## What is the smallest object that has gravity?

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algorerhythms
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### Re: What is the smallest object that has gravity?

There was once a colloquium speaker at my physics department that told a story somewhat related to this thread... His group was working on gravitometry (if I remember correctly, it was to be used for oil prospecting), and they would calibrate their devices by measuring the gravitational field in their lab. They noticed that every afternoon, at around the same time, their measurement would change, and then it would change back shortly afterward. It took them a while to figure out the cause of it. Turned out the change corresponded to when the garbage truck would come by to empty the dumpster outside the building. So, at the very least, a garbage truck is big enough to have a measurable gravitational field.
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flownt
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### Re: What is the smallest object that has gravity?

Cool story! I wouldn't have expected that to work, because of the (assumedly) large distance, but apparantely it does...

davidstarlingm
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### Re: What is the smallest object that has gravity?

flownt wrote:Cool story! I wouldn't have expected that to work, because of the (assumedly) large distance, but apparantely it does...

Well, let's see here. Rough estimate of a garbage truck's mass -- 15 tonnes. Rough estimate of the distance -- 10 meters. Rough estimate of the test mass -- 10 kg. By the power of Newton:

F = Gm1m2/r2

**maths**

That's a force of about 0.1 micronewtons, or about the weight of an eyebrow hair. If the instrumentation was sensitive enough to detect the weight of an eyebrow hair, then yep, the gravitational field of a garbage truck about thirty feet away would definitely do it.

mfb
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### Re: What is the smallest object that has gravity?

davidstarlingm wrote:
flownt wrote:Cool story! I wouldn't have expected that to work, because of the (assumedly) large distance, but apparantely it does...

Well, let's see here. Rough estimate of a garbage truck's mass -- 15 tonnes. Rough estimate of the distance -- 10 meters. Rough estimate of the test mass -- 10 kg. By the power of Newton:

F = Gm1m2/r2

**maths**

That's a force of about 0.1 micronewtons, or about the weight of an eyebrow hair. If the instrumentation was sensitive enough to detect the weight of an eyebrow hair, then yep, the gravitational field of a garbage truck about thirty feet away would definitely do it.
Or simply 10-9 as relative value. That can be detected.

davidstarlingm
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### Re: What is the smallest object that has gravity?

mfb wrote:
davidstarlingm wrote:
flownt wrote:Cool story! I wouldn't have expected that to work, because of the (assumedly) large distance, but apparantely it does...

Well, let's see here. Rough estimate of a garbage truck's mass -- 15 tonnes. Rough estimate of the distance -- 10 meters. Rough estimate of the test mass -- 10 kg. By the power of Newton:

F = Gm1m2/r2

**maths**

That's a force of about 0.1 micronewtons, or about the weight of an eyebrow hair. If the instrumentation was sensitive enough to detect the weight of an eyebrow hair, then yep, the gravitational field of a garbage truck about thirty feet away would definitely do it.
Or simply 10-9 as relative value. That can be detected.

Well, the concept of measuring a particular force is more easily conceptualized if we think about what weight would or wouldn't affect instrumentation. Hence the eyebrow hair example. I'm guessing a small grain of sand is in the same ballpark. Anything around 10-7 grams will work, and it's not terribly hard to think of instruments sensitive enough to be thrown off by a grain of sand.

mfb
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### Re: What is the smallest object that has gravity?

davidstarlingm wrote:Well, the concept of measuring a particular force is more easily conceptualized if we think about what weight would or wouldn't affect instrumentation. Hence the eyebrow hair example. I'm guessing a small grain of sand is in the same ballpark. Anything around 10-7 grams will work, and it's not terribly hard to think of instruments sensitive enough to be thrown off by a grain of sand.
No that's not right, you cannot ignore your test mass if you consider absolute values. There are certainly scales that note a grain of sand, but most of them are designed to measure objects of milligrams or grams - they will break if you put 10kg on them.

davidstarlingm
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### Re: What is the smallest object that has gravity?

mfb wrote:
davidstarlingm wrote:Well, the concept of measuring a particular force is more easily conceptualized if we think about what weight would or wouldn't affect instrumentation. Hence the eyebrow hair example. I'm guessing a small grain of sand is in the same ballpark. Anything around 10-7 grams will work, and it's not terribly hard to think of instruments sensitive enough to be thrown off by a grain of sand.
No that's not right, you cannot ignore your test mass if you consider absolute values. There are certainly scales that note a grain of sand, but most of them are designed to measure objects of milligrams or grams - they will break if you put 10kg on them.

...so what about what I said is "not right"?

