We still don't know what the PM will do should the ruling goes against him? The judges asked this question yesterday. Will they try again, asks legal expert Joshua Rozenberg?

BBC Radio 5 Live

Human rights lawyer Dinah Rose says one of the central questions in the case is: "Where do you draw the line between politics and law?"

She adds: "It's a problem that's particularly acute in the UK because we don't have a written constitution.

"What we have are principles of public law which have been developed over centuries about the ways in which courts will keep a check on the government.

"And it's well established that courts will keep a check on governments if they abuse powers they have been given under an act of Parliament.

"But this is rather different. Proroguing Parliament is not done under statute, it's an exercise of a royal prerogative."

Ms Rose tells the Emma Barnett Show: "And while there are some cases that say there are some circumstances where courts can control that, we're right on the cutting edge here of the constitutional limits of what courts can do".

Legal representatives from both sides are now in the courtroom. We await the 11 judges.

Image source, UK Supreme Court

Image source, Getty Images

Today's proceedings are due to get under way at 10:30 BST, with Sir James Eadie QC - responding for the government on the Miller case - providing submissions until around 13:00.

Clive Coleman
BBC legal correspondent

We've got a system in this country where we have something called judicial review.

It's an incredibly democratic process whereby you, me or anyone can go before a court and ask it whether a decision of a public authority - could be a minister, or a prime minister - is unlawful or not.

That process of judicial review has really grown exponentially since the early 1980s.

And in many people's view it's dragged judges into the area of political decision-making.

Eminent judges like Lord Sumption are very much of that view - that judges have been drawn far more into political decision-making than they should have done.

There's almost no area now of government policy that can't be judicially reviewed.

On the other hand, some people think this is a critical way of protecting against the abuse of government power.

It somewhat divides opinion, but if people want a different system we're going to have to change the law and change the constitution.

Barrister and legal commentator Jo Maugham, who was at the Supreme Court for yesterday's proceedings, says Gina Miller - who is leading one of the appeals, faced 'visceral hatred' outside court on day one.

He notes similar abuse was not directed at other (white) anti-Brexit campaigners such as Joanna Cherry, who is leading the Scottish case.

While most eyes are on London and the Supreme Court this week, political parties have been trying to make their voices heard.

The Liberal Democrats' party conference in Bournemouth concluded yesterday, with leader Jo Swinson saying she could not wait to "take on" Boris Johnson, Jeremy Corbyn and Nigel Farage in an election.

And she vowed a Lib Dem government would stop Brexit "on day one".

Labour, meanwhile, has vowed to "carry out whatever the people decide" in another referendum on Brexit.

The party leader said he would hold a fresh vote if he became PM.

Read more from Mr Corbyn here.

BBC News Channel

If Parliament was so worried about being prorogued, they could have acted to legislate against it.That was one of yesterday's arguments put forward by Lord Keen - the government lawyer trying to overturn the Scottish ruling that the suspension was unlawful.

"I can understand what he's saying," says Cambridge University law professor Alison Young.

"But you also have to put it in the context of the short amount of time that Parliament had after it came back after summer before we then had the period of prorogation.

"MPs were thinking about other issues, trying to get other pieces of legislation through."

Ms Young believes the argument today from Sir James Eadie - the government's lawyer - will be something like: "Really when we're talking about length [of prorogation], that's for politicians to decide, and not the courts."

Image source, Reuters

Mr Juncker continues his briefing on Britain's Brexit negotiations. He tells MEPs any alternative to the backstop - the insurance policy designed to avoid a hard border in Ireland - must safeguard the EU's single market and protect all-Ireland economic co-operation, without any physical infrastructure on the border.

He stresses, however, that he is open to alternatives to the backstop.

"I said to Mr Johnson that I have no emotional attachment to the backstop but I stand by the objectives it is intended to achieve.

"That is why I called on the PM to come forward with operational proposals in writing, practical steps that would allow us to achieve those objectives."

Read more from Mr Juncker here.

Image source, Reuters

Away from London, the EU's chief negotiator Michel Barnier says the UK and EU "should not pretend to be negotiating" a Brexit deal if there are no new proposals on the table.

Mr Barnier said the UK telling the EU what it does not like about the current agreement was "not enough".

At the European Parliament in Luxembourg, EU Commission chief Jean-Claude Juncker tells MEPs that while lunch with Boris Johnson on Monday had been "friendly and constructive", there had been no progress on the Northern Irish backstop, and the the UK's demand that it be removed from the current agreement.

Read more about the latest Brexit developments here.

BBC News Channel

Barrister and legal commentator Jeremy Brier says today is an "absolutely critical day, particularly for the government".

"They had a difficult time yesterday," Mr Brier says. "Lord Pannick was on his feet yesterday, for Gina Miller, really putting that case against the government as to why prorogation was unlawful.

"Today, it's the government's chance - through Sir James Eadie QC - to really put their case."

He says he expects the government lawyer will start with the issue of justiciability, which means looking at where the court can get involved, or where it draws the line and says it's not a legal matter, but a matter of politics.

"That's going to be the real crux of James Eadie's submissions this morning," he adds.

Speaking to the BBC earlier this week, Boris Johnson - when asked what he would do if the Supreme Court ruled against him - said he wanted to "wait and see" what the judges had to say.

BBC home affairs editor Mark Easton explains what happened yesterday:

Boxes of legal documents are wheeled into the Supreme Court ahead of the 10:30 BST hearing.

Yesterday, there were some problems with paperwork, with lots of discussion about "tabs" and "bundles" as some of the judges struggled to find the correct documents.

Image source, PA Media

As on day one, you can watch a live stream of the Supreme Court proceedings on this page from 10:30 BST.

You will also be able to follow coverage live on the BBC News channel, which you can watch via this link.

Image source, The Times

Many of the morning papers dedicate their front pages to the Supreme Court hearing into the prorogation of Parliament.

"Judges warned to stay neutral" is the headline in the the Times,, externalwhich highlights Boris Johnson's written submission to the hearing, in which he warned the court to steer clear of the political arena.

Inside the paper, Daniel Finklestein reflects on the significance of the hearings: "They may mark the moment Britain stopped being a political democracy restrained by law, and became a legal democracy tempered by politics."

The "i", external focuses on the case made by lawyers who are challenging the suspension - "PM abused his power to 'silence' MPs," reads its headline.

Continue reading our paper review here.

Clive Coleman
BBC legal correspondent

Good question. We've got another day of hearings tomorrow. We'll have interventions from various people, including former Tory prime minister Sir John Major.

It's possible they could even give a ruling at the end of tomorrow. I think that's extremely unlikely. It could be Friday, it could be Monday.

What I think they're very likely to do - because there's so much in this case and there are 11 justices - is to give a ruling, I would suggest, on probably Friday or Monday. That would be a bare ruling as to who has won and who has lost.

And then we will get detailed reasons to follow.

By around 08:00 BST on Wednesday morning, at least 40 people were already queuing outside the Supreme Court in Parliament Square to watch the second day.

Yesterday, the courtroom was packed, and there were crowds of protesters and media outside.

During the morning, the Supreme Court's live stream was accessed 4.4 million times - with 2.8 million stream requests between 12:00 and 13:00.

Typically, the live streaming service is accessed about 20,000 times a month.

On Wednesday morning, two men at the front of the queue in central London said they had been waiting since 6:30 in the morning.

There is also a strong police presence outside the court building.