Visiting Temple Mount

Answer: Know that not all lofts are the same and not all directions are the same. One needs a proper measurement to ascertain which are permitted and which are forbidden. It is clear that under the Dome is the Foundation Stone (“Even Shetiyah”) without a doubt—which they call Al-Sakhrah.
And if you ask: The Mishna states: “There was a stone there from the days of the prophets, called Shetiyah; it was three finger-breadths above the ground, and the Ark was placed upon it.” Yet recently we asked them and they said that it is three human-lengths above the floor of the Dome. Also, we see from outside that they ascend many steps up to the Dome. I have already written in a responsum (§639) that the floor of the Temple has been excavated several times in order to expose the foundations, and so it is [currently] much lower than it was. Consider: the Mishna states in several places that the Temple Mount was higher than Jerusalem, but now the opposite is the case...I also heard that past kings excavated there to find the foundation of that stone, and they did not find it.

Nevertheless, there is no doubt that this stone under the Dome is the Even Shetiyah, upon which was the Ark, in the Holy of Holies, toward the west side. Therefore, one who ascends into the lofts along the west side, or one who enters to peer through the opening on the west side, must measure that there are more than eleven cubits between himself and the Dome [17-20 ft.], for that was the distance from the western wall of the Courtyard (Azarah) to the wall of the Sanctuary, including the thickness of the wall, for the walls were themselves sanctified. I have measured that there is no opening closer to the Dome than the small opening to the left of the Bab al-Qattanin (Cotton Merchants’ Gate). Therefore, one must be careful regarding the lofts above that opening. I have already heard about some sages who did not wish to enter the market al-Qattanin (Cotton Merchants’ Market), but this is an excessive stringency, because I measured that from there to the Dome is more than eleven cubits. Perhaps their reasoning is that it extends to the north a bit, as we will explain, with God’s help...
[A]nd if the lofts are on the north side, one must measure, moving eastward from the western wall, a length of 187 cubits [around 95 Meters]. All lofts built along that length are built above the length of the Courtyard that runs from east to west, and all lofts outside of that length, toward theeast or the west, are not included in the prohibition.
Regarding the width, you already know that the width of the Temple Courtyard from north to south is 135 cubits [~70 Meters]. It is apparent that the southern wall remains in its original position, as one standing at the southeast corner can see that from there southward lies the Valley of Jehoshaphat. The Courtyard did not extend further south than this point. [See FN1 below, for a picture of the stones the Radvaz is talking about regarding the platform walls; R' Ovadia Yosef seems to have misunderstood the Radvaz and his ruling]Additionally, the foundational stones, which are large, indicate ancient construction. Therefore, the southern end of the structure known as the Midrash [Mikdash?] Shelomo aligns with the southern end of the Courtyard, but it is beyond the 187 cubits from east to west, and it is part of the Temple Mount....and until this day it is built as vaults upon vaults [chambers].
Nevertheless, we have ascertained that this wall itself was the wall of the Temple Courtyard on its southern side. If so, we must measure: if the lofts facing this wall on the north side are more than 135 cubits distant from this wall they are not part of the Temple Courtyard. I measured, from the southern wall to the homes and lofts built along the north side, more than 135 cubits. They are not part of the sanctified area, and one may enter them. Another way is to imagine that a string is extended from the Dome eastward: all the houses and lofts within forty cubits of this string are within the sanctified area, and anything outside of that measurement is not sanctified. This calculation is not precise, because the Sanctuary was narrow behind and wide in front, as Scripture states: “O, Ariel, Ariel!” However, to avoid uncertainty, one must avoid a thread stretched forty cubits from the [northern platform ]wall of the Dome to the north along a length of 187 cubits (324.9ft) from west-to-east.
If the lofts are built on the east side, it has been explained that the present eastern wall is the eastern [outer] wall of the Temple Mount, since from that point on is the Mount of Olives. Further, the Gates of Mercy (Golden Gate) are in that wall, and the author of Kaftor Va-ferah (R. Eshtori Ha-farhi) wrote that these are the gates through which mourners and grooms entered. It is permissible to enter all of the houses and lofts on the east side, because from the eastern wall of the Temple Mount to the eastern wall of the Courtyard there are 313 cubits, and one who has been defiled by a corpse may enter the Temple Mount...
