Interesting question and as you can see from earlier answers, your question is open to a degree of interpretation.
As Ralph has mentioned, the ice at the North Pole is mobile, it moves in response to oceanic and atmospheric conditions. Earlier this year for example, there was an unusual Arctic dipole anomaly that resulted in the negation of the normal Arctic Oscillation and instigated opposing cyclonic conditions that caused widespread dissipation of the ice-mass.
If you look at the plot for Arctic sea-ice extent you can see an obvious change in the slope of the graph occurring on 29th - 30th June, the time when the anomaly started.
Because of this mobility, even the multiyear ice isn’t that old. There are different electromagnetic properties between new and multiyear ice and this enables remote sensing satellites to track both types of ice. I don’t think anyone could say just how old the oldest piece of ice is but the figure of 10 years cited by Ralph seems a reasonable average age.
At the precise point of the North Pole* the oldest piece of ice has to be less than 38 months old as the North Pole itself was ice free in July 2007, it may have been ice free since then, I’m not sure.
If your question is approached in the way Bravozulu has, and you’re looking to establish when the Arctic was last free of ice then the answer is that it was more than 700,000 years ago. There is nothing in any scientific research, reconstruction or paleoclimatic evidence to suggest the Arctic has been completely ice free at any point in this time.
It was probably ice free some 4 million years ago, it may be more recent than that. It was almost certainly ice-free between 15 and 25 million years ago, the same time at which the Antarctic was comparatively ice free (last completely ice free about 50 mya).
* There isn’t actually a precise point for the magnetic north pole as it constantly moves. Each day it goes on an 80km journey, roughly in a loop but never quite returning to the same point it started from, hence there is a 40km drift each year and thus it’s necessary to allow for magnetic declination when taking accurate compass or cartographic readings.
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RE: YOUR ADDED DETAILS
Typically the flat parts of the Arctic ice are just a few feet thick with multiyear ice being up to about 9 feet. New ice is 1 to 3 feet thick but can often be just a few inches. Where the ice buckles and ridges form it can be up to about 15 feet thick.
Think of your stereotypical Eskimo drilling through the ice to catch some fish, that’s what the Arctic sea-ice is like.
Unlike Antarctica and Greenland, the Arctic ice isn’t land based. This means it forms as a thin frozen layer of sea-water and is eroded from both above and below.
It’s this vulnerability that allows for rapid melting of the ice in summer and refreezing in winter. In the past the maximum winter sea-ice extent was about 15 million km², in recent years this has receded to about 14 million km². During the summer months the ice rapidly melts, it used to retreat to about 11 million km² but in recent years it’s been down to about 6 million km².
At it’s annual peak, the Arctic ice expands to cover an area the same size as Antarctica and forms a frozen mass between Canada, Greenland and Russia.
We’re very close to the time of year when minimum sea-ice extent is reached (probably in about 11 days time) and at the moment there’s just under 5.2 million km² of ice in the Arctic. This recent decline in ice extent has opened up new shipping routes enabling vessels to sail around the north of Canada and the north of Russia.
Yesterday the MV Nordic Barents, a bulk carrier, set off to sail from Norway to China via the north of Russia, in doing so it will become the first commercial non Russian vessel to have made the passage.
The ice that is “thousands of feet thick” that you refer to, would have to be based on land. There are only two places where ice of this thickness exists (other than some mountain glaciers) and that’s Greenland and Antarctica.
In Greenland the ice cap has a maximum depth of 3,207 metres (10,519 feet) and the oldest ice here is about 100,000 years old. That’s not to say there was no ice 100,000 years ago. The Greenlandic ice is effectively one giant glacier, slowly creeping towards the surrounding seas and oceans.
As the snow falls it compresses under the effects of gravity and beneath overlying snow deposits, compressed enough it becomes ice and starts it’s long journey to the sea. There’s a constant cycle of ice calving into the sea and being replaced by new formations of ice.
The same thing happens in Antarctica but being much larger and generally at a lesser incline than Greenland, the ice takes a lot longer to flow to the sea. The oldest ice here is about 1 million years old, the oldest so far extracted from cores is 850,000 years old. The maximum thickness of Antarctic ice is 4,776 metres (15,670 feet).