As detailed in the Gemara (Yoma 16a with Rashi there), the Sanctuary entrance was elevated 22 amos above the floor of the Temple Mount, while the eastern Temple Mount gate (like all Temple gates) was only 20 amos high. Therefore, if someone looked straight through the gate near the very top of the opening they would still be 2 amos short of seeing the Sanctuary entrance. It was therefore necessary to look over the gate. See diagram.
|Line of sight when looking up through the Temple Mount gate at an angle.|
If the red line looks almost identical to the previous diagram, that is because the angle of elevation is so slight — less than half of a degree —that it is nearly parallel to the previous one. To be exact, the line of sight only has to rise 2 amos over a horizontal distance of 342 amos, which is an angle of 0.34˚. [342 amos is the distance from the Temple Mount wall to the Sanctuary entrance.]
If so, why does the Gemara not consider this possibility? To answer this question I would like to contrast the Red Cow procedure with another Temple practice which was also done in front of the Sanctuary entrance. When describing the slaughter of offerings the Torah states (Leviticus 3:8): וְשָׁחַט אֹתוֹ לִפְנֵי אֹהֶל מוֹעֵד, and he shall slaughter it in front of the Sanctuary [entrance]. Now the Gemara (Zevachim 55a-b) derives that these offerings may be slaughtered anywhere in the Courtyard which is in view of the entrance, not just in the 10 amos in front of the entrance. The truth is that even if the offering was slaughtered in those 10 amos it still would not be directly in front of the Sanctuary because — in the Temple — the entrance was elevated 6 amos above the floor. It emerges that for the slaughter of offerings, being in view of the entrance is good enough, even if you are off to one side and looking up at it on an angle.
When it comes to the sprinkling of the blood of the Red Cow the Torah states (Numbers 19:4): וְהִזָּה אֶל נֹכַח פְּנֵי אֹהֶל מוֹעֵד, and he shall sprinkle [the blood] opposite the front of the Sanctuary [entrance]. The Torah adds an important word here — נֹכַח, opposite — to emphasize that this procedure must be done directly opposite the 10x20-amah area which makes up the Sanctuary entrance. It may not be done off to the side and it may not be done either higher or lower than that area, even though these locations may still afford a view of the entrance.
The word נֹכַח carries this same connotation as used elsewhere in the Torah. For example, when describing the placement of the Menorah the verse states (Exodus 26:35) that it must be located נֹכַח, opposite, the Shulchan, and the Gemara (top of Yoma 33b) derives from here that these two utensils must be directly across from one another with nothing between them.
Rashi also lends support to this stricter requirement for the Red Cow procedure. In Zevachim 55b he is discussing the slaughter of offerings in the Courtyard and he explains that there is a difference between having to slaughter them "in front of" [לפני] the Sanctuary entrance versus "opposite" [כנגד] the entrance. When the Torah uses the former expression it permits the slaughter in any spot which is in view of the entrance, while the latter expression would only allow it in the space directly opposite the area of the entrance.
|Rashi to Zevachim 55b s.v. וחד|
Since the Torah uses a more limiting expression regarding the Red Cow [i.e., נֹכַח, opposite] it would emerge according to Rashi's distinction that the sprinkling of the blood may only be done in the area directly opposite the entrance.
Thus, the Gemara did not consider the possibility of the Kohen looking up through the Temple Mount gate at an angle since he would not be directly opposite the 10x20-amah area of the Sanctuary entrance, but below it. He must therefore be standing at an elevation which is high enough to allow him to look over the gate toward the entrance.
Practically speaking, only a relatively small portion of the Sanctuary entrance is visible through the Temple gateways from the Mount of Olives. Assuming that the Temple Mount wall was low enough (that is, it just barely covered the top of the gate), the Kohen would be able to see no more than the lower 4 amos of the entrance. [The upper portion of the entrance is blocked by the Women's Courtyard wall.] Therefore, when standing on the Mount of Olives his eyeballs would have to be located between 22 and 26 amos above the Temple Mount floor. See diagram.
|Defining the requirement of נֹכַח, opposite.|
I am curious to see how the real-life elevations of the Mount of Olives compare with my conclusions here, also taking into account the range of possibilities for the placement of the Temple upon the Temple Mount as discussed in the last post.