Are state of the art artillery pieces included, ICBMs, or the private ownership of nuclear weapons? If not, where is the limit in size and firepower drawn?
The entirety of the second amendment is:
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
That's it. Pretty vague, eh?
It does not define "well regulated Militia". It does not define "security of a free State". It does not define "Arms" or even what "shall not be infringed" encompasses.
As such, it's an amendment that has been argued back and forth for a long time and likely will continue to be argued back and forth for some time to come. What the amendment does and does not pertain to is decided in court cases, for the most part.
There are some regulations out there codified in law. For example, The National Firearms Act does put some restrictions on certain weapons and accessories such as machine guns and silencers.
So, to answer the question: no, there are no real restrictions regarding the size or type of firearm directly under the second amendment. There are restrictions that were created afterwards and codified into various laws.
The 2nd Amendment is subject to government regulations.
This is known as the National Firearms Act
First enacted in 1934 as a reaction to the St Valentine's Day Massacre in Chicago, it required registration with the federal government, and placed a heavy (for the time) transfer tax on what was categorized as NFA firearms: fully automatic, shotguns and rifles with barrels less than 18", firearms that had a bore larger than .5", explosive devices (grenades) and projectiles (mortar and cannon shells), and silencers. Registration was not a right: one can be denied the license for a NFA firearm. The specific target for the NFA of 1934 was the model 1928 Thompson, which had become the weapon of choice for gangsters.
The second part came in 1968, as a reaction to the shootings of Martin Luther King and Robert Kennedy. It banned the sale of firearms through the mail and across state lines, except for licensed dealers, who are required to keep records of all transactions - the Federal Firearms License. Also stopped registration of existing NFA firearms - if you hadn't registered them by then, you couldn't register them.
In 1986, sale of new NFA firearms was banned for the general public - only military and law enforcement. Existing NFA firearms were grandfathered in, and can still be purchased... with the price being substantially higher.
It is quite possible (and highly illegal) to modify existing semi-automatic firearms into fully automatic. The working theory right now is that this is what the Las Vegas shooter did, although there are a number of peculiarities about that incident - the alleged shooter doesn't fit the profile of the usual lone psycho shooter.
Rockets, being flying machines, are subject to FAA regulations. There are hobbyists who operate model rockets capable of reaching over 30,000 feet (carrying almost no payload), but their operation is strictly regulated due to the possibility of hitting an aircraft. One can build their own rocket, but testing it will draw government attention... and ire. Today, getting the materials for rocket fuel in sufficient quantity to build an ICBM will also draw a lot of attention, as those materials can also be used to build large scale explosives.
Nuclear materials in general are subject to other government regulations. It is illegal for a US citizen to possess fissionable material, under NRC regulations, as well as extremely difficult. Fissionable U-235 is very rare, and plutonium can only be made in a functioning reactor.
One ambitious young man tried to build his own reactor, using isotopes salvaged from smoke detectors, camping lanterns, and old clocks. He didn't succeed, but he did create high levels of radiation, enough to have his mother's home declared a superfund site for cleanup.
To answer your question in short:
- Explosives (Grenades, bombs, det charges)
- Chemical weapons (viruses, nerve gas, caustic gas)
- Flamethrowers of any significant power
- Anything you could not reasonably consider a personal armament (Field artillery, tank cannons, helicopter gunship missile pods)
Legal, with restrictions (see also NFA Items): These are items that are regulated by the National Firearms Act, and require paperwork + licenses in order to own, but are generally obtainable by private persons.
- Short barreled shotguns and rifles
- Fully automatic weapons (very rare and expensive)
- Exotic, hard to categorize weapons like ballistic knives (can be registered as an AOW or "Any other Weapon")
- "Large bore" firearms with a bore over 0.5 inches in diameter
Federally no problem, but many states regulate:
- Semi automatic rifles and shotguns
- Belt fed and crank fired weapons
- Weapons with detachable magazines (i.e. you can reload them with a new magazine)
Generally OK even in hostile states:
- Bolt action rifles
- Pump action shotguns
Surprisingly lightly regulated everywhere:
- Black powder weapons and antique muskets
Now for the long answer:
So, US constitutional law is a complex beast, because there is a lot of effort spent trying to "read the intent" of the authors. This can lead to some interesting results, such as Roe v Wade's implied right to privacy.
