Antipodes for Dummies

four quarters of the globe

Although there's no geographer or cartographer on staff at the Antisocial Network, several of our science-y types have a long history of working with maps. They're the ones who are responsible for lambasting the freelancers who get confused about "State Place Coordinate Systems" and commit other map projection boo-boos. One of them brought a simple little freelance article to the table for today, a post called "How to Calculate Antipode" at Sciencing.com, penned by Bob Barber.

Barber, who claims a couple of science degrees, started out by defining "antipode" in his introduction. In the process, Bob spit out all you need to know about how to find the antipode of any latitude-longitude location:

"Geographers define antipode as a point exactly opposite a reference point on the opposite side of the earth. To calculate the latitude of an antipode, change the sign and direction of the latitude of the reference point. To calculate the longitude of an antipode, subtract the absolute value of the reference-point longitude from 180 degrees and change the sign and direction of the answer with reference to the reference point." Barber was almost right: in the last sentence, however, Bob blew it. No, not in the doofus construction, "with reference to the reference point"; it's where he said to "change the sign and direction..."

What Bob forgot or, more likely, didn't know; is that a latitude or longitude has either a sign or a direction, but not both. By convention, south latitudes and west longitudes are assigned negative values while east longitudes and north latitudes are positive.

So when Bob trotted out his example, finding the antipode of his local airport, he started out on the wrong foot by telling his readers that the lat-long of,

"Tampa International Airport (TPA) are +27.97 degrees north and -82.53 degrees west."

No, Bob, the latitude is either 27.97° or 27.97°N; and the longitude is either -82.53° or 82.53°W. You do not use both the sign and the direction. If you do, you end up with a problem... and that problem is just where Barber ended up:

"The latitude and longitude of the antipode to TPA are -27.97 degrees south latitude and +97.47 degrees east longitude, a point in the Indian Ocean west of Australia."

We hate to tell you this, Bob, but "+97.47 degrees east longitude" is redundant. That pales, however, against the stupidity of "-27.97 degrees south latitude": if you plug -27.97°S into a navigation system, you'll end up with 27.97°N; so your (incorrectly) calculated antipode comes out somewhere in the northernmost reaches of Myanmar, near the Chinese border.
The math behind that is pretty simple: Barber essentially said that your latitude is -(-27.97°), which works out to a positive number. Don't make the same mistake, or you'll be a Dumbass of the Day, too.

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