Michael Byers holds the Canada Research Chair in Global Politics and International Law at the University of British Columbia.

From 34,000 feet, I scan an iceberg-strewn ocean for two red and white specks of Canada, sailing up the east coast of Greenland.

My vantage point is an Air Canada Boeing 777 travelling from London to Vancouver. While commercial airliners regularly fly this route, the presence of Canadian Coast Guard icebreakers in the area below is highly unusual.

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Earlier this month, the Canadian government announced that the CCGS Louis S. St. Laurent and CCGS Terry Fox were heading north to conduct scientific surveys in support of a claim to the North Pole.

Prime Minister Stephen Harper, who is visiting the Arctic this week, knows that the North Pole is deeply rooted in Canada's national mythology.

But the North Pole is not the idyllic location envisaged by many Canadians. It's located more than 700 kilometres from land, in 4,000 metres of water covered with drifting sea ice. Powerful winds, frigid temperatures and seasonal darkness add to the misery.

Like all waters more than 200 nautical miles (370 kilometres) from shore, the ocean at the North Pole is international. The only sovereign rights that could possible exist concern seabed resources.

Yet according to Mr. Harper, claiming the North Pole is central to defending Canada's Arctic sovereignty.

In reality, sovereignty over Canada's vast Arctic territory is uncontested, with the exception of tiny Hans Island and a segment of the Beaufort Sea north of the Yukon. The dispute over the Northwest Passage concerns the extent of Canada's regulatory powers, not title over the waterway.

Although Canada has rights over extensive areas of seabed elsewhere in the Arctic Ocean, it has no basis for a claim at the North Pole. This is because international law uses the "equidistance" principle to delimit maritime boundaries. According to this principle, boundaries between adjacent coastal states are drawn along a line, every point of which is an equal distance from the respective shores.

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In 2012, Canada and Denmark used the equidistance principle to delimit a boundary 200 nautical miles into the Lincoln Sea, north of Canada's Ellesmere Island and Denmark's Greenland.

Although the boundary does not extend beyond 200 nautical miles, the principle of equidistance will serve as the basis for an eventual agreement separating rights beyond this point.

Like it or not, the North Pole falls on the Danish side of the equidistance line – it will never be Canadian.

A separate issue concerns the extent of Canada's rights along the Lomonosov Ridge. This underwater mountain range runs from Ellesmere Island and Greenland toward Russia's New Siberian Islands.

The Lomonosov Ridge passes near but not over the North Pole, which remains off to the Danish side of the Arctic Ocean.

According to international law, Canada, Denmark, and Russia may assert rights over this submarine structure if they are able to scientifically demonstrate that the formation is a "natural prolongation" of their land mass.

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Canadian and Danish scientists believe the Lomonosov Ridge is a prolongation of both Ellesmere Island and Greenland, while Russian scientists believe the Lomonosov Ridge is a prolongation of Asia.

Scientists on both sides may well be right, since North America and Asia were once a single continent. Consequently, Canada, Denmark, and Russia could all have legitimate claims over the Lomonosov Ridge.

All three countries are preparing submissions to the Commission on the Limits of the Continental Shelf, an international body of scientists that issues recommendations that help legitimize well-supported claims.

The commission does not adjudicate overlapping claims. These must be resolved through negotiation or recourse to an international court – which would, again, base its decision on the equidistance principle. As between Russia on the one side, and Canada and Denmark on the other, the Lomonosov Ridge would be divided by a boundary that is an equal distance from Ellesmere Island/Greenland and Russia.

Canada has already mapped enough of Lomonosov Ridge to cover this scenario where the commission finds the ridge is a prolongation of Ellesmere Island, Greenland, and Asia.

In the unlikely event that the commission finds the Lomonosov Ridge to be a natural prolongation of Ellesmere Island and Greenland, but not of Asia, Canada could at that point collect more data and update its submission. There is no need for the current mapping mission, and even this scenario would not give Canada the North Pole.

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These legal realities would have been explained to Mr. Harper before he sent Canadian icebreakers to map the North Pole.

In other words, the Prime Minister knows that Canada's claim will fail. But he also knows that the failure will emerge only after he leaves office.

In the meantime, the North Pole presents him with an opportunity to rehabilitate his image as a champion of Canada's Arctic sovereignty.

After eight years of inaction, promises of new ice-strengthened patrol ships, a powerful icebreaker and an Arctic naval port have worn thin. But is there any need to dwell on this now? Look, Canadian icebreakers are headed to the North Pole!

Michael Byers is the author of International Law and the Arctic, which won the 2013 Donner Prize.