There is split opinion over how much to weight the original intent of the founders when writing legislation, and even beyond that, considerable disagreement, even at the level of the Supreme Court, over what the Bill of Rights actually protects.
The "Majority" opinion is that rights in the Bill of Rights are individual, actively protected rights. As in, no state government, nor the federal government, may make laws that are in abrogation of the terms of those amendments. Some justices have historically believed that the Bill of Rights merely ties the hands of the federal government, and not the state government. You can read more on that topic here. As in, if the state of Kentucky wanted to make a law banning free speech, they are free to do so, but Congress may not pass a similar law.
I'm not nearly a studied enough scholar to tell you what the Second Amendment actually means, but I can give you a run-down on how it is commonly interpreted. Other people have given better blow-by-blows leading up to the Hughes Amendment and the NFA, but firearms were not very tightly regulated until rather recently. Generally the distinction was made between "firearms" and things that really weren't "personal arms", like cannons, artillery, rocket launchers and so on. Also "explosives" are tightly regulated under separate laws, so anything that uses explosives is part of a whole different discussion.
But as we approach the present, you had much more effort spent on categorizing and banning weapons by features, usually driven by high-profile criminal incidents. The "high water mark" of regulation was under Bill Clinton, with the Clinton Assault Weapons Ban, that introduced unprecedented restrictions on the sale of weapons.
It set a bunch of frankly arbitrary categories that separated "weapons" from "assault weapons", like bayonet lugs, muzzle brakes, pistol grips on rifles, detachable magazines and so on. The rhetoric being that "assault weapons" were only useful for soldiers in war, and not suitable for a civilian to own. The ATF has a term called "no sporting purpose" that they use to regulate certain weapons. In the US, a weapon with a muzzle bore of greater than 0.5 inches in diameter is considered a "destructive device" (that is, more a cannon than a firearm).
However, you will not that a common 12 gauge shotgun has a bore diameter closer to ~0.60 inches. Shotguns are exempt from this regulation because they are "common sporting weapons", and attempting to ban them would have upset millions more people than regulating semi-automatic rifles. However, many "combat shotguns" like the "Street Sweeper" were determined by the ATF to have "no sporting purpose" and subsequently banned by being re-labeled as "destructive devices".
I bring up "common use", because the biggest piece of law in US Firearms history came in 2008 with DC vs. Heller in a highly controversial 5-4 decision, the Justices found that the Second Amendment was an individual right, and that individuals had the right to own "weapons in common use".
The whole "common use" thing, is more or less their attempt to interpret how the framers of the constitution talked about guns and gun regulation in their various writing and correspondence, as well as to let the "social bellwether" regulate the issue, much like censorship and obscenity laws often have "reasonable person" or "community standard" components to them.
Of course, this brings up a whole other nest of hornets; what is common use? The gun rights folks would tell you the AR-15 is a "common weapon", and in a numerical sense, they are absolutely correct, as they are extremely popular, common, and frequently used by sportsmen and hunters. However, many people are unsatisfied with this, feeling that semi-automatic rifles place too much power in the hands of people.
Now, this is all interesting history, but what does this come down to in the end? Basically, the law is pretty sure Americans have the right to buy guns, but they're not sure how much power the state has to regulate the purchase of them, and the ATF is more or less winging it when it comes to defining "acceptable" vs "unacceptable" weapons.
When you regulate a constitutional right, a common standard is "undue burden", as in, does this law place a substantive barrier between the citizen and the exercise of that right. For example, a 3 cent tax on book shops doesn't stop anyone from distributing literature, but a 100000$ tax on printer ink would place an unacceptable barrier in front of anyone who tried to spread their political views in writing. Similarly, it seems to be fair game to make people get a background check before buying a gun, but some states like New York put into place months of waiting and hundreds of dollars in fees.