HarvesteR
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### Re: What is the smallest object that has gravity?

It's not just the mass of the object that you need to think about... Any amount (mass) of material will have some gravitational pull to it, but the key thing, assuming your intention is to be drawn into its gravity well, is to consider its gravitational pull in relation to the pull of other objects around it.

It comes down to spheres of influence, and whether your object is dense enough to be smaller than its own SOI radius.

I read somewhere (can't remember where, sorry), that while in theory you could conceive of an astronaut on EVA being able to orbit the space shuttle, in practice this isn't possible, since because the shuttle isn't dense enough, it is larger than its own SOI, so you couldn't get close enough to orbit it without already being inside it.

So, to answer the OP question, it's not so much about size, it's about density, and how far away you are from other denser objects (like a planet, those tend to get in the way quite a lot when you try to test these ideas).

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### Re: What is the smallest object that has gravity?

wumpus wrote: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 did it in my 2nd year in uni. It was quite fun. We had it set up in the basement of the building, and measured during the night (automated, thank god). There was some heavy machinery at the other side of the building that was sometimes turned on in the morning, and that gave very visible spikes in our data. We could also track the position of the moon, which was even more awesome.

In the end I think our result was about 20% off from the actual value. Cavendish did a lot better. Of course he used much bigger spheres and probably had much more tightly controlled circumstances. On the other and he didn't have a computer to measure for him during the night.
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PM 2Ring
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### Re: What is the smallest object that has gravity?

Pity you can't make the spheres out of hassium (41 g/cm³) or meitnerium (37.4 g/cm³).

lgw
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### Re: What is the smallest object that has gravity?

PM 2Ring wrote:Pity you can't make the spheres out of hassium (41 g/cm³) or meitnerium (37.4 g/cm³).

It would have to be one heck of a fast experiment. But I was surprised the half-life of hassium is so long at multiple seconds - maybe there really is an island of stability up there somewhere.
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### Re: What is the smallest object that has gravity?

Which would be only sligntly cheaper to produce in bulk than antimatter. Easier to hold on to, at least.

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### Re: What is the smallest object that has gravity?

To rephrase the OP's question (sort of) - if the universe was the same size as now, but contained just two hydrogen atoms at opposite ends of the universe, would they still attract each other?
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### Re: What is the smallest object that has gravity?

tomandlu wrote:To rephrase the OP's question (sort of) - if the universe was the same size as now, but contained just two hydrogen atoms at opposite ends of the universe, would they still attract each other?

That's a meaningless question. If the universe contained just 2 hydrogen atoms it wouldn't have the same shape and size. Also, the universe has no ends, so you can't put 2 hydrogen atoms on opposite ends. You can put them arbitrary far away from each other, in which case they wouldn't be able to observe each other unless your universe is also arbitrary old.

The question should be: Is there a quantum of gravity? Is there a minimum size to a gravitational interaction?
The answer is: We don't know.
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### Re: What is the smallest object that has gravity?

tomandlu wrote:To rephrase the OP's question (sort of) - if the universe was the same size as now, but contained just two hydrogen atoms at opposite ends of the universe, would they still attract each other?

That's a meaningless question.

Thought it might be...

The question should be: Is there a quantum of gravity? Is there a minimum size to a gravitational interaction?
The answer is: We don't know.

Wouldn't the question also potentially include distance? Could a quanta of gravity be a function of mass and distance or is that a meaningless statement?
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### Re: What is the smallest object that has gravity?

tomandlu wrote:Wouldn't the question also potentially include distance? Could a quanta of gravity be a function of mass and distance or is that a meaningless statement?

Quite the opposite. Distance and mass should be functions of it!
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### Re: What is the smallest object that has gravity?

tomandlu wrote:To rephrase the OP's question (sort of) - if the universe was the same size as now, but contained just two hydrogen atoms at opposite ends of the universe, would they still attract each other?

That's a meaningless question. If the universe contained just 2 hydrogen atoms it wouldn't have the same shape and size. Also, the universe has no ends, so you can't put 2 hydrogen atoms on opposite ends. You can put them arbitrary far away from each other, in which case they wouldn't be able to observe each other unless your universe is also arbitrary old.

The question should be: Is there a quantum of gravity? Is there a minimum size to a gravitational interaction?
The answer is: We don't know.

