As I understand the US supreme court, they rule on the constitutionality of issues. Therefore it seems like the question of whether Trump's 2nd impeachment is constitutional is something they should be deciding. Why is the US Senate voting on it instead?
Because the US Supreme Court does not have the authority to rule on whether an impeachment is constitutional. That power lies solely with the US Senate, as part Article I, Section 3 of the US Constitution:
The Senate shall have the sole Power to try all Impeachments.
It is worth remembering that the President is not the only position that is subject to impeachment. Congress has, in the past, impeached and convicted members of the judiciary for various reasons. If the courts had the ability to rule on whether the impeachment of one of their members was constitutional, that would undermine one of the checks and balances in the constitution.
@divibisan but this question isn't about reviewing impeachments. It's about whether impeaching a former president is constitutional.
@divibisan I do not understand your question. OP asks why it is the Senate voting on the question as opposed to the Supreme Court.
The supreme court never rules on the constitutionality of anything unless that question has a bearing on a case that has been brought before it. Nobody has sued anyone on any question that turns on the constitutionality of this impeachment, so the supreme court can't rule on its constitutionality. Furthermore, nobody is likely to sue, because it is in principle not possible to bring a suit unless the person bringing the suit has been harmed.
Furthermore, if such a question did come before the court, it's likely that it would determine that only the house and senate can make this determination, as described in Joe C's answer.
Part of the senate's sole power to try impeachments is the power to dismiss an impeachment as moot because the impeached party has left office (or for any other reason) or as unconstitutional (for any reason). The idea that the supreme court is the only body that can decide something is unconstitutional is incorrect. The executive can decide all by itself not to enforce a law because it believes the law to be unconstitutional, and the senate can decide all by itself that an impeachment is unconstitutional. Similarly, if the senate finds that a bill passed by the house is unconstitutional, the senate can refrain from acting on the bill for that reason.
If the supreme court is supposed to rule on this, how come after Rand Paul objected, the Senate didn't refer the question to the supreme court?
The supreme court does not issue advisory rulings. The senate cannot refer the matter to the supreme court.
As I said in a comment and phoog's answer also emphasized, (in the US unlike in some European countries) there's no accepted method by which the legislative body can "pre-inquire" the (supreme) judiciary as to the constitutionality of anything the legislative does. In fact
The United States Supreme Court has determined that the case or controversy requirement found in Article Three of the United States Constitution prohibits United States federal courts from issuing advisory opinions.
Furthermore, there's precedent against any individual Senator (or Representative) suing on behalf of the whole body by arguing their (voting) rights are being diminished. This was reiterated (by a lower court) recently in the lawsuit that Rep. Gohmert brought against the election of Biden:
Because Congressman Gohmert is asserting an injury in his role as a Member of Congress rather than as an individual voter, Raines controls
That refers to (the SCOTUS decision in) Raines v. Byrd.
Thus, there's no way for Rand Paul or any Senator to pass this buck, at this stage, to SCOTUS, even if they wanted to. (If they tried somehow, it's very likely SCOTUS would decline, finding that Paul or any other Senator does not have standing.)
Also of some interest in this case/controversy, although the Chief of SCOTUS normally presides over presidential impeachments, John Roberts has declined to do so for this 2nd impeachment of Trump, because under Roberts' interpretation of the relevant clause
When the President of the United States is tried, the Chief Justice shall preside.
Since it's no longer the case that Trump is president, Roberts concluded he doesn't have to preside. But that's all (someone from) SCOTUS has decided on this matter and can decide until the case progresses through the Senate.
On the other hand, SCOTUS found/decided in Nixon (the judge, not the president) case that the Senate has very wide latitude as to what constitutes an impeachment trial. So it's not entirely clear what they might decide if this case does end up in their lap somehow (with a conviction of Trump).
But the political odds of the Senate voting to convict Trump don't look good, given the votes on that motion of Paul. One interesting bit is that the House managers (i.e. the "prosecution") is planning to argue that the impeachment is constitutional. There's nothing (in theory) that prevents some Senators from changing their mind on that either, except public embarrassment etc.
The House managers are also preparing to make the constitutional argument -- they're led by Rep. Jamie Raskin of Maryland, a former constitutional law professor -- that the Senate can convict a former President, just as it's held trials for other former officials in the past. It's a case that's taken on newfound importance in the wake of the Senate's vote Tuesday that Sen. Rand Paul forced as part of his argument that most of the Republicans think the trial is unconstitutional -- and there simply aren't 17 Republican votes needed for conviction.
Indeed, CNN argues that focusing on the constitutionality issue gives the GOP (Senators) cover from actually having to discuss the evidence against Trump:
Senate Republicans have coalesced in recent days around the argument that the trial is not constitutional, giving them a way to push back on House Democrats' impeachment without condoning Trump's conduct when rioters attacked the Capitol on January 6, breaching the very chamber where the impeachment trial will be held.
Questions of constitutionality are determined by the Supreme Court, not Congress or the President. Why, then, is the Senate voting on the question? Because Rand Paul wanted to make a point – that's all.
The Senate has no power to rule on whether the impeachment is constitutional. If it passed, Paul's motion would dismiss the case, but it would have no effect on the Constitutionality of the impeachment. What it does do is say that most Republicans don't want to have the trial and are likely going to vote for acquittal.
“If you voted that it was unconstitutional, how in the world would you ever vote to convict somebody for this?” Paul told reporters. “This vote indicates it’s over. The trial is all over.”
As for why the Supreme Court isn't ruling on this: the Supreme Court doesn't simply hand out declarations; there has to be a court case, filed by someone with standing, which gets appealed to them. Further, as addressed in several other questions, the Supreme Court ruled in Nixon vs US that they do not have power to review impeachment: the House has sole power to impeach and the Senate has sole power to convict.
Here's the simple answer. The Senate can vote on anything it wants, but that doesn't mean the vote settles the issue. The Senate has no authority to determine any constitutional question; only the federal courts can do that with the Supreme Court as the final authority. Rand made the motion solely for political reasons to telegraph the potential outcome of the actual trial. He knows the Senate has no authority to determine constitutional questions.
There's a simple answer that has so far been overlooked, which is that there really isn't any serious question about the Constitutionality of Trump's impeachment and trial. What you are seeing is a bunch of Republican Senators frantically trying to find some halfway plausible excuse not to hold a trial.
They are caught in a serious political bind. A majortity of Americans want to see Trump tried and convicted. (Per recent polls, e.g. https://www.politico.com/news/2021/01/25/majority-supports-trump-impeachment-462264 ) However, a majority of Republicans don't.
So if the trial is held and they vote to convict, they will likely face serious primary opposition from Trump supporters in the next election. But if they vote to acquit, they will win the primary but are very likely to lose in the general election.
Thus claiming that a trial can't be held is an obvious, and somewhat defensible, way of trying to weasel out of their bind.
If the senate wants to hold an impeachment trial, then the senate can hold an impeachment trial - end of story.
It would violate the principle of separation of powers for the supreme court to forbid the senate from holding certain proceedings. There's really no question - it's up to the senate to hold a trial or not.
Where the supreme court could potentially step in is after the fact. It might rule on the legal effect of whatever the senate did. However, a suit would need to be filed first and injury must be alleged. It's not clear to me what basis such a suit would have. Most likely such a suit would go nowhere because the point is moot.
However, if the senate votes to convict by a 2/3 majority and if congress also votes to forbid Trump from holding federal office again and if Trump runs for such an office anyway and if Trump wins that election, then there would be a reason for the supreme court to rule on the matter. But there are a lot of ifs there.