APOD: Hammer Versus Feather on the Moon (2011 Nov 01)

[zloq]

I'm just talking about simple Newtonian physics - nothing else. No photon pressure or rotation. A big spherical, solid moon and a small, spherical solid mass dropped onto it. A heavier mass will hit the surface in less time than a lighter one.

This is a small effect, but it's worth noting here since people seem to be implying that the fall time is exactly the same for any object, regardless of its mass, as a fundamental consequence of the equivalence principle. That isn't true.

zloq

[Chris Peterson]

I'm just talking about simple Newtonian physics - nothing else. No photon pressure or rotation. A big spherical, solid moon and a small, spherical solid mass dropped onto it. A heavier mass will hit the surface in less time than a lighter one.

Yes, that is obvious, but has nothing to do with the equivalence principle (which posits a fixed gravitational field, not a fixed mass). The point made by Art is that the time difference resulting from the different total system masses is lost in the noise of things like photon pressure.

[zloq]

I don't see evidence in this thread that it is obvious - since the implication throughout is that the fall time is independent of mass - due to the equivalence principle. You both brought up esoteric compounding effects, which aren't needed as complications when simple Newtonian physics plays a role - and no one has mentioned the non-fixed aspect of the moon. For people who don't know what I'm referring to - the moon gets pulled up toward the mass as the mass is pulled toward the moon. For a larger mass, the moon is accelerated upward more rapidly and the two will make contact sooner. This isn't a violation of the equivalence principle - it just says that when an object falls, it's a dynamic two-body phenomenon. But it is a very tiny effect - so don't think that I am saying this is observable in the feather/hammer video.

The equivalence principle is being tested with more and more precision - apparently approaching 1 part in 1E16. It wouldn't take much mass or too high a height for the motion of the moon to affect the timing of the fall at that level of precision - so this isn't a purely theoretical issue.

I find that many topics like this, meant as teaching devices, can actually do more harm than good - especially when these details are glossed over. Here is a list of related confused ideas I hear from people, along with corrections:

1) A heavy mass falls faster because it weighs more. No - the equivalence principle says that the gravitational pull is stronger, but so is its resistance to acceleration.

2) Galileo dropped spheres of different masses off a tower and they landed at the same time to prove his point. No - due to air resistance the heavier mass would hit first. Galileo did do experiments with rolling balls on a ramp to demonstrate the concept, and there is speculation he fudged the results.

3) A heavy bicyclist or skier will go down a hill just as fast as a lighter one due to the equivalence principle (as Galileo proved with his tower and spheres - etc.) No - a heavier mass will probably have a higher terminal velocity if friction and air resistance don't change much.

4) A hammer will hit the surface of the moon in exactly the same time a feather will. No - the moon rises up to meet the hammer sooner.

zloq

[NoelC]

A hammer will hit the surface of the moon in exactly the same time a feather will. No - the moon rises up to meet the hammer sooner.

Are you speaking theoretically or practically? In other words, are you implying the moon will stretch an infinitessimal amount toward the heavier object? Or did you just not notice that the experiment was performed where both objects were dropped at the same time, so if the moon moved, it moved essentially toward the feather as well. And what magnitude is this motion we're talking about here? Femtometers? Irregularities in even the most perfect surface man could conceive, let alone the dusty moon beneath David Scott's feet, would overshadow this.

And though you point out how air affects experiments on Earth, you failed to mention the miniscule but non-zero amount of "air" acting on the feather in the pictured lunar experiment. The moon is considered "airless" but that doesn't mean there's a perfect vacuum. But again, the effect was neglgible.

Let's face it...

Within the measurement parameters available - i.e., masses of people viewing the experiment visually via a really sucky video signal - the two fell at the same rate.

This experiment and APOD re-publishing of same were clearly meant to make ignorant or young people think basic thoughts about the physics of the world around them.

Reminds me of the old joke where an engineer and a scientist were told that a prize at the other end of a small field could be theirs if only they followed a simple rule: Each ten seconds they can only travel half the remaining distance to the object. The scientist never starts, because he does some quick math and states, "it's easy to see I would never actually get there, so why try?". Meanwhile the engineer is over there, picking up the prize, exclaiming "close enough!"

-Noel

[Ann]

When I was a kid, everyone went "oooh" and "aaaah" over the fact that Galileo was correct, and that the hammer and the feather would fall with the same speed, even though that is so counterintuitive. We saw this demonstration as an amazing tribute to the glories of science, the same science that had sent people to the Moon.

