What Happens If the US Invades and Annexes Greenland?

What would happen if Donald Trump makes good on his threat to invade and annex Greenland unilaterally?
It's a preposterous question, but here we are. It's a throwback to pre-1939 Europe and Asia, and this time, we are the baddies.
The lead up to World War 2 included the following invasions and annexations (the list is not exhaustive):
⸻ Japanese invasion of Manchuria
⸻ Italian invasion of Ethiopia
⸻ German troops entering the demilitarized Rhineland
⸻ Annexation of Austria by Nazi Germany
⸻ German annexation of the 'Sudetenland' of Czechoslovakia
⸻ Polish invasion and annexation of the Polish-speaking portion of Czechoslovakia
⸻ German invasion and annexation of the rest of Czechoslovakia
⸻ German invasion of Poland (officially starting World War 2)
⸻ Soviet invasion of the Baltic States
⸻ Nazi Germany's invasion of all of Western Europe
⸻ Nazi Germany's invasion of the Soviet Union
⸻ Japan's invasion of the Philippines, Guam, and all of Southeast Asia
⸻ Japan's invasion of Burma
After World War 2, the American and Soviet-led world order eschewed concepts like 'irredentism' – the idea of annexing neighboring territories that contain ethnic and/or linguistic kin. All territorial disputes would have to be settled diplomatically or were simply 'frozen' by an American or Soviet enforced peace. When Iraq invade Kuwait in 1990, the US rallied an international coalition to expel Iraqi forces and uphold the principle of no border changes by force of arms. This principle is even enshrined in the UN Charter.
Yes, the US invaded Panama and Grenada in the 1980s, and Iraq and Afghanistan in the 2000s, but these were seen as operations to protect American interests. Panamanian dictator Manuel Noriega threatened the Panama Canal and US personnel in the Canal Zone. In Grenada, US forces swept in following a Cuban-led overthrow of the Grenadian government. The invasions of Iraq (wrongly) and Afghanistan was in response to the 9/11 terrorist attack that killed thousands in New York City, Pennsylvania, and Washington DC.
The Soviets invaded Afghanistan in 1979 in an effort to prevent the spread of Islamism into Soviet Central Asia following the Islamic Revolution in Iran.
None of these countries were annexed as part of the United States or the Soviet Union.
Aside from these police actions by the two Post-WW2 hegemons, the only other major invasions were in the divided states of Vietnam and Korea – and they both drew in American forces directly.
Apart from separatist conflicts, the principle of no border changes by force of arms has held sway for over 80 years. Russia's invasion of Ukraine is the first attempt by a major power to gobble up and annex a neighboring state in Europe since World War 2. But Russia isn't what it used to be, and the West rallied behind Ukraine with weapons and intelligence. Russia is now tied up and bogged down in Ukraine's eastern-most oblasts.
An American armed takeover and annexation of Greenland would directly threaten modern Europe in a way that Russia can't. Europe – both the European Union and non-EU states – would be beset on both sides by two nuclear armed great powers: Russia on its eastern front, and America on a suddenly live western front.
There is also the issue of Article 5 of the NATO alliance: an attack on one member of NATO is an attack on all members of NATO. Ukraine is not a member of NATO, and so NATO is under no obligation to defend it from Russia. Doing so would most probably lead to a nuclear war between Russia and NATO (including the United States).
Denmark is a member of NATO. If the US attacks and annexes Greenland, then the rest of NATO would be obligated to come to Denmark's defense. If people are actually killed in America's move on Greenland, then the unthinkable specter of a major war between former allies would become a looming reality. Maybe just as likely is the alliance simply unraveling and dissolving. I do not see how NATO survives – and I don't see how any of this enhances American security, which is the whole premise of America's infatuation with Greenland in the first place.
Lastly, if America unilaterally annexes Greenland by force of arms, we all know it doesn't stop there. Any number of places could be next: the Baja Californias, Cuba, the Maritime Provinces – certainly the list goes on.
I would hope that the President would be impeached and removed from office if he goes down that path. But hope isn't a guardrail, and Congress is in disarray.
This is what 'no guardrails' looks like.
Mark James is the Kirkus-starred author of geopolitical thrillers Friendship Games and The Compass Room. He has taught political and economic geography for over twenty years.