What is the smallest object that has gravity?

[liveboy21]

Gravity is the force that attracts objects to large masses and is what allows us to fall after we jump away from the Earth's surface. Presumably, such a force should be measurable, so what is the smallest object from which we can measure its gravitational force using our current instruments?

[Dinosaur!]

I'm not sure if this is a troll post, but I'll go ahead and give you the benefit of the doubt.

As far as I know (which is not terribly far, I'm a layman here), any object in a gravitational field will be affected by it, regardless of the 'size' of the object. Planets, baseballs, bacteria, photons, everything is affected by gravity. In large (bigger than atoms) objects, the amount of attractive force felt by that object is proportional to its mass. In small (subatomic) particles, the gravitational force still exists, but it is dwarfed by the other forces. For example, most subatomic particles feel some sort of electromagnetic force, which is some 10^40 times or so stronger than the gravitational force it feels.

So, I guess to answer your question, the smallest object you can measure the force of gravity on is essentially the same thing as the smallest object your instruments can measure the motion of. So, it depends on the instruments you're using. If you're using your eyeballs and looking up, maybe it's the moon. If you're using your eyeballs and looking down, it's probably something like a dust mite or a particle of silt. If you're using a microscope it might be a virus of some sort whereas I guess an electron microscope I would yield something like helium or hydrogen.

Wikipedia has a huge amount of information on gravitation if you want to learn more: http://en.wikipedia.org/wiki/Gravitation

[Yakk]

There is a famous Cavendish experiment in the 18th century that detected gravity on items weighing 158 kg:

http://en.wikipedia.org/wiki/Cavendish_experiment

Modern experiments seeking to check for medium-sized space like dimensions that gravity travels through in order to dilute it have attempted to detect gravity over increasingly short distances.

http://www.npl.washington.edu/eotwash/sr

I do not know what masses they are using, but they are not large, and they not only detecting gravity, they are detecting (a lack of) violation in the inverse-square law of gravitational strength.

[liveboy21]

Just to clarify, I'm not talking about measuring the force that attracts small objects to the Earth, I'm talking about finding out if a small object can attract other objects to it.

Edit: Slight edit for grammar.

[Dopefish]

Yeah, small objects attract things too. Since they're small it's not a very big attractive force, but it's still there.

It's hard to tell what your physics experience is, but it falls out of newtons 3rd law if you're ok with classical theory. Perhaps more intuitively, 'big' things are just collections of a whole bunch of small things, and it'd be very strange indeed if gravity only 'turned on' after a certain number of small things (e.g. atoms) got together.

I don't know what specific experimental things theres been, but I'm sure theres been a bunch. Still, since theory is awesome, even if you're not convinced of newtons laws you can still imagine a world where things below a certain mass didn't attract gravitationally, and see what logical consequences follow. I'm fairly sure you'd quickly find yourself with perpetual motion machines and otherwise getting free energy, and a universe where those things are possible doesn't seem to jive with what we've observed at all.

That said, things might possible get weird in the world of quantum gravity, but I'm still pretty sure it's more a question of how the dynamics work out rather than if quantum things exert a gravitation force at all.

[Jplus]

It's hard to tell what your physics experience is, but it falls out of newtons 3rd law if you're ok with classical theory. Perhaps more intuitively, 'big' things are just collections of a whole bunch of small things, and it'd be very strange indeed if gravity only 'turned on' after a certain number of small things (e.g. atoms) got together.

While you are right about gravity, this particular reasoning by itself is not very convincing. Temperature, viscosity and hardness are all physical quantities that only "turn on" after a sufficient number of atoms has lumped together. The fact that such quantities exist is well known as the "more is different" principle, or it may be called emergence (unfortunately that word is a bit hyped and over-used). In order to distinguish from emergent quantities, quantities like gravity and charge that are simply the sum of the parts are sometimes called "aggregate".

[jaap]

Just to clarify, I'm not talking enquiring about measuring the force that attracts small objects to the Earth, I'm talking about finding out if a small object can attract other objects to it.