Nowadays many people claim that the Moon landings were a string of hoaxes (although some of the proponents of the Moon landing hoax may not know that there was more than one Moon landing), and here people are fighting for their right to their common-sense conviction that the hammer must fall faster than the feather.

It's threads like these that make me feel that the Age of Enlightenment is coming to an end.

Ann

[geckzilla]

I don't see how being curious or discussing the specific details of the hammer and feather demonstration can be equivocated to the superstition of moon landing hoax believers. Admittedly the niggling details of the first few posts bothered me at first but followup posts by Chris and Art were actually kind of interesting.

[Ann]

I don't see how being curious or discussing the specific details of the hammer and feather demonstration can be equivocated to the superstition of moon landing hoax believers. Admittedly the niggling details of the first few posts bothered me at first but followup posts by Chris and Art were actually kind of interesting.

I certainly agree that the follow-up posts by Chris and Art were interesting. Many other posts were well-written and very much to the point, too.

My point is that today science is questioned in a way it wasn't when I was a kid. To be sure, science needs to be questioned. But today much of the "reasonable doubt" appears to be about asking for "equal time" for "common sense ideas", even when science directly disproves these ideas.

Ann

[Beyond]

It plum 'tickles' me to see everyone 'hammering' out their own conclusions about things.
As for the moon landing hoax.... I've seen the video, many years ago, that was used to protray the landing as a hoax. I figure it was made by someone back then that was very good at editing. Now-a-days it would be easier to do it by computer.
As for UFO's, I've seen one and a part of another. My sister has kind of seen one. She was too scared to try and look closer.

[Chris Peterson]

A hammer will hit the surface of the moon in exactly the same time a feather will. No - the moon rises up to meet the hammer sooner.

Are you speaking theoretically or practically? In other words, are you implying the moon will stretch an infinitessimal amount toward the heavier object? Or did you just not notice that the experiment was performed where both objects were dropped at the same time, so if the moon moved, it moved essentially toward the feather as well. And what magnitude is this motion we're talking about here? Femtometers?

All good questions.

It is obvious that as previously stated, where the objects are dropped separately, the more massive object will fall faster (although I think that saying the Moon "rises up to meet the hammer" is very sloppy language- especially from somebody lambasting education <g>). It is obvious because Newton's law of universal gravitation tells us the force between the two objects is proportional to the product of their masses, and Newton's second law tells us that if the force is greater, the acceleration will be greater (that Newton covered a lot of ground, didn't he?)

However, when the objects are dropped together, the situation is more complicated. Certainly, the moment of inertia of the system needs to be considered as well, along with the possibility that the difference in time is less than the Planck time, which would mean that by any reasonable definition, the bodies land at the same time.

I think that, outside of a physics classroom, it is generally more appropriate to say that the two objects of different masses will strike the surface at the same time. That's because the principle is based on two objects which experience the same gravitational acceleration, not on two objects which are attracted by a third.

[zloq]

I'm describing everything in the specific context of Newtonian physics and the equivalence principle - which is also the context of the demonstration. This thread, and the demonstration, imply in very absolute terms that a fundamental principle of nature will cause the falling of one body onto another to be independent of the mass of the smaller body, and that isn't true. If you are standing on the moon and you drop a heavy object - sure - the moon will rise up to meet it, just as the object will fall down to meet the moon. There is nothing wrong in my language. It's the symmetry of the interaction of the moon to the object and the object to the moon that is part of the Newtonian lesson here - and it is as fundamental as the conservation of momentum - and shouldn't be overlooked.

I was very careful to talk about dropping one object at a time because the two-body dynamics are easier to understand than more complicated 3-body dynamics of a feather, hammer and moon. If you replace the hammer with a small object that has the mass of the sun (no need to worry about black holes since this is Newtonian - it is just a small, very dense object) then the mass won't "fall" much at all and instead the moon will shoot straight up while the feather slams sideways into the object.

So- when people talk about how fundamental this stuff is and the mass doesn't matter at all - conservation of momentum is also fundamental in Newtonian physics, as are equal and opposite reaction forces. These two things were ignored in this thread but shouldn't be forgotten. Anyone who quietly pondered, either in this thread or in a classroom, "What if the hammer was REALLY heavy?", might think it doesn't matter due to "the equivalence principle." What never changes is the acceleration the hammer, of any mass, experiences toward the fixed center of mass of the moon/hammer - but both the moon and the hammer accelerate toward, and "fall", to that center of mass. How much the moon accelerates and moves before they make contact depends on the mass of the hammer.

