It seems like you would create tidal waves, maybe even a tsunami, if you split the moon in half. So how can I explain the splitting of the moon in terms of scientific facts or history?
Since this is a science question, an impartial scientist would also have to consider possibilities which directly violate Islamic beliefs, e.g., the "moon split in two" hypothesis is false. Putting aside my religious beliefs momentarily...
The splitting of the moon in two cannot be explained physically. An actual splitting the moon in two through natural causes is physically impossible; it radically violates gravity in multiple ways (along with the conservation of energy). Moreover, collapsing back together would cause catastrophic and global extinction events on Earth, like how the dinosaurs were wiped out (K-T extinction), except to a much larger scale.
There some plausible psychological explanations. For example, peer pressure or even mass delusions (some examples are at Mass Delusions and Hysterias: Highlights from the Past Millennium).
There some plausible mythological explanations. It resembles other "God editing things in space" myths in other religions (see my answer to Do Muslims believe that the moon was split in two and put back again?), so the story may have developed over time.
An impartial scientist would not accept that the moon split in two; there are more plausible explanations, and the anecdotal evidence given in ahadith does not meet the need for extraordinary evidence required for such a extraordinary claim.
Two Islam-related points:
This hadith indicates that this event was known in advance to the Prophet:
Narrated 'Abdullah: The moon was split (into two pieces) while we were with the Prophet (ﷺ) in Mina. He said, "Be witnesses." Then a Piece of the moon went towards the mountain. -- Sahih al-Bukhari 3869 (sunnah.com), and also Sahih Muslim 2800 (sunnah.com)
The only way the Prophet could know this would happen is through Allah.
Muslims believe that Allah created the moon to begin with:
And it is He who created the night and the day and the sun and the moon; all [heavenly bodies] in an orbit are swimming. -- Qur'an 21:33
It seems hardly audacious to believe Allah could subsequently split it in two as a miracle.