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How come the travel time by air from South America to New Zealand, via the polar route, is SHORTER than the travel time going North first and then South again?

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How come the travel time by air from South America to New Zealand, via the polar route, is SHORTER than the travel time going North first and then South again?

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The airline pilots are guided by their GPS. Remember that satellites don’t exist. The replacement data given from pseudolites deliberately throwing distorting all the paths to make it the flights take different times. The curvature of these paths can add or subtract great distances without the overall turning being obvious to someone traveling it.

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