Agreed. I think what we want here instead is a minimum angular momentum. The only orbits that will crash into the earth will either be very low energy or very low angular momentum (or both). The former requirement can be approximately derived (assuming a circular orbit) from whozum's equation. For the latter case, I think you can derive the answer by considering:Tide said:The question is highly ambiguous. The minimum speed a moon could have without crashing into the Earth would be zero - if it were situated very far away (infinity!).
Too late, you just did!Tide said:Nice! But I will resist the temptation to mention the tidal force! :)
Well, that would be another reason to view the calculation as OOM, but I don't think it makes sense to include it explicitly. For one thing, the moon getting torn apart is not that same as it colliding with earth...and I don't think there's much hope of calculating a priori the orbits of the individual pieces that remain after it's broken. Presumably their average angular momentum per unit mass will be comparable to the original value, so they may well continue on their orbits if the moon's original angular momentum exceeds the above value.Tide said:You'll need to use a somewhat larger value for the moon's perigee if you include tidal forces. At those near distances the moon would be torn apart.
Quite true. But let's suppose he meant "at its current distance (apogee)".Tide said:The question is highly ambiguous. The minimum speed a moon could have without crashing into the Earth would be zero - if it were situated very far away (infinity!).
As do I.DaveC426913 said:Now, the minimum it needs to maintain its current orbit is the velocity it is doing now. But if, at apogee, we slowed it down a touch, it would change to an elliptical orbit. Say its perigee were to graze the atmo, (or more practically, the Roche Limit) what is the minimum velocity *at apogee* that it would need to be moving?
I have no idea whether this is what the OP was asking or not, but I think it's an intriguing question.