At a NATO summit last June member countries, including Europeans and Canada, committed themselves to raising their defence spending to 5% of GDP by 2035. (In reality, the figure is 3.5%, with the remainder to be devoted to spending that is related to defence in a looser way.) European defence spending is already 50% higher in nominal terms than it was in 2022. Over the next five years it is expected to rise to €500bn-700bn ($588bn-823bn) a year, with about 30% of the total going to buy new weapons.

European countries also agreed last year to be the primary providers of military support for Ukraine. They now buy American weapons for Ukraine (which the Biden administration would have donated) under a NATO initiative known as the Prioritised Ukraine Requirements List (PURL). Europe has so far spent $5bn (€4.3bn) through PURL, and the aim is to continue at a rate of about $1bn a month for the rest of this year.

In the longer term, Europe’s plan has been to flatter and appease Mr Trump, hoping to keep NATO’s American-led architecture in place for as long as possible, while preparing for the possibility of its demise. The assumption has been that any American withdrawal from NATO would be gradual. Europe would have at least five years, perhaps a decade, in which to rearm and replicate uniquely American capabilities. Those include airborne and geospatial intelligence, surveillance and reconnaissance (ISR); command and control (C2); strategic airlift; ground-based, precision long-range attack; and hyperscale cloud-computing capacity.

The International Institute for Strategic Studies (IISS), a think-tank, puts the cost of replacing the American non-nuclear capabilities assigned to NATO at $226bn-344bn for new weapon systems platforms alone. But even if Europe’s rising defence budgets can bear that price, many capabilities will take years to replace, particularly if the heavy lifting must come from Europe’s own defence industry.

Even if the still-vague “framework” deal that Mr Trump said will be struck on Arctic security materialises, he has repeatedly displayed contempt for NATO allies, and has a habit of using threats to get his way. It is not hard to imagine him using Europe’s continued military dependency to exert pressure on it. He might, for example, suspend PURL, claiming that America itself needs the weapons Europeans want to buy.

The impact on Ukraine might not be decisive, but it would be serious. The country’s depleted missile defences are already unable to stop enough of the Russian drones and missiles that are pulverising its electric grid. Suspending deliveries of Patriot ground-based interceptors and of the AIM missiles used by Ukraine’s F-16 fighter jets could be devastating. Europe is also unable to supply Ukraine with GMLRS, a type of ground attack rocket.

But NATO’s dependence on America goes well beyond Ukraine. The Pentagon is yet to publish the latest revision of its plan for deploying forces around the world, known as Global Posture Review. Most analysts expect American troop levels in Europe will be cut, perhaps by about 30,000. But America could go further, announcing an accelerated withdrawal from NATO of critical American intelligence and command-and-control systems.

To subject Europe to even greater pressure, Mr Trump could target the operations of the American-made F-35 fighter jets that increasingly form the backbone of European air forces. Spare parts are largely held in America and like a smartphone the aircraft depends on continual software upgrades. A particular point of vulnerability, says Douglas Barrie, an airpower expert at the IISS, is the mission data file (MDF). The MDF is like an electronic battle manual that needs frequent updating, especially if the plane is flying in a combat environment.

Britain is uniquely exposed to Mr Trump’s mood swings. Its nuclear deterrent is based on submarine-launched Trident D5 missiles. Although they use a British-built warhead, these are leased from America and drawn from a shared storage pool in Kings Bay, Georgia. Britain’s nuclear forces are operationally independent, but experts such as Sir Lawrence Freedman, a British strategist, believe that without American co-operation, keeping them running would become difficult within two or three years.

Yet there are good reasons why even a vengeful Mr Trump might hesitate to cut Europe off. The Europeans have some leverage. “Without their European bases and commands, the US military would be diminished and limited in its future operations,” Sir Lawrence points out. “The generals and their friendly senators would strongly object to too drastic a withdrawal from NATO.”

Defanging European F-35s, even temporarily, would establish a disastrous precedent that would do lasting damage to American defence exports. Moreover, the supply chain of the F-35 is highly international. Britain’s BAE Systems produces both the aft fuselage of the plane and its electronic-warfare suite. And reneging on the 68-year-old nuclear agreement with Britain would be an assault on the world’s closest security and intelligence-sharing relationship.

In short, although Mr Trump could exploit Europeans’ dependence on American arms, it would have significant long-term costs. Even suspending PURL would deny American defence firms valuable sales. For their part, Europeans who have had enough of being bullied should think twice about giving up on NATO prematurely, not least because the benefits of an integrated command structure are real. At an emergency EU summit on January 22nd, Friedrich Merz, Germany’s chancellor, repeated his admonition earlier that day in Davos that “we should at least try to preserve NATO. I also have the impression that many Americans see it the same way as we do. You don’t just give up this transatlantic alliance easily.” However emotionally satisfying the idea of strategic autonomy, big gaps in defence capabilities cannot be overcome quickly or cheaply.