Jewish custom prohibits formal mourning on the Sabbath.  Biblically, however, grief over the death of a loved one cannot be banned on the Sabbath.  The Sabbath is to be a day of joy and delight (Isaiah 58:13), but this precept falls in the heirarchy of law.  It is not meant to be a burden if your house burns on the Sabbath, or if some grievious disaster happens.  You are allowed to be sorrowful and sad.  I do agree with the halakhah, though, that you are not allowed to publically grieve in the presence of others who do not share the grief.  Therefore formal grief, or the hiring of professional mourners, or calling in the community on the Sabbath for comfort is prohibited.  The shock of loss is usually so great, in any case, that the mourner cannot prevent feeling sad; but making everyone else feel sad  can be prevented. 
     All of the disciples were still in shock on the third day.  They had every human right to feel sorrowful and sad.  Just as the need to defend oneself in war superceeds the Sabbath, so also the need to deal with the psychological and physical trauma of loss superceeds the precept to be joyful on the Sabbath.   This is the Netzarim Halakhah on mourning of the Sabbath,  and is in accord with Yayshua's reformation of many of the legalistic strictures of the Rabbinic Halakhah. 
    For those who cannot accept this explanation of Miryam's grief, and the grief of the disciples, I will point out that  Peter fell to the point of denying Yayshua, and that all the disciples fled.  Would you be sad if your Rabbi, who did many miracles, and who you thought would usher in the age to come, had been executed?  Are you superman or superwoman?  Are you superhuman?   A little violation of such a halakhah might be in order.
   And if you are so foolish as to not see the point yet, then did not Yahweh know ahead of time that this day would turn out to be the most joyful day in their life, and indeed in all of creation, save the day of the second coming?  So that Sabbath was called a delight to them, and did become a delight.  And if you absolutely need an excuse for the woman to go to the tomb, then why not have Yahweh predestine them to unwittingly go, knowing that it will turn their sorrow into joy.  That would be much preferable to rejecting the plain and clear texts that say the Resurrection was on the first of the Sabbaths. 
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