General relativity does allow for asymptotically flat solutions where you have some finite concentrations of mass/energy and vacuum everywhere else, and the curvature approaches zero at large distances from any of the concentrations. And the question is meaningful if you use the word "universe" to mean observable universe, as cosmologists often do (the observable universe is thought to have a diameter of about 93 billion light-years). Then the question would be "if you had an asymptotically flat universe where the only mass/energy consisted of two hydrogen atoms 93 billion light-years apart, would they attract each other?" In general relativity the answer would be yes, and I suspect it would still be yes in a theory of quantum gravity but I don't know for sure what a physicist would say about that (it's interesting to note that a hydrogen atom does have a mass smaller than the Planck mass, but I doubt that would mean they wouldn't emit gravitons in quantum gravity--unlike Planck length and Planck time, Planck mass isn't thought to be the smallest possible unit of mass in a theory of quantum gravity, more like the mass of a black hole whose size is on the scale of the Planck length).

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### Re: What is the smallest object that has gravity?

Hypnosifl wrote:In general relativity the answer would be yes, and I suspect it would still be yes in a theory of quantum gravity but I don't know for sure what a physicist would say about that (it's interesting to note that a hydrogen atom does have a mass smaller than the Planck mass, but I doubt that would mean they wouldn't emit gravitons in quantum gravity--unlike Planck length and Planck time, Planck mass isn't thought to be the smallest possible unit of mass in a theory of quantum gravity, more like the mass of a black hole whose size is on the scale of the Planck length).

Thanks for that.

Apologies in advance for any glaringly erzatz science in the next bit...

So, there would seem to be 3 possibilities:
1. There is no minimum mass/maximum distance for interaction between discrete particles
2. There is a minimum mass required for interaction, but distance is not a factor
3. Both mass and distance are factors in determining whether interaction will take place

and, currently, number 1 is favoured? 2 looks the oddest to me. 3 looks reasonable, but somehow manages the trick of being both intuitive and anti-intuitive...

On a related question, if a single photon is emitted into a pure vacuum, what happens to it over distance? Normally, light is spread according the inverse square law, but what happens when we focus on a single photon that cannot be subdivided?

BTW in the planck mass article, it says:

If two quanta of the Planck mass or greater met, they could spontaneously form a black hole whose Schwarzschild radius equals their de Broglie wavelength. Once such a hole formed, other particles would fall in, and the black hole would experience runaway, explosive growth

Just how explosive is 'explosive growth'? What does 'met' mean in this context to distinguish it from day-to-day chemical and physical interactions? (which, afaik, don't generally lead to the creation of runaway black holes. Or raptors.)
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### Re: What is the smallest object that has gravity?

photons can be in more than one place at once prior to interacting, so it obeys inverse square just fine.
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### Re: What is the smallest object that has gravity?

tomandlu wrote:On a related question, if a single photon is emitted into a pure vacuum, what happens to it over distance? Normally, light is spread according the inverse square law, but what happens when we focus on a single photon that cannot be subdivided?

Remember that quantum measurements are probabilistic, so at the single photon level the inverse square law tells us about the probability of detecting the photon in a given region of spacetime.

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### Re: What is the smallest object that has gravity?

PM 2Ring wrote:
tomandlu wrote:On a related question, if a single photon is emitted into a pure vacuum, what happens to it over distance? Normally, light is spread according the inverse square law, but what happens when we focus on a single photon that cannot be subdivided?

Remember that quantum measurements are probabilistic, so at the single photon level the inverse square law tells us about the probability of detecting the photon in a given region of spacetime.

Ah, of course. I'm being stupid. Apart from anything else, I think I just rephrased the double-slit experiment with a slightly different emphasis.
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DrZiro
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### Re: What is the smallest object that has gravity?

We did the torsion thing in first year physics, using a couple of metal balls about 1 dm in diameter. So the gravity from a few kilos is easily measurable, without any top modern equipment.

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### Re: What is the smallest object that has gravity?

If I understand this experiment correctly, we've measured the effect of gravity on individual neutrons. Gravitational potential is apparently quantized similarly to other potentials. In constant Earth's surface gravity, neutrons' potentials are in increments of about 13.7 um. Or a 22.7 g bouncing ball would only be able to bounce in increments of 10^-30 meters.
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### Re: What is the smallest object that has gravity?

@Quizatzhaderac: It is easy to show that gravity acts both on neutrons and protons+electrons. The other direction - showing that small objects do attract other objects - is harder to show. Lab experiments are down to distances below 1mm, and there is no reason to expect a minimal mass (those experiments are mainly looking for a deviation from the inverse square law) as that would be a very weird world where the gravitational attraction of a+b is completely different from the gravitational attraction of a plus b.

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### Re: What is the smallest object that has gravity?

If you can cite a paper measuring individual electrons, please link it. This is the smallest example of measuring passive gravitational mass I've seen, also additionally interesting because it's on a