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All Places > Coordinate Reference Systems > Blog > 2014 > December

What is an antipode?

Any point on the surface of a sphere, in this case the Earth, that lies diametrically opposite from a given point on the same surface, so that a line drawn between the two points through the center of the sphere forms a true diameter (e.g. through the Poles of a Sphere). The Antipodes islands of New Zealand, in the South Pacific, are named after this phenomenon because of there "closeness" to the antipodes of London.


The image below shows the relative distribution of landmasses on opposite sides of the Earth.


How can you calculate the antipodal point for any point on the Earth's surface?


The method using decimal degrees:

Take the latitude and convert it to the opposite hemisphere. This is done by multiplying by minus 1 (e.g. -x * -1 = x).


The longitude is calculated by taking the maximum possible longitudinal value and subtracting the input longitude value. The if statements allow for "which way round the Earth" the calculation is conducted this is important because the values are bounded to +180 and -180. For example a longitude of -10 has an antipodal location of ((-180) - (-10))*-1 = 170.


# Original latitude and longitude values in Decimal Degrees
Latitude =  33.918861
Longitude = 18.4233

# Convert latitude to opposite hemisphere (e.g. −x* −1 = x)
AntiLatitide = Latitude *-1

print "Antipodal Latitude: " + str(AntiLatitide)

# Convert Longitude to opposite hemisphere (e.g. (180 - x)*-1 = y)
# Note this binds the maximum values to be -180 and 180 degrees
if Longitude > 0:
    AntiLongitude = (180 - Longitude)*-1
elif Longitude < 0:
    AntiLongitude = (-180 - Longitude)*-1

print "Antipodal Longitude: " + str(AntiLongitude)


A result...the Antipodal point of London

Combining the above code with the XY to Line tool allows me to construct a geodesic line joining the two points thus producing this result!



A free map calculating the antipodal point of any location: