The point of greatest eclipse (totality phase during 1 min 54 sec) lies just at the edge of the Antarctic continent, just north of the Filchner-Ronne Ice Shelf. This eclipse is the next in Saros after the historic total on 2003 November 23 near Novolazarevskaya, one of the Russian research stations in Antarctica.
Antarctica and the entire Southern Ocean are renowned for wild weather and the most important factor in witnessing a solar eclipse is of course clear skies. So I’ll propose three options: first for about 38,000€, an aircraft will fly you straight from Punta Arenas in southern Chile, or Ushuaia in Argentina, to Union Glacier in Antarctica from where the eclipse can be observed; second an exclusive eclipse flight (10,000 to 28,000€) with marvelous sightseeing and third an eclipse cruise on an expedition yacht (21,000 to 78,000€).
You can use this solar eclipse calculator to compute the local circumstances of the eclipse, and the solar eclipse timer notifies the beginning of the various events. A time exposure calculator is there to help you choose your camera settings.
Click on thumbnails for a larger version
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There are three possibilities to witness this eclipse: icecap-borne, seaborne or airborne. Weather-wise the airborne option is the only one that can nearly guarantee you to see it, moreover with a totality duration at its highest. The icecap "ground" option has reasonably good weather prospects, while the seaborne one is questionable although thanks to some mobility your chances become acceptable. Budget-wise the least expensive option is the airborne one, followed by the cruise one and last the "ground" one. In the end your final choice will necessarily be a compromise based on your expectations and preferences, each option having its advantages and drawbacks.

Union Glacier camp in Antarctica
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