Depending on how long you can fly your chopper on a single supply of fuel -- because refueling would be necessary -- you'd travel from 38.9° N 77.0° W to 64.8° S 64.1° W to reach the US Palmer Station from Washington DC, the closest US station in Antarctica to you, geographically.
Depending on your calculations, you can factor in your speed per hour and calculate the distance and speed to determine how long you would be in the air.
Best practices indicate that this is probably not a good idea.
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