Gemara

(Mishnah 6): Ezras Yisrael was 135 Amos long and 11 Amos wide. Ezras Kohanim was the same.

The entire Azarah (including Ezras Yisrael and Ezras Kohanim) was 187 Amos long and 135 Amos wide.

Shevu'os 17a - Question (Rava): If Reuven (became Tamei and) suspended himself in the air above the Azarah, what is the law?

Does the Shi'ur of time for bowing (to be liable) apply only to one who could bow?

Rishonim

Rambam (Hilchos Beis ha'Bechirah 6:14): The Kedushah that Shlomo gave to the Beis ha'Mikdash and Yerushalayim is permanent. It was due to the Shechinah, and the Shechinah is never Batel.

Rebuttal (Ra'avad): The Mishnah (Ma'aser Sheni 1:5) refutes this. One who goes there nowadays does not get Kares.

Kesef Mishneh: Shevuos 16a concluded that all agree that the Kedushah was permanent. Even in the Hava Amina, the Halachah follows R. Yehoshua (who says that it was permanent) against R. Eliezer

Rambam (Hilchos Bi'as Makdish 3:19): One who enters the Heichal through roofs is exempt from Kares. It says "v'El ha'Mikdash Lo Savo" - one is liable only for entering normally. He is exempt form Kares, but he is lashed mid'Rabanan, whether he entered [in a Migdal, i.e. a tower or cabinet] through roofs, or through doorways.

Tosfos (Shevu'os 17a DH Talah): In some texts, the question was whether or not the air above the Azarah has Kedushas ha'Azarah. This is difficult, for a Tamei who stuck his hand into the Azarah is liable (Zevachim 32a)! This implies that the air was Mekudeshes. Also, if not, blood and limbs would become Pasul when brought to the Mizbe'ach, for they left (Kedushas) ha'Azarah! Rather, the Gemara asked the Shi'ur for bowing applies to one who cannot bow.

R. Baruch (cited in Kaftor v'Ferach 6): Nowadays, we are Tamei Mes. One who enters the place of the Mikdash is Chayav Kares.. However, R. Yechiel of Paris intended to come to Yerushalayim in 5017 (1256 or 1257 CE) and offer Korbanos nowadays. I did not ask him about Tum'ah; then I realized that this is not a problem, for Korbanos Tzibur override Tum'ah Mes. A Mikveh is Metaher from other Tum'os. The Kedushah of the wall around the city is permanent, to permit eating Ma'aser Sheni inside if the Mizbe'ach is built.

Radvaz (2:691): People considered it permitted to enter roofs built around the Beis ha'Mikdash that stick out into the Mikdash through ledges. I say that not all ledges are the same. One must estimate well! It is known that (the rock called) Even Shesiyah is under the dome they call Alsachra. The Mishnah (Yoma 53b) says that there was a stone from the days of early Nevi'im. It was three fingers above the ground, and the Aron rested on it. They say that it is three (in Teshuvah 639, the Radvaz wrote 'two') stories above the floor of the dome. The Nochrim say that early kings wanted to know what is there, so they lowered people there, and they died. It seems that they heard that the Aron was hidden there, therefore they tried to excavate it. The Aron was in the Kodesh ha'Kodoshim, to the west.

Radvaz (ibid.): One who alights upper stories west (of the dome), or goes through the western opening door (of the dome building) must gauge that that he is more than 11 Amos west of the dome, for there were 11 Amos from the western wall of the Heichal to the western wall of the Azarah. Also the thickness of the walls was made Kodesh. I gauged that the closest opening to the dome is the small one of cotton sellers, so one must be careful about Aliyos on that opening. Some Chachamim did not want to go to the cotton market; this is an excessive stringency, for it is more than 41 Amos from the dome. Perhaps this is because it is a little north. For Aliyos on the north, one must measure 187 Amos from east to west. Aliyos built along here are along the length of the Azarah. There is no Isur for Aliyos further than this. The width of the Azarah is 135 Amos. We can see that the southern wall is in its initial place. Its rocks are big, which shows that it is very old. However, the end of the wall is past the 187 Amos. It extends to Har ha'Bayis. Even today, it is domes on top of domes. The wall itself is the southern wall of the Azarah. Aliyos more than 135 Amos north of the southern wall are not over the Azarah; one may enter them. Alternatively, what is within 40 Amos east of the dome is Kodesh, and what is past 40 Amos is Chulin. The calculation is not exact, for the Heichal was narrow in back and wide in front; one must be stringent for the width of 187 Amos within 40 Amos north of the dome. The eastern wall that stands nowadays is the eastern wall of Har ha'Bayis, for past it is Har ha'Zeisim. One may enter all the houses and Aliyos on the east, for there are 313 Amos from it to the Azarah, and a Tamei Mes may enter Har ha'Bayis.