According to the wiki, the accuracy of some standard gravimeters is 2 parts in a billion. If I did my sums right, compared to earth's gravity that would just about allow you to detect a mass of 300kg one metre away*. I guess this just goes to show how amazing Cavendish's experiment was.


* This assumes the equipment is a point. This is obviously not true, as they consist of a tube in which a mass is dropped and measured, so the gravitational force arising from a very nearby 300kg mass would be different at the two ends of the tube, but I'm not going to try to work out exactly how that would change the measurements. It's just a ballpark figure anyway.
Edit to add: If the figures on the wiki page are correct, just raising the gravimeter up by a centimetre changes the earth's gravity reading more than shoving a 300kg mass underneath it. Gravity is incredibly weak.

[FancyHat]

How direct would you like the measurements to be?

If we're allowed to use the principle that each force is matched by an equal and opposite force, then we can indirectly measure the (Newtonian) gravitational force exerted by a small mass, m₁, on another mass, m₂, by measuring the force exerted by m₂ on m₁. So, for example, when m₁ is a smoke particle, and m₂ is the earth, we can indirectly measure the force exerted on the earth by the smoke particle by measuring the force exerted on the smoke particle by the earth.

But I guess you probably didn't mean measuring in that kind of way.

Perhaps more intuitively, 'big' things are just collections of a whole bunch of small things, and it'd be very strange indeed if gravity only 'turned on' after a certain number of small things (e.g. atoms) got together.

I like this point. Measuring the gravitational force exerted by a tonne of clay and by two tonnes of clay would give us a difference in the forces exerted due to the extra tonne. We can then ask: what if we only increased the original mass of clay by 100 kg? Or 10 kg? 1 kg? 1 gramme? What if we added only one, single clay particle? What if we added a whole extra tonne, but did so one clay particle at a time? And what if we went the other way, and removed one clay particle at a time, until there was no clay left?

If the question is effectively what's the smallest difference in gravitational force that can be measured, then it would be a question of what's the smallest amount of clay that can be added or removed without the difference in gravitational force being measurable. But even then, I'd start thinking of statistical methods. For example, just to illustrate the concept, with a range of many different initial masses of clay, I'd want to add a constant mass of clay to each such mass, and see how often the difference in gravitational force was measurable. I guess I'd want to use some sort of digital meter for this, to see how often the last digit on the display changed. And I'd repeat this experiment with different sized extra masses, to see how clear a signal I got in the resulting data.

So, suppose I had an initial mass of 100 kg, and I added 1 kg to it at a time, and each time measured the force exerted on a 1 kg mass 1 m away. If my equipment can measure to the nearest 1 nN, I'd expect to see my measurement change about 6.67% of the time. Though that looks much like adding all the extra clay all in one go, and dividing the total change in measured force by the extra mass.

Anyway, I'm basically wanting to do a lot of sampling, to get a weak signal in a lot of noise to show up.

Would that approach work? If so, could that kind of approach answer the original question?

Edited to add:-

What about using a torsion balance, interferometry to detect very small changes in torsion balance position, and making use of harmonic oscillation to amplify extremely weak gravitational signals by (extremely carefully) adding and removing the mass being measured at the torsion balance's natural frequency?

[Qaanol]

Gravity is the force that attracts objects to large masses and is what allows us to fall after we jump away from the Earth's surface. Presumably, such a force should be measurable, so what is the smallest object from which we can measure its gravitational force using our current instruments?

Gravity is a fictitious force.

[elasto]

Perhaps more intuitively, 'big' things are just collections of a whole bunch of small things, and it'd be very strange indeed if gravity only 'turned on' after a certain number of small things (e.g. atoms) got together.

While you are right about gravity, this particular reasoning by itself is not very convincing. Temperature, viscosity and hardness are all physical quantities that only "turn on" after a sufficient number of atoms has lumped together.

And actually, as I learnt only this week, it's not out of the question that gravity could be another such quantity: http://en.wikipedia.org/wiki/Entropic_gravity

In 2009, Erik Verlinde disclosed a conceptual model that describes gravity as an entropic force...

