So it’s official: The formerly remote Arctic is now open to summer cruise ships, and you can go along if you’re willing to pay. And to hear scientists tell it, this is only the beginning.

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Cruises are one thing — but as Arctic sea ice melts and covers less of the ocean for less of the year, we should see all kinds of maritime incursions. Most significant, perhaps, is shipping — being able to use the Arctic could save a great deal of time and money for companies currently using the Panama and Suez canals for transit between Asia and the United States, or Asia and Europe.

In a new study in the journal Geophysical Research Letters, a team of researchers from the University of Reading in England used climate models to present a highly detailed analysis of how open the Arctic will become to shipping routes circa 2050 and 2100. And the answer is quite open indeed, depending of course on precisely how many greenhouse gases we actually emit in this century.

For the moment, Arctic shipping is growing but remains a bit of a niche activity, explained Nathanael Melia, the study’s lead author. “What we’ve seen over the last 10 years is that shipping companies have been doing some test voyages,” Melia said. (The work was co-authored with two other colleagues, Ed Hawkins and Keith Haines.)

Here’s an image Melia provided of the routes that are already being tested out so far, for the maximum low-ice month of September:

But the new study finds that for different greenhouse-gas emissions scenarios, and for different types of ships — some standard open water vessels, some ice-strengthened vessels — the opportunity for using swifter Arctic routes could greatly increase.

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The study in particular considered shipping to Yokohama, Japan, from either Rotterdam — a key European port — or New York, a key U.S. one. At present, the route from Europe would tend to use the Suez Canal and take about 30 days, and the route from New York would use the Panama Canal and take about 25.

But if the European-Asian trip instead used the Northern Sea Route, along the north coast of Russia, the trip could be cut to 18 days, and the distance would shrink from 11,580 nautical miles to 6,930 nautical miles. For the U.S.-Asian trip, meanwhile, using the Northwest Passage, through the Canadian archipelago, could take 21 days, rather than 25.

Clearly, then, there are savings to be gained here, if the ice permits it.

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And there’s little doubt that in the future, the Arctic will have even less sea ice than it does now, especially in the low-ice month of September. (Current Arctic sea ice extent is on pace for the second minimum extent on record.)

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But precisely how little ice will still depend on how much we heat the planet — whether we achieve something like a (very difficult) Paris policy of limiting warming to below 2 degrees Celsius above preindustrial levels, or whether we let it rip and continue high levels of emissions throughout the century.

Here’s the study’s result for what ships would be able to do by mid-century under different emissions scenarios, in the month of September. The thicker the lines below, the more frequently these routes would probably be used:

That’s the potential future, but the changes will come gradually at first, Melia said.

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“Initially, the Northwest Passage, say for the next 15 or so years, can be navigated every now and again, but it’s pretty unreliable, and it can end up taking longer,” he said, referring to September trips for open-water vessels, rather than ice-specialized ships. “So that route, at the moment, is a real specialist route.”

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“But around mid-century, that route becomes more reliable,” he continued.

Even in a low-emissions scenario, Melia said his study forecasts a “twofold increase in the prospect of these routes becoming open” by the middle of the century (again, in September and for standard open-water ships). But if we’re really going for broke with emissions, the expansion is even more dramatic, and by the middle of the century, we could even see non-ice-strengthened ships going straight over the pole.

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Indeed, one of the most striking things about the image above is that for ice-strengthened vessels (pink) in the Paris scenario, and for both open-water and ice-strengthened vessels in the high-emissions scenario (pink and blue), it could become possible to take this Earth-capping route that nobody is even attempting now. Dubbed the Transpolar Sea Route, it saves even more time on the trip between Europe and Asia.

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“By mid-century in a high-emissions world, it’s common,” said Melia of September transits of the Transpolar Sea Route.

Granted, we won’t move into this world immediately, nor will it be the case that shipping through the Arctic will be available year round — it will still have seasonal constraints. The dark polar night during winter will still be very cold, and the seas in winter will still be full of ice. So business models may have to adjust to shipping sometimes through the Arctic and sometimes through the established canals.