If there are lofts in the southern wall, within the length of 187 cubits from west-to-east, they are also part of the sanctified area. In general, I say that the houses or lofts along the north and east sides are not the subject of uncertainty, and one may enter them as long as they do not protrude a great deal into the Temple, in which case it is necessary to estimate. Similarly, those on the south and west sides require estimation.
Know that the Talmud queries: “What is the law if he suspended himself in the air above the Temple Courtyard?” It is resolved in a stalemate, and this is a Torah prohibition according to a rabbi who maintains that [the Temple’s] sanctity remains, so we are stringent, and it is forbidden. According to Tosafot, it is clear that the air of the Temple Courtyard has been sanctified, and even though a beraita in the chapter “Yedi’ot Ha-tum’ah” (Shevu’ot 17b) teaches: “A defiled person who enters the Temple Courtyard via roofs is exempt, as Scripture states: ‘He shall not come into the Temple’—the Torah only forbids the normal way of coming in,” though he is exempt from punishment, it is nevertheless forbidden, and he is given the beatings of the rebellious. Maimonides writes likewise in chapter 3 of the Laws of Entering the Temple: “Although he is exempt from extirpation, he is given the beatings of the rebellious, whether he entered the Temple through roofs or through openings in a chest, crate, or large closet. One may ask: Since the roofs and lofts were not sanctified, and Tosafot concede that no lofts were sanctified except for the loft above the Sanctuary, why would it not be permissible to enter into the all of the lofts even now? In answer, you should know that we only say that the roofs and lofts that were built when the Temple stood were not sanctified, but the roofs and lofts that are now built around the Temple may be built into the air of the Temple Courtyard or the air of the chambers that existed them. Thus, we have not eliminated uncertainty. Therefore, if it is clear according to the calculations I wrote that they are built in the sanctified zone, we will not pay attention to the height and suggest that perhaps they are built above the roofs of the chambers that were not sanctified, since the air of the Temple Courtyard is like the Temple Courtyard.
Nevertheless, I must offer a reason for the widespread practice whereby people go up into those lofts to observe the entire Temple, and we have neither seen nor heard anyone objecting. Consider that Ra’avad maintains that nowadays there is no punishment of extirpation for one who enters the Temple. Thus, the black-letter law is disputed, and it is uncertain whether these lofts are built in the sanctified area or not. And even if they are built in the sanctified area, perhaps the air of the Temple Courtyard was not sanctified, for there is an interpretation that Rava’s query about one who suspended himself in the air above the Temple Courtyard is really asking whether the air of the Temple Courtyard was sanctified or not according to the text of our books, and it is not resolved. And even if the air of the Temple Courtyard is like the Temple Courtyard, perhaps they are built above the air of the roofs of the chambers, which were not sanctified. Therefore, since there are all these uncertainties, they inclined this matter toward leniency out of their great desire to gaze upon the sacred place.
The rationale that the Torah forbade the normal way of coming in, and so via roofs does not constitute a Torah prohibition, is not a basis for leniency. It would be fine if one were to ascend and descent immediately, without delaying for the amount of time in which one can prostrate himself. However, if they are built in the sanctified area, granted that one is exempt from “He shall not come into the Temple,” however he is still liable as a defiled person who remained in the Temple.
I have this written to you the reason for the practice, but you shall be one of the scrupulous and will enter neither house nor loft unless it is very far from the Dome. I have also heard that there is an underground tunnel whose opening is on the west side and which runs under the Dome, and that there are Jews who enter there. This is forbidden, as we maintain that tunnels that open into the Temple Courtyard were sanctified, and who says that this is not in the category of tunnels that open into the Temple Courtyard? And even if we accept that this [tunnel] was made recently, the floor of the Temple Courtyard was sanctified all the way down to the abyss, as stated in Zevahim. I have now seen, and I have been told by people who know how to measure, that there is no opening and no loft whose distance from the Dome is not greater than the measurement I wrote. Therefore, one may come close to the openings and ascend to the lofts, especially given the concatenation of uncertainties that I wrote.FN1: https://www.ritmeyer.com/2020/10/05/new-discovery-on-the-temple-mount-in-jerusalem-gate-in-the-eastern-wall-of-the-dome-of-the-rock-plaza/