Reversing the logic of over 300 years, it argued that gravity is a consequence of the "information associated with the positions of material bodies"...

It implies that gravity is not a fundamental interaction, but an emergent phenomenon which arises from the statistical behavior of microscopic degrees of freedom encoded on a holographic screen...

The paper drew a variety of responses from the scientific community. Andrew Strominger, a string theorist at Harvard said “Some people have said it can’t be right, others that it’s right and we already knew it — that it’s right and profound, right and trivial."

[davidstarlingm]

While you are right about gravity, this particular reasoning by itself is not very convincing. Temperature, viscosity and hardness are all physical quantities that only "turn on" after a sufficient number of atoms has lumped together.

Not really. Temperature, viscosity, and hardness aren't attributes of an object; they are attributes of the interactions of the component atoms and molecules of an object. And with that, it's not a case of "turning on"; it's simply a case of how much a given group of atoms/molecules are going to interact.

[eternauta3k]

Let's not turn a thread about experimental challenges into a thread about theoretical vs experimental physics.

[Zamfir]

Not really. Temperature, viscosity, and hardness aren't attributes of an object; they are attributes of the interactions of the component atoms and molecules of an object. And with that, it's not a case of "turning on"; it's simply a case of how much a given group of atoms/molecules are going to interact

People where studying and measuring temperature, viscosity and hardness of objects, long before these phenomena were modelled as arising from the interaction of molecules. It's not a priori clear that gravitational attraction should be different.


Even under our present understanding of gravity, a large object's gravity is not strictly the sum of the attraction of its components on all size scales. At subatomic levels, binding energy becomes a significant factor.

[Dopefish]

Well, how 'big' is a photon, and do they count as an 'object' for the purposes of the question? I'm fairly sure it's been shown light has gravity, although I don't know if that's theory or experiment at work.

What gravity 'is' might not necessarily be the same as what someone thinks it is, be it along the same lines as electromagnetic forces, or GR spacetime curvature shinanigans, but it's always still there at all the scales we know things about.

Perhaps if one squints really hard and looks at sub-atomic levels (or sub-sub-atomic, or deeper still) it might turn out that gravity is an emergent property, but that's deep territory to dive into if one isn't sure if the OP is asking on that level.

The impression I got was more along the lines of "Planets have gravity because they're big and massive [but I certainly don't feel a gravitational force from a speck of dust so it doesn't seem to exert one]. What's the smallest thing that we've discovered that does exert one?". I apologize if I underestimated the level of the question/OP.

[Copper Bezel]

It's not in the thread title, and I think it should be, but he specifies the smallest object with measurable attractive force, using current technology, in the post. Obviously, the balls in the Cavendish experiment would qualify as a small object with a measured gravitational pull, but how much smaller can we go? And yeah, it would be passing strange if smaller objects had no attractive force, like, we know they really do, but it's still a fair question, I think.

[speising]

the absolutely smallest object would have to be a higgs boson,wouldn't it?

[Yakk]

No.

The Higgs Boson is a particle of the Higgs field. The Higgs field binds to certain subatomic particles in such a way that they gain rest mass.

Despite this, almost all of the mass we experience is due to inter-Quark binding energies within protons/neutrons: all other sources of mass are an order of magnitude or more smaller. (electron mass, Quark rest mass, other bindings within the nucleus, electron-nucleus bindings)

However, without the Higgs field, the non-zero rest mass of particles not composed of Quarks was difficult to explain. And them having a non-zero rest mass was important to explain how their other interactions occurred.

[speising]

ah, so i fell into the popular science journalism trap.

[zukenft]

slightly modifying the OP's question, what is the smallest object that has visible gravity? that is, objects that we can see attract each other with our naked eye? let's assume that we can observe it very closely, so something like a movement rate of 1 cm/s is visible enough.

edit:
using the formula a=G.m/r^2, taking a = 0.0001 m/s^2, and r = 1 meter. I got mass = 1.5 million kg.

