How can we be sure that both of the BCE destroyed Jewish Temples were destroyed on exactly the 9th of Av?

Hi, thank you for your thoughtful question!

This is a fascinating topic in Jewish history, but it's beyond the scope of what Hebcal.com covers — we focus on providing Jewish calendar dates, holiday times, and Torah readings rather than historical analysis.

Here are some great places to dig deeper:

• Wikipedia's "Tisha B'Av" article has a good overview: https://en.wikipedia.org/wiki/Tisha_B%27Av

• TheTorah.com has an excellent scholarly article called "Tisha B'Av: On What Day Were the Jerusalem Temples Destroyed?" that directly addresses your question: https://www.thetorah.com/article/tisha-b-av-on-what-day-were-the-jerusalem-temples-destroyed

• The Talmud itself (Ta'anit 29a) discusses this — you can find it on Sefaria.org

Hope that helps point you in the right direction!