,430 miles around this particular latitude, which is over 1500 miles wider than Earth is supposed to be at the equator, and many more thousands of miles wider than it is supposed to be at such Southern latitudes.”

“Apparently, latitude doesn't matter.

The two points named are:
Cape Horn, Chile, Latitude:-55.983333° Longitude:-67.266667°
Melbourne, Australia, Latitude:-37.814251°Longitude:144.963169°

They then state a distance between these two points and calculate the radius from the longitude difference. I'm sorry, but the latitude matters too. Using the Pythagorean approximation we used earlier, the distance they give, a radius of 6371km and the difference in longitude they give, we find that

dθ≈s2r2−dϕ2−−−−−−−−√≈15.5272o

Drat, it was ~56−38=18. Well, that's the spherical earth disproven, that is.

Oh, wait. They still agree.”

“1st Sydney and Nelson are not on the same latitude. That means you have to go southeast from Sydney to Nelson and not just east. It's just the wrong line to begin with.

2nd Even if they were on the same latitude, the shortest distance between them wouldn't follow the latitude and the true angular distance wouldn't be 22°. That is because no latitude (except for 0° at the equator) represents the true diameter of earth.

If you were to calculate the distance between these two places following the latitude, you would have to use the diameter of your latitude and not the diameter of earth. Anyway, take a piece of string and try to connect two places on the same latitude (except 0°). You will see that the line will NOT follow the latitude, but actually spans an arc around it. It only works for places that lie exactly on the equator.”