1500 tons? that's the mass of a ship, isn't it? so if we put two ships close enough, would it slowly collide with each other due to gravity?

[eternauta3k]

If your ships are point masses, sure.

[thoughtfully]

slightly modifying the OP's question, what is the smallest object that has visible gravity? that is, objects that we can see attract each other with our naked eye? let's assume that we can observe it very closely, so something like a movement rate of 1 cm/s is visible enough.

edit:
using the formula a=G.m/r^2, taking a = 0.0001 m/s^2, and r = 1 meter. I got mass = 1.5 million kg.

1500 tons? that's the mass of a ship, isn't it? so if we put two ships close enough, would it slowly collide with each other due to gravity?

That's a very small ship. Cargoes are thrown about the globe in multiples of 10,000 tons. 1500 tons I expect is a big boat, but I'm not looking it up.

[davidstarlingm]

slightly modifying the OP's question, what is the smallest object that has visible gravity? that is, objects that we can see attract each other with our naked eye? let's assume that we can observe it very closely, so something like a movement rate of 1 cm/s is visible enough.

One cm/s is a speed, not an acceleration. Gravity provides acceleration, which can build up over time to any speed (theoretically).

Of course, the acceleration of gravity weakens with distance, so there's a practical limit to how much speed two objects can build up before they collide, even if they start an arbitrary distance apart. If our test objects are each one meter wide, they'll need to weigh 375 tonnes each in order to build up 1 cm/s of combined speed when they hit each other -- and that's if they are "dropped" from opposite ends of the universe. Yeah, gravity is a REALLY weak force.

But weak though it may be, it's very persistent. In the absence of any other forces or fields, any two objects WILL eventually reach each other.

[FancyHat]

If our test objects are each one meter wide, they'll need to weigh 375 tonnes each in order to build up 1 cm/s of combined speed when they hit each other -- and that's if they are "dropped" from opposite ends of the universe.

If I've done my sums right, a lead sphere of radius 0.397 m has an escape velocity at its surface of 1 mm/s. That lead sphere would have a mass of nearly three tonnes.

[davidstarlingm]

If our test objects are each one meter wide, they'll need to weigh 375 tonnes each in order to build up 1 cm/s of combined speed when they hit each other -- and that's if they are "dropped" from opposite ends of the universe.

If I've done my sums right, a lead sphere of radius 0.397 m has an escape velocity at its surface of 1 mm/s. That lead sphere would have a mass of nearly three tonnes.

Holding radius constant, the mass of an object is proportional to the square of the escape velocity. You need 100 times more mass to get an escape velocity of 1 cm/s than you would to get 1 mm/s. Of course, my radius was slightly larger, at 0.5 m to your ~0.4 m.

[Copper Bezel]

If the force between small objects is so trivial, how did the Cavendish experiment work?

[FancyHat]

If the force between small objects is so trivial, how did the Cavendish experiment work?

Torsion balances can have very, very tiny torsion coefficients. The experiments also take a long time.

If you've got a uniform, spherical mass of, say, 10kg, the acceleration due to its gravity at a distance of 0.1 m from its centre will be 66.74 nm/s². One second of that acceleration gives a velocity of 66.74 nm/s, and a distance covered of 33.37 nm. One minute gives just over 4 μm/s, and a distance of 120 μm. An hour gives 240 μm/s, and a distance of 432 mm! Obviously, such a huge distance means that constant acceleration is not a reasonable simplification for such calculations, but it gives an idea of how such experiments are able to achieve usefully measurable and easily visible results.

Torsion balances also harmonically oscillate. So, if you (very carefully) keep adding and removing nearby masses at the torsion balance's natural frequency, you should be able to gradually build up an easily measurable oscillation. Even tinier gravitational forces could be amplified and measured this way. The lower the damping factor of the torsion balance, the higher the gain.

And if we start using interferometry to detect oscillations with very, very tiny amplitudes, how tiny could the attracting masses be while still being gravitationally detectable this way? I'm betting less than a gramme.

