Can you even imagine what the night must have been like for Mary (Jesus mother) and the rest of Jesus close friends? The Sabbath day must have dragged on at a snails pace. Jesus' burial wasn't even completed and yet they couldn't do anything about it. I'm also certain that Jesus' apostles kept asking themselves over and over again through out this day what more could they have done to prevent the death of their master. In the end they surely came to the conclusion that this crucifixion wasn't an accident. For some reason that they couldn't understand Jesus allowed this to happen.
At one point during this sabbath day the Sanhedrin came to a frightening realization. Jesus had prophesied that on the third day he would be resurrected. They suddenly became afraid that the disciples of Jesus would take his body from the tomb and make the claim that he was risen from the dead. Once again they went complaining to Pilate who finally agreed to post a guard at the tomb to make certain no one took the body of Jesus.
While the Gospels don't make it clear, it is likely that Jesus friends gathered together somewhere in Jerusalem so as to be closer to the tomb on Sunday morning. No one wanted to be alone and they were anxious to get a good start and to have a proper fair well with their Master.