If Denmark refuses to sell Greenland to Trump, what options short of war and invasion does Trump have? Can he hit Denmark with economic sanctions? Or can he impose a sea and air blockade around Greenland? Or is there something else that Trump can do?

By Tudor Florescu
Trump threatening to take Greenland is not about Greenland. Such questions miss the point of Trump’s threats. It doesn’t really matter how he would go about “taking Greenland”.
What Trump is hoping to achieve with such threats is not to take Greenland or to make Canada the 51st state, but to disband NATO with the other NATO members’ own hands. Because Trump’s hands are tied by US Congress approval. He will not get a 2/3rds majority to pass any law repealing the application of the North-Atlantic treaty in US legislation.
So the only way he can do it is by antagonising the other NATO members so much – for example by making territorial threats – that eventually they will “get the message” and declare NATO dead themselves. Or they will have to act as if NATO does not really matter anymore, it’s just words on paper if the US ally behaves like an enemy.

Watershed — the melting Sermeq glacier, south of Nuuk, Greenland
You can’t sue the US for not meeting its obligations under this treaty, as the treaty itself does not stipulate any specific obligations in terms of defence contributions. How the NATO treaty gets enforced is up to its members and its power so far rested on the willingness of its members to act as one to maintain its credibility. The famous article 5 of NATO only specifies that a member “will assist the Party or Parties so attacked by taking […] such action as it deems necessary”.
If its members reach such a situation that the treaty is unenforced law, then it’s just as good as void.