Re: How would a planet like Earth be affected by two moons when one is broken?

Dear Francesca,
You are correct in stating that the tidal effects of a moon depend on distance. In fact they depend on the cube of the distance -- so if Earth's Moon were moved twice as far away, its tidal effects would be 8 times smaller. See this MadSci answer for more details. Tidal effects also depend on mass, so if you have two moons, their relative effects will be propotional to M/R^3 where M is the moon mass and R^3 the cube of its distance from Earth.

I'm not sure what you mean by a "broken" moon. If you took the current Moon and smashed it with a hammer, then right after the smashing the tidal effects would be the same as before (same mass, same distance from the Earth). If the pieces didn't have too much energy imparted to them, then their own gravity would pull them back together and you'd be right back to the original situation. If the pieces were somehow spread out into a ring around the Earth, they would not cause any tidal effects as long as the ring was perfectly symmetrical.

Pauline