Let's say you'd put a whooping big rocket engine on the surface of the moon, and slow down its orbital velocity.
Not to a complete stop, mind you. Just a bit slower than it was going before (a couple of m/s?).
Intuitively (i.e. without doing the maths, or even knowing the maths involved), I'd say it would start spiralling towards earth, eventually crashing into it.
I was wondering about this due to this YT video about Kerbal Space Program that talks about how much it would take to stop a moon. I figured that you don't need that much delta-V, that a much smaller amount of slow-down would already (eventually) de-orbit a moon already.
Is that correct?