Imagine we observe the impact of a meteor on the moon. What would be the effect on the Earth of a gigatonne impact? How about a teratonne impact?
I’d imagine the main issue for the Earth would be whatever fragments of asteroid and moon would come raining down on the Earth. There’s no real way to know how big or small those might be- it would depend on the angle of impact, where the asteroid hit relative to the Earth, and what the asteroid was made of.
The effects could be anything from a terrific light show from a whole lot of medium-sized meteors, all the way to thousands of Winnebago-sized meteorites (or bigger!) hitting the earth in a short time frame.
If fragments were to hit Earth, they would also probably be taking out our satellites as well.
How much would those impacts affect the orbit of the Moon?
Well, something on the order of 100,000 meteor fragments currently reach low Earth atmosphere each year, without taking out many satellites.
Here’s an almost identical GQ thread from last month: Asteroid hits moon, debris hits Earth ? - Factual Questions - Straight Dope Message Board
Damn little. The Moon’s orbit is stable, now, after billions of years of such impacts.