[eternauta3k]

You'd need the oscillation period to be huge so you can ignore the vibrations from moving tonnes of stuff around.

[FancyHat]

You'd need the oscillation period to be huge so you can ignore the vibrations from moving tonnes of stuff around.

Yeah. I guess it would need to be done somewhere very still and very quiet.

[mfb]

If you've got a uniform, spherical mass of, say, 10kg, the acceleration due to its gravity at a distance of 0.1 m from its centre will be 66.74 nm/s².

It is fascinating that this acceleration is easy to measure today - in real-time.

[FancyHat]

It is fascinating that this acceleration is easy to measure today - in real-time.

If you search, say, YouTube, you might find some demonstrations of such torsion balances. However, one such video I found seemed to show implausibly rapid movement, suggesting that air movement or something else might have been responsible. The few videos I looked at didn't seem to show much being done to avoid such problems.

[lgw]

It's hard to tell what your physics experience is, but it falls out of newtons 3rd law if you're ok with classical theory. Perhaps more intuitively, 'big' things are just collections of a whole bunch of small things, and it'd be very strange indeed if gravity only 'turned on' after a certain number of small things (e.g. atoms) got together.

While you are right about gravity, this particular reasoning by itself is not very convincing. Temperature, viscosity and hardness are all physical quantities that only "turn on" after a sufficient number of atoms has lumped together. The fact that such quantities exist is well known as the "more is different" principle, or it may be called emergence (unfortunately that word is a bit hyped and over-used). In order to distinguish from emergent quantities, quantities like gravity and charge that are simply the sum of the parts are sometimes called "aggregate".

I just wanted to point out that this isn't entirely right about gravity. Most of the gravity of normal matter comes not from individual quarks and leptons, but from the binding energy between quarks in protons and neutrons, right? Heck, at this point I'd easily believe that all of the gravity of normal matter comes from binding energy, and we just don't know enough about quarks yet to see it yet.

[eternauta3k]

Heck, at this point I'd easily believe that all of the gravity of normal matter comes from binding energy, and we just don't know enough about quarks yet to see it yet.

That would mean one kind of energy gravitates and the other kind doesn't.

[thoughtfully]

It's estimated to be 96-97 percent, with a lot of uncertainty because QCD is evil. There's also lots of other binding energies, the next most significant being electrons around nuclei, but there's more as you scale up, wherever clumpiness is to be found. The Higgs-derived masses of constituent particles are more significant than any except the QCD variant, however.

Mr. QCD: http://www.frankwilczek.com/

EDIT: I'm pretty sure the constituent particle masses are more significant. Big atoms with very tightly bound inner electrons make me wonder. Still, with all the binding energies of a particular sort added up then compared to the masses being bound, I would expect the bound masses to win in aggregate.

[lgw]

Heck, at this point I'd easily believe that all of the gravity of normal matter comes from binding energy, and we just don't know enough about quarks yet to see it yet.

That would mean one kind of energy gravitates and the other kind doesn't.

No, that would mean that quarks are made of something smaller, and what we see as the mass of a quark is in fact just the binding energy of those smaller things (or to put it differently, "rest mass" is just a simplification that works at large enough scale, but doesn't actually exist).

It's estimated to be 96-97 percent, with a lot of uncertainty because QCD is evil. There's also lots of other binding energies, the next most significant being electrons around nuclei, but there's more as you scale up, wherever clumpiness is to be found. The Higgs-derived masses of constituent particles are more significant than any except the QCD variant, however.

Mr. QCD: http://www.frankwilczek.com/

EDIT: I'm pretty sure the constituent particle masses are more significant. Big atoms with very tightly bound inner electrons make me wonder. Still, with all the binding energies of a particular sort added up then compared to the masses being bound, I would expect the bound masses to win in aggregate.

That's really a neat website! Thanks. It seems as time goes on, ever less of what we think of as mass turns out to be "rest mass", which is why it wouldn't surprise me if we eventually discover that none of mass is "rest mass of fundamental particles".