Note: Teshuvos v'Hanhagos (5:164) points out that one who had an emission may not enter Har ha'Bayis without Tevilah. Nowadays men are not careful about Chatzitzos when immersing, e.g. to shampoo.

Radvaz (ibid.): The Gemara (Shevu'os 17a) asked about one who suspended himself above the air of the Azarah and did not resolve this. This pertains to an Isur Torah according to the Rambam, that the Kedushah endures, so we are stringent. Tosfos is sure that the air is Kodesh. Even though one who enters the Heichal through roofs is exempt, because it is not the normal way to enter, it is forbidden, and he is lashed mid'Rabanan. Also the Rambam says so. Since Tosfos agrees that only the roofs and Aliyos of the Heichal are Kodesh, why aren't all the other roofs and Aliyos permitted? This rule applies to only to what was built at the time of the Mikdash, but perhaps what is built today was built over the Azarah or chambers around the Azarah. The custom is to be lenient because people want to see the entire Bayis, and we never heard anyone protest. The Ra'avad holds that nowadays there is no Kares. There is an argument about this law, and perhaps the Aliyos are not over the Kodesh, and even if they are, perhaps the air over the Azarah is not Kodesh. Some explain that this was the question about being suspended in the Azarah, which was not resolved. And even if the air of the Azarah is like the Azarah, perhaps these Aliyos are over chambers that were not Kodesh. Since there are so many Sefekos, people are lenient due to their great desire to see the Kodesh. We cannot permit due to the reasoning that this is not the way of entering, for this would not permit delaying there.

Radvaz (2:648): If one was forced to enter between the Kosel ha'Ma'aravi and the Kodesh ha'Kodoshim, and the time for Tefilah came, he should pray towards the Kodesh ha'Kodoshim, with his back to the Kosel. Even though Chazal said that the Shechinah never left the Kosel ha'Ma'aravi, it is a separate Reshus, and the Kodesh ha'Kodoshim retained its Kedushah. Also, the Shechinah is everywhere. I cannot fathom that the Kosel retains its Kedushah nowadays in the hands of the Nochrim. Chazal said that the Shechinah never left the Kosel ha'Ma'aravi, i.e. the Shechinah is in the west of the world.

Yabi'a Omer (5 YD 26:7): This is unlike the apparent meaning. The Yalkut Shimoni (Shir ha'Shirim 2) and Zohar say that the Shechinah is in back of the wall of the Beis ha'Mikdash. Hash-m swore that it will never be destroyed. If the Kodesh ha'Kodoshim kept its Kedushah, why can't we say that also the Kosel kept its Kedushah?

Poskim

Magen Avraham (OC 561:2): One who enters the Mikdash nowadays is Chayav Kares. Also the Agudah says so.

Mishnah Berurah (5): See what I wrote in Likutei Halachos (Zevachim p. 66b, and Zevach Todah, that many Rishonim agree with the Rambam. The Ra'avad is a lone opinion.)

Yabi'a Omer (8,9): Malki ba'Kadosh brings the episode in which R. Moshe Montefiori and his Rebbi entered the place of the Mikdash. When R. Yosef Moshe (the son of the Chavas Da'as) found out, he excommunicated them. Rabanan of Yerushalayim said that the Niduy is invalid, for they were Shogeg; they relied on the Ra'avad. In my youth, I heard that Nochrim carried them in. They thought that just like the roof and attics were not Mekudash, likewise one may enter in a box. David was Mekadesh the floor down to the depths, but not the air. If so, one may fly over in a helicopter. However, Tosfos proved that the air has Kedushah. The Ramban, Rashba and Ran agreed, and showed that even the text Tosfos that rejected can agree.

Yabi'a Omer (11): There is an Isur Kares even for flying above the Mikdash in a plane or helicopter. It is a Mitzvah to publicize this.