If people think this stuff is so small that it gets lost in the noise somehow - humans often aim probes near to other planets so they can experience this symmetric dynamic, resulting in a tiny perturbation of the planet's position and orbit around the sun, that is transferred to the probe. That's another 3-body problem, but the point is - planets do respond to human-made objects in their gravitational fields.

zloq

[neufer]

I was very careful to talk about dropping one object at a time because the two-body dynamics are easier to understand than more complicated 3-body dynamics of a feather, hammer and moon. If you replace the hammer with a small object that has the mass of the sun (no need to worry about black holes since this is Newtonian - it is just a small, very dense object) then the mass won't "fall" much at all and instead the moon will shoot straight up while the feather slams sideways into the object.

We all understand your point, zloq.

Do you understand our points?

[zloq]

Actually no - I don't get how this is somehow confused with the moon landing hoax, for example. People are bringing in other complicating effects that would make it hard to measure this effect - but they are outside the Newtonian realm of the demo.

Deepstar1 showed insight that - surely - something else is going on here that would affect the fall - and his point was glossed over. Somehow the combined masses would make a heavier object hit the surface sooner? Aren't they pulling on each other more so they would collide faster? Well - yes - that's exactly right, but it's a very small effect if one mass is a lot smaller than the other.

Early on, some people requested really good empirical measurements to confirm the times are the same, and were told - there is no need. The fall time is the same due to the equivalence principle. Well - it isn't, and careful measurement would in fact reveal this effect.

As for the impracticality of the point I'm making - ironically if there is anything impractical it is the concept that heavy objects fall as fast as light objects. On earth, with friction and air resistance, this is never true. Yet - somehow - people who see this demo, and who hear the fable of Galileo dropping spheres off towers, believe that a wooden ball would hit the ground at exactly the same time as an iron one, on earth, in air. I think a very large percentage of people have that image in their heads - even though it is completely counter to what would actually happen, and to common sense.

For people who don't care for these details - as usual they don't need to bother with them. For others - this is a description of the actual dynamics, and how they relate to the equivalence principle - that was missing in this thread - and that a few people seemed correctly puzzled about.

zloq

[neufer]

For people who don't care for these details - as usual they don't need to bother with them. For others - this is a description of the actual dynamics, and how they relate to the equivalence principle - that was missing in this thread - and that a few people seemed correctly puzzled about.

Science is nothing more than a hierarchy of different approximations that seem to work quite well at their own individual levels.

It is fine to mention a higher level of approximation if you like but you shouldn't dismissively jump over intermediate levels of approximation as if they didn't exist.

For people who do care about details we have tried to enumerate numerous considerations that are much more important to the actual dynamics than the miniscule movement of the moon.

Most people, however, don't care about details and that also is in the tradition of good science.

[zloq]

I think it's important to separate an accepted principle from the complexities that result when that principle is applied to a dynamic process. As a principle, it is regarded as an absolute. When applied to a time-dependent two-body problem, the results are not absolute at all. The principle is absolute, the resulting timings are not. Nothing to do with potential experimental error or compounding factors, since it is all Newtonian theory. You seem to view it as an engineering problem where little errors don't matter to the customer, but I'm talking about a fundamental principle and its scientific application.

This distinction is not subtle at all if you consider the paradox of the moon falling onto the earth, vs. the earth falling onto the moon. The principle of equivalence still applies - but if you think all objects fall to the surface of the moon at 1.6 m/s^2, while at the same time all objects fall to the surface of the earth at 9.8 m/s^2, then something has got to "give." If you think 1.6 m/s^2 "always works pretty good" for objects falling on the moon - then I have provided a counter-example fairly close to home where a better guess is around 11.4 m/s^2, and your approximation is off by an order of magnitude.

It's clear that some people are not interested in this distinction - but again I refer to earlier comments by others that were alluding to it in their questions, and to the simple fact that the distinction I make here is not well known, and I think should have been mentioned in this discussion - assuming people did in fact know about it before I brought it up.

Good science has a tradition of not caring about details? Wow.

zloq

[neufer]

Good science has a tradition of not caring about details? Wow.

• Absolutely!

[Chris Peterson]

I think it's important to separate an accepted principle from the complexities that result when that principle is applied to a dynamic process. As a principle, it is regarded as an absolute. When applied to a time-dependent two-body problem, the results are not absolute at all. The principle is absolute, the resulting timings are not. Nothing to do with potential experimental error or compounding factors, since it is all Newtonian theory. You seem to view it as an engineering problem where little errors don't matter to the customer, but I'm talking about a fundamental principle and its scientific application.

I honestly don't know what you're getting worked up about. Theoretical physics has long recognized the difference between two bodies undergoing gravitational attraction and a single body moving under fixed gravitational acceleration. Practical applications of that physics recognize that there are cases where the two can be considered equivalent- such as a feather and hammer on the Moon- because the deviation between them is orders of magnitude smaller than our best ability to measure that deviation, and cases where they cannot- because the two masses are not radically different.

Good science has a tradition of not caring about details? Wow.

Good science recognizes which details are important or relevant to an experiment, and which are not. In the case of the hammer/feather experiment, Newton's law of universal gravitation is not relevant, and the equivalence principle is.

[zloq]

I am discussing correct theory vs. incorrect theory. The video on the moon is meant as a demonstration of theory in action, and I think it should be explained as follows:

The equivalence principle says that one mass in the gravitational field of another mass will feel a force proportional to the product of the two masses, but its acceleration will be inversely proportional to its own mass, based on second law. As a result, its own mass cancels and its acceleration toward the other mass is independent of its own mass.

For a small mass suspended over a larger mass and released, each mass will accelerate toward the other based solely on the "other" mass. As a result, small changes in either mass will change the time to collision. The hammer "sees" the big moon and accelerates rapidly toward it; the moon "sees" the small hammer and accelerates slowly toward it. The interaction is symmetric, but the rates are different, and the acceleration of each mass depends only on the other mass.

So - when someone asks - does a hammer hit the moon faster than a feather in a vacuum - the only correct answer is a resounding yes, with the above explanation and a clarification that it's all based on the equivalence principle and Newtonian mechanics - and the effect would be very, very small for objects like hammers, but dramatic if you "dropped" the earth onto the moon. The key benefit of explaining this is it conveys the underlying symmetry of the interaction, and nails down the role of the equivalence principle. And it is correct rather than incorrect.

Apparently you want to say, "The moon is so super big, it doesn't move at all as the hammer approaches. Don't worry your little head about it." That is pre-Newtonian thinking in the year 2011, in an astronomy forum - and ignores the symmetric role of gravitational interaction, along with conservation of momentum.

For some reason you both want to maintain a certain level of dumbing down of this discussion, and I think it's better to describe the actual theory involved. I'm not sure why the two versions - dumbed down and theoretically accurate - can't both be presented and either absorbed or ignored by readers. You have presented yours: Times are "effectively" (?) identical "due to the equivalence principle" (?) and good science never sweats the details. I have presented mine: Times can be very different depending on mass, and symmetry helps the understand the dynamics.

Either way - thanks for the two lectures on how Good Science works.

zloq

[Chris Peterson]

So - when someone asks - does a hammer hit the moon faster than a feather in a vacuum - the only correct answer is a resounding yes...

No, that isn't the case at all. On the Moon, there are many other forces at play which alter the speed objects fall, and those forces massively dominate over Newton's law of universal gravitation. As previously noted, on the Moon the feather probably falls faster. So if you want to frame the question, you need to consider the abstract case of isolated masses with no other physical forces present. And if you do that, you need to consider that there will be a point where the mass difference between the dropped objects and the large body is so large that the difference in velocity is less than 10^-43 seconds, which means that the two land at exactly the same time.

Or, you can just recognize that the fundamental question here has to do with objects of different masses falling under identical gravitational acceleration. Under that condition, which is extremely closely approximated by a feather and hammer falling on the Moon, both objects land at exactly the same time.

[zloq]

The video is meant to demonstrate a *theory* in action. I am talking about the *theory*, quite separate from the experimental difficulties of measuring small, but real, effects. Just because an effect is difficult to measure, or swamped by noise *in a measurement*, it doesn't mean it isn't playing a role.

If I can't measure the change in the velocity of jupiter as a spacecraft goes by, does that mean I should say it doesn't change, or that it is of no consequence? No - I say what theoretical assumptions I am making and I describe the expected effect as delta V even if I don't measure it. You are saying that if something is hard to measure because it is small, it should be regarded as zero - and should be taught to students that it is zero (ugh!). I am saying that some things truly are zero, according to theory, and other things are not. The difference in acceleration of two different masses toward another is expected, by the equivalence principle, to be ZERO. The difference in time to collision, based on Newtonian mechanics, is NONZERO. The difference in velocity of jupiter due to a small spacecraft slingshot is NONZERO.

I am not interested in debating this since I think my description is sound, but if others gained anything from the detail I presented, I welcome postings here. My point has been to provide an accurate theoretical description of what happens when an object falls, and I have heard no criticisms of the theory - in fact an early response was that it was "obvious." I am not lecturing on how science works or something - I am describing the details of how mass does play a role in a falling object in the specific context of this thread and its Newtonian assumptions - in hopes the detail is of interest to some readers here, including those who early in the thread expressed an inkling of puzzlement that the answer, ZERO, didn't seem right.

zloq

[Chris Peterson]

My point has been to provide an accurate theoretical description of what happens when an object falls, and I have heard no criticisms of the theory - in fact an early response was that it was "obvious."

Then you have failed, because you have not described, in general, the behavior of a falling object. You have described the behavior of a pair of objects undergoing mutual gravitational attraction- at best, a subset of what it means to "fall". You have not described the theory which is actually being demonstrated: that objects of different masses fall at the same speed when subjected to identical gravitational acceleration.

[zloq]

I clearly have failed for you - but I am not concerned about that. I don't know how to make this more clear for others: a videocamera on the moon recording a falling hammer would see it fall fairly slowly. A videocamera on the moon would see the earth fall much faster. There is nothing subtle about the distinction. The demo video would look very different, and show very different rates, if a very heavy object replaced the hammer. Of course - in the case of the earth, the camera would be noticeably accelerating upwards while attached to the surface of the moon - but it accelerates upwards, based on theory, for the hammer also. Either way - the video would show a different speed for the process, and the resulting time to impact would be different.

And none of this violates the equivalence principle.

And this answers some of the questions that came up earlier - correctly.

Anyone who says the difference in fall time is zero, regardless of mass, is espousing a theory that violates multiple physical laws. You can build perpetual motion machines with similar concepts, and I thought such crazy ideas weren't allowed here. I'm just going by Newton in this scenario. Whether or not the small motions are easily measurable is an irrelevant detail since I am describing the fall time based on theory - and we all know that good science abhors details.

zloq

[Chris Peterson]

Anyone who says the difference in fall time is zero, regardless of mass, is espousing a theory that violates multiple physical laws.

Fortunately, nobody seems to have made that claim.

[zloq]

And if you do that, you need to consider that there will be a point where the mass difference between the dropped objects and the large body is so large that the difference in velocity is less than 10^-43 seconds, which means that the two land at exactly the same time.

Or, you can just recognize that the fundamental question here has to do with objects of different masses falling under identical gravitational acceleration. Under that condition, which is extremely closely approximated by a feather and hammer falling on the Moon, both objects land at exactly the same time.

Here are two conclusions where two different masses will land at *exactly* the same time. The first brings in quantum effects way outside the realm of Newtonian mechanics - and says they land at exactly the same time. The word "exact" does not apply and is inappropriate in a complex macroscopic quantum context - and dragging in quantum concepts is outside the scope of the demo anyway - as is relativity.

The second I think refers to the fact that the actual demo video involves both objects dropped at the same time, and again uses the phrase, "exactly the same time." This is a more complex 3-body problem (than dropping each mass separately) and whichever one hits first depends on the masses, geometry, surface curvature if present, etc. I don't see how they would land at exactly the same time unless the surface was specifically contoured to make this happen based on the trajectories of the masses involved.

zloq

[Chris Peterson]

The second I think refers to the fact that the actual demo video involves both objects dropped at the same time, and again uses the phrase, "exactly the same time." This is a more complex 3-body problem (than dropping each mass separately) and whichever one hits first depends on the masses, geometry, surface curvature if present, etc. I don't see how they would land at exactly the same time unless the surface was specifically contoured to make this happen based on the trajectories of the masses involved...

I think you're taking a simple concept, well demonstrated by the video, and turning it into something complicated, and confusing for most people. I certainly wouldn't suggest in my 6-8 grade classroom that the objects don't land at the same time, since to do so would not be constructive to the point being made.

[zloq]

Yes - keep it simple by bringing in quantum effects.

My point was that you said "exactly equal" twice in a single note - and all along I have been saying the difference in fall time is nonzero, strictly based on Newtonian mechanics.

My hope is that kids in grades 6-8 are given a correct explanation for how things work - especially if they ask probing questions such as, "What if the falling object is really massive?" More likely, they will be silenced and told that mass has no effect on how things fall on the moon, due to its lack of atmosphere and the equivalence principle. "Just look at the video!" Not to mention - how Galileo dropped wooden and iron cannonballs off the Tower of Pisa - and they landed at "exactly" the same time, as proof of the same point. A sketch of this historic moment may well be in their textbooks.

zloq