We like to say that Galileo was right that more massive objects don’t fall any faster than lighter ones, at least if we abstract away from friction.
But it occurred to me that there is a sense in which this is false. Suppose I drop an object from a meter above the moon, and measure the time until impact. If the object is more massive, the time to impact is lower. Why? Because there are two relevant gravitational accelerations that affect the time of impact: the moon pulls the object down, but simultaneously additionally the object pulls the moon up. The impact time is affected by both accelerations, and the more massive the object, the greater the upward acceleration of the moon, even though the object's acceleration is unaffected by its mass.
Of course, if we are dropping a one kilogram ball, the gravitational acceleration it induces on the moon is about 1/1023 of the gravitational acceleration the moon induces on it. It’s negligible. But it’s still not zero. :-) A heavier object of the same size will impact sooner.
If all this is unclear, think about the extreme case where we are “dropping” a black hole on the moon.
Thank you for this, this just reassures me that I'm not crazy. I have maintained this for years and have been somewhat embarrassed about it because so many scientists are so adamant when they repeat the truism that Galileo was right that more massive objects accelerate no faster towards the earth than do less massive ones. I kept thinking I must be missing something obvious (at least, to them, though not at all to me) and theoretically fundamental. I have never been able to figure out what I was missing, and I have always remained suspicious of what sounded to me like an over-simplification, a technical error in service of a story which runs something like: empirical science has emerged victorious yet again in its struggle against a rationalist philosophical conviction/intuition. However, I have been prevented from arguing the point out of embarrassement - I thought surely, surely I must be missing something, and if I argue this point I would just be revealing my ignorance - and so I just kept searching for the something I was missing, the missing piece which would finally help me understand how Galileo was literally and technically correct. I just could not, no matter how hard I tried, find what I was evidently missing.
ReplyDeleteApparently, I was missing not a thing.
Sorry, sorry - the object doesn't accelerate any faster, I should be more careful. What I mean iis that the two objects in question reach each other sooner the more massive they are.
ReplyDeleteDr Pruss have you watched The Principle?
ReplyDelete