Our Gemara on Amud Beis discusses the status of an animal purchased from a gentile while it was still young, and presumably not yet matured enough to become a mother. In that case, the animal that appears to be first born will go to the Kohen, as we do not assume the animal had an earlier child when it was not physically mature. According to Rabbi Yishmael, the cutoff date is the third year. That is to say, if a cow or donkey gives birth within its third year, we assume it was its first child, as it is not capable of getting pregnant while still in its second year of life.

There is an interesting Midrash Rabbah (Bamidbar 19:7) regarding Moshe’s encounter with Hashem, whom he found learning the sugya of Parah Adumah (the Red Heifer purification ritual, Bamidbar 19:2) and Eglah Arufah (the ritual regarding the unknown murder victim, Devarim 21:1):

“When Moses ascended on High, he heard the voice of the Holy One, blessed be He, who was sitting and engaging in the portion of the red heifer and saying the halachah in the name of the one who said it. Rabbi Eliezer says: A calf within its first year, a heifer within its second year. He said before Him: ‘Master of the universe, may it be Your will that he be from my descendants.’”

We must wonder: of all the different teachings that Moshe could have learned, why did Hashem expose him to this one, and why was it so important to him that he prayed one of his descendants be the author? Chasam Sofer (Ki Sisa) explains that we have a tradition that the Parah Adumah is an atonement for the sin of the golden calf, much as a mother (cow) has to clean up after its young child (the Golden Calf). Yet the Torah has a deeper meaning in dimensions that go beyond the physical behavior or historical realities. (I say this is similar to the idea expressed by Ramban, Bereishis 9:12, that the rainbow existed before the flood. It just became a symbol utilized for the covenant after the flood.) 

This is why Moshe was enamored with Rabbi Eliezer’s opinion that the Parah Adumah is in its second year. Since we have seen that a cow in its second year cannot yet be a mother, this refutes the idea that the mitzvah of Parah Adumah is solely for the purpose of atonement for the sin of the golden calf. Otherwise, it would need to be a cow that is three years old, that can actually become a mother. Therefore, Moshe took solace that the sin was not inevitable, and there would be other dimensions to fulfill this mitzvah. This was especially meaningful to him, because he had not sinned with the Golden Calf, so he may have been concerned that this would somehow reduce his ability to participate in that mitzvah.

What has not been addressed yet in this discussion is, what does the Eglah Arufah have to do with this sequence? I’ll suggest that the core of the Eglah Arufah ritual is the elders stating they are not responsible for the sin of murder that was committed under their watch. Of course, whenever there is a statement, it implies that there is some trend in the opposite direction that needs to be countered. Meaning to say, in some way, the elders are responsible, or at least fear that they’ll be held responsible. Here too, Moshe is troubled about his potential liability and complicity in the sin of the Golden Calf, much as the elders of the city are responsible for a murder that occurs because they did not sufficiently elevate the spiritual level of its inhabitants. This is why that Midrash includes a discussion of the Eglah Arufah: to hint that Moshe was troubled, and then ultimately relieved in knowing that it was not destiny or fate. The sin did not have to happen. The fact that it did, was unfortunate, but not necessarily his liability.