The major Halachic authorities from the Rambam in Yad Chazaka to the Chofetz Chaim in Mishna Brurah are unanimous in prohibiting Jews from entering the Makom Kodesh on the Temple Mount. While it is true that Halachically one could enter a specific area that was not part of the Temple, there is no clear agreement on the definition of this area -- but even to enter here requires certain purification rites. Some say the Rambam ascended, contrary to his ruling in Mishneh Torah, but others say he means he prayed adjoining the Temple Mount, as we do today at the Kotel. Muslims claim their mosque is built on the Holy of Holies, but others disagree and we are not sure of the exact location because the Romans ploughed over the Mount destroying too much for us to be sure. The measurements of the present Temple Mount are larger than those given in the Mishna. From an Halachic point of view there is today an issur kares on entering the holy area in our present state of impurity.
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from the article: Share the Temple Mount