All of this is separate from issues about what is moral, and what is right, but New York, California, and other places with stringent gun laws are frequently and repeatedly sued over them, California is currently a hotbed of lawsuits over the raft of gun control bills Jerry Brown signed recently. Interestingly enough, because in the US you have the right to appeal to a higher court if you don't like the decision of a lower court, many times states will find very popular gun control bills struck down by a Federal court who tells them that in the pure legal sense, their gun control laws are unconstitutional.
California, Illinois, and New York have all lost significant lawsuits related to gun regulation, but the payouts are usually not huge enough to cause a stir.
Gun rights as a political lobby is unusual. Most lobbying groups in congress exert power through having a lot of money, like oil and agriculture. Gun groups exert power on politicians by having huge mailing lists of "single-issue voters" who will vote against anyone who wants to pass gun control. The "NRA-ILA", the NRA's lobbying arm, actually doesn't have very much money. But they are the boogeyman of politics, because in any state with a significant gun culture, they can make or break politicians with a single mailing campaign. They give politicians a "letter grade" form A+ to F, . The Supreme Court can be considered somewhat "pro gun" at this moment due to its makeup (Roberts, Thomas, Gorsuch, Alito, Kennedy), something likely to become more pronounced with Trump having the opportunity to appoint two Justices.
EIDT: Whew, that was long, someone feel free to edit me down into coherence, that was a long ramble.
Because of the nature of the Second Amendment and its relative ambiguity, the line where something becomes permissible to prohibit is not clear. This was a longstanding question until the case of Heller v. DC (PDF). In the majority opinion written by Justice Scalia, the Court came to a partial conclusion that the right to bear arms is not unlimited, and the Second Amendment applies only to those arms "in common use." Starting on page 52:
We may as well consider at this point (for we will have to consider eventually) what types of weapons Miller permits. Read in isolation, Miller’s phrase "part of ordinary military equipment" could mean that only those weapons useful in warfare are protected. That would be a startling reading of the opinion, since it would mean that the National Firearms Act’s restrictions on machineguns (not challenged in Miller) might be unconstitutional, machineguns being useful in warfare in 1939. We think that Miller’s "ordinary military equipment" language must be read in tandem with what comes after: "[O]rdinarily when called for [militia] service [able-bodied] men were expected to appear bearing arms supplied by themselves and of the kind in common use at the time." The traditional militia was formed from a pool of men bringing arms "in common use at the time" for lawful purposes like self-defense. "In the colonial and revolutionary war era, [small-arms] weapons used by militiamen and weapons used in defense of person and home were one and the same." Indeed, that is precisely the way in which the Second Amendment’s operative clause furthers the purpose announced in its preface. We therefore read Miller to say only that the Second Amendment does not protect those weapons not typically possessed by law-abiding citizens for lawful purposes, such as short-barreled shotguns. That accords with the historical understanding of the scope of the right.
The Court went on to further narrow this, and to essentially lock in at current tech levels what kind of arms can be carried. From page 55:
We also recognize another important limitation on the right to keep and carry arms. Miller said, as we have explained, that the sorts of weapons protected were those "in common use at the time." We think that limitation is fairly supported by the historical tradition of prohibiting the carrying of "dangerous and unusual weapons."
It may be objected that if weapons that are most useful in military service—M-16 rifles and the like—may be banned, then the Second Amendment right is completely detached from the prefatory clause. But as we have said, the conception of the militia at the time of the Second Amendment’s ratification was the body of all citizens capable of military service, who would bring the sorts of lawful weapons that they possessed at home to militia duty. It may well be true today that a militia, to be as effective as militias in the 18th century, would require sophisticated arms that are highly unusual in society at large. Indeed, it may be true that no amount of small arms could be useful against modern-day bombers and tanks. But the fact that modern developments have limited the degree of fit between the prefatory clause and the protected right cannot change our interpretation of the right.
A legislative body could expand the concept of arms in "common use" by permitting (or at least not prohibiting) civilian ownership, and if it reached a point where the courts found it to be "common," then it would fall under Second Amendment protection.