IANAL, but the short answer is basically judges can order whatever they want in theory, although in practice there are significant limitations (more on that below). Another big point to mention is that the United States uses a common law system, meaning that large parts of the law have never been defined by a statute (i.e. a law passed by a legislature). The major limitations:

1. The judicial selection process almost always picks people who are not going to go off the deep end and start issuing crazy orders, but generally stick close to what is authorized by statutory, regulatory, or case law.

2. Orders from lower courts can be appealed and overturned by appellate courts.

3. There are mechanisms in place to impeach judges.

Within the law, there are various factors that limit orders judge are supposed to issue, and I suspect a relevant one here is jurisdiction. Divorce is a matter for state courts, and if the divorce is occurring in a state where Facebook doesn't have enough of a presence to bring it under the judge's jurisdiction, ordering the parties to swap passwords may be a lot simpler (from a legal perspective) compared to whatever they would have to do to bring another action in Federal court or in a state court with jurisdiction over Facebook to compel Facebook to turn over the data. I'm not sure why the court didn't just ask Facebook to turn over the relevant data. Of course it's also possible they did and Facebook refused, or the court knows that Facebook has refused similar requests (as distinguished from orders) in the past.

This is a very good point. The Federal Reserve currently holds about $1.6 trillion in U.S. Treasury securities. So it would be possible to sell those securities (which pulls the money that others use to buy them out of the economy) so that the the coin hack had no net effect on the money supply until the Federal government spent more than $1.6 trillion.

I would argue that we need the additional fiscal stimulus given the weakness in the economy, and that stimulus would not be inflationary. For the people worried about inflation, though, having the Federal Reserve sell Treasury securities would delay any theoretically possible inflationary impact of the coin hack for about a year.

I am the OP. As several people have posted, this approach is exactly equivalent to printing money. The reason it needs to be platinum coins rather than paper bills is that there is a law that limits the total value of paper bills that can be printed, but there appears to be no limit on the value of platinum coins that can be minted.

Of course, if you were to print a large enough amount of money, it would lead to inflation (or asset price bubbles, which actually seem to occur first in the current economy). The mechanism by which excess money supply causes inflation is by increasing demand to the point where bottlenecks appear in the economy. For example, people want cars, have money to buy them, but there aren't enough factories right now to supply demand - so the price of the limited pool of available cars is bid up. If labor markets are tight, employers looking for people to work to fill the demand created by the extra money will need to bid up wages to attract workers.

The key point is that all those mechanisms only work if an economy, or significant parts of it, are operating near peak capacity. This is the complete opposite of the situation we are in right now. Industrial capacity utilization was at 76.7% in June, several percentage points below the 1972-2010 average (80.4%) an well below the 85.1% peak in the 1990's. Unemployment is also high compared to historical averages.

In the current environment, it is vastly more likely that increasing the money supply will improve economic conditions without triggering inflation. Even at its pre-financial crisis recent peak (when unemployment was much lower than it is now), annual inflation (CPI-U, Dec 2006 to Dec 2007) was only 4.1%. Also keep in mind that the entire amount created ($5 trillion in my example in the OP) will not hit the economy at once. Initially it will be in an account at the Federal Reserve, and only as the government spends the money would it reach the economy.

I am the OP. The reason this approach counts as an 'escape hatch' is that it appears that the executive branch already has the authority to carry it out (in 31 USC 5112(k) ). To stop it, Congress would need to pass a law. To do that in the face of a presidential veto would require 2/3 supermajorities in both the House and Senate. As long as Obama can get 34 of the 51 Democrats in the Senate (or 53 Democrats plus independents who caucus with the Democrats) to back this approach, there is nothing that the House can do to stop it.

Almost all of the US Treasury debt owned by China (and in general) is in the form of book-entry securities. This means there is no physical document for the treasury bill, note or bond. It exists as an entry in the database of a broker or the US Treasury. The court could simply order ownership of an appropriate value of those securities to be transferred from the Chinese government to the successful plaintiff.

Take 3: Foreign Sovereign Immunities Act

The posting system mangled the link. I'll try again: Foreign Sovereign Immunities Act.

The Foreign Sovereign Immunities Act is the US federal law that regulates suits in US courts (federal or state) against foreign governments. It lists exceptions to the general rule that foreign states are immune to suit because of sovereign immunity. The exception that this suit is probably based on is the one that says a foreign state can be sued when it is engaged in “commercial activity”.

Assuming the plaintiff wins the suit, damages would be collected by seizing assets of the foreign state under US jurisdiction. Since US Treasury bonds owned by China are essentially promises by the US Treasury to pay a certain amount of money when the bond comes due, transferring ownership of those bonds to the plaintiff would seem to be a way of collecting damages. Of course, that might have diplomatic consequences.

IANAL either.

Because gravity is different from all other forces, and in some sense, is not a force at all. Mass (or more precisely, all components of the stress-energy tensor) changes the geometry of space-time so that the distances between objects, free of any forces acting on them, are different than what they would be in a flat Minkowski space-time.

An analogy is the difference in behavior between objects moving along lines that are initially parallel on a flat 2D plane and the 2D surface of a 3D sphere. On a plane, the objects will never meet. On a sphere, objects that start on adjacent lines of longitude at the equator (assuming the sphere is marked with latitude and longitude lines like the Earth), and move (initially in parallel) North will eventually meet at the North Pole. There is no force that pushes the objects together: they move together because of the geometry of the surface that they travel in.