[andyisagod]

That's really a neat website! Thanks. It seems as time goes on, ever less of what we think of as mass turns out to be "rest mass", which is why it wouldn't surprise me if we eventually discover that none of mass is "rest mass of fundamental particles".

The recent discovery of the Higgs boson would really put pressure on that idea. The measurement of the coupling of the standard model particles also agrees with the standard model prediction that it is proportional to their masses. So at least current the data suggests that the gauge bosons and fermions of the standard model gain their mass through the higgs mechanism although we are still far from understanding if the higgs is indeed a fundamental scalar itself or a composite particle.

[wumpus]

Quick answer: an electron. (There may be other, even more basic particles with no known size, but electrons are reasonably familiar, have a rest mass, and (when I learned physics) no known volume.) No idea how to balance electrons in such a way as to measure the gravitation. Charge is so overwhelming so as to make such measurements essentially impossible.

Something I remember my Physics professor saying in passing was that the Cavendish experiment is one of the more difficult classical experiments to do. He claimed it was useful for giving a cocky grad student a few years to discover that he isn't the greatest physicist ever, and that there were those who could do this thing in the 18th century.

[PM 2Ring]

Quick answer: an electron. (There may be other, even more basic particles with no known size, but electrons are reasonably familiar, have a rest mass, and (when I learned physics) no known volume.) No idea how to balance electrons in such a way as to measure the gravitation. Charge is so overwhelming so as to make such measurements essentially impossible.

Neutrinos are even lighter, and they don't have that pesky electric charge. However, slowing them down to weigh them may not be easy.

Something I remember my Physics professor saying in passing was that the Cavendish experiment is one of the more difficult classical experiments to do. He claimed it was useful for giving a cocky grad student a few years to discover that he isn't the greatest physicist ever, and that there were those who could do this thing in the 18th century.

Sure. But if you don't care about making accurate measurements and just want a qualitative demo, it's not that hard. John Walker (of Autodesk fame) reckons that it was possible to do with the technology available in Archimedes' day. See Bending Spacetime in the Basement for a discussion, photos, and some crude videos.

[lgw]

Quick answer: an electron. (There may be other, even more basic particles with no known size, but electrons are reasonably familiar, have a rest mass, and (when I learned physics) no known volume.) No idea how to balance electrons in such a way as to measure the gravitation. Charge is so overwhelming so as to make such measurements essentially impossible.

Something I remember my Physics professor saying in passing was that the Cavendish experiment is one of the more difficult classical experiments to do. He claimed it was useful for giving a cocky grad student a few years to discover that he isn't the greatest physicist ever, and that there were those who could do this thing in the 18th century.

I started a thread about this topic a while back. Turns out that any way you look at it, asserting any difference between the inertial mass, the active gravitational mass, or the passive gravitational mass of the electron runs you into contradictions (with relativity IIRC).

Edit: Ah, here it is.

[Sprocklem]

Quick answer: an electron. (There may be other, even more basic particles with no known size, but electrons are reasonably familiar, have a rest mass, and (when I learned physics) no known volume.) No idea how to balance electrons in such a way as to measure the gravitation. Charge is so overwhelming so as to make such measurements essentially impossible.

Since we're talking about size, would a singularity not match/beat an electron and be more convenient? We can measure the force exerted* from a distance without slowing it down or dealing with significant charge.

*I don't know the accuracy of these measurements.

[davidstarlingm]

Quick answer: an electron. (There may be other, even more basic particles with no known size, but electrons are reasonably familiar, have a rest mass, and (when I learned physics) no known volume.) No idea how to balance electrons in such a way as to measure the gravitation. Charge is so overwhelming so as to make such measurements essentially impossible.

Since we're talking about size, would a singularity not match/beat an electron and be more convenient? We can measure the force exerted* from a distance without slowing it down or dealing with significant charge.

*I don't know the accuracy of these measurements.

We don't exactly know whether a singularity actually exists.

And though "smallest" could be ambiguous (e.g., volume vs mass), an electron is probably going to be considered "smaller" than a black hole based on its mass even if their volumes are theoretically equal.