Where does “moonrise” come from?

I can't write this etymology with confidence. The chain appears corrupted or incorrectly ordered—it mixes unrelated roots (Latin ridere "to laugh," sapere "to taste/know," and riso "rice") that don't plausibly lead to "moonrise." Could you verify: Is this the correct chain for "moonrise"? A legitimate etymology should show how component parts (moon + rise) developed, with each step linguistically sound.

moonrise (English): The time of day or night when the moon begins to...

Definitions

  1. The time of day or night when the moon begins to...

Ancestry of “moonrise”, step by step

moonrise traces back through two separate lines of ancestry.

via English Moon

StepLanguageWordMeaning
1EnglishMoonThe Earth's moon; the sole natural satellite of the Earth, represented in astronomy and astrology by ☾
2Middle EnglishMoneA lamentation; a sorrowful moan or expression
3Old Englishmānbad, criminal, false; shameful act; crime;...
4Sanskritमहादेवthe "great God"
5Sanskritमहाcombining form of महत्; buffalo; great, large,...
6Proto-Indo-Aryanmaźʰā́
7Proto-Indo-Iranianmaȷ́ʰā́big, great
8Proto-Indo-Europeanméǵh₂sbig, great

via English rise

StepLanguageWordMeaning
1EnglishriseTo move, or appear to move, physically upwards...
2Middle Englishrisento rise
3Old Englishrīsanto rise; to seize, carry off
4Proto-West Germanic*rīsanto scale; move vertically (either up or down)
5Proto-Germanicrīsanąto scale; move vertically; to rise
6Proto-Indo-Europeanh₁rey-to arise, arise; to rise, arise; to rise; arise
Every word from Proto-Indo-European méǵh₂sEvery word from Proto-Indo-Iranian maȷ́ʰā́Every word from Proto-Indo-Aryan maźʰā́