The court has just finished today's sitting.
This morning, the Supreme Court's 11 judges heard arguments from the government's representative, Sir James Eadie QC.
He said prorogation was "a well-established constitutional function exercised by the executive" and decisions about it were "squarely… within that political or high policy area".
Sir James argued Parliament had previously passed laws addressing aspects of prorogation, but there was no law relevant to this particular case.
Therefore, he said, the courts could not intervene in the decision.
This afternoon we heard from Aidan O'Neill QC, who was defending a Scottish court’s previous ruling that the prorogation was “unlawful”.
He argued Boris Johnson’s decision to prorogue Parliament was "an improper purpose" to stop MPs holding the government to account over Brexit.
He said one of the advantages of the ruling from Edinburgh was it had "distance" from the “Westminster bubble”, which lends "perspective".
On Thursday, we will hear submissions from those who have been given permission to intervene in the appeals, including former prime minister Sir John Major.
Join us tomorrow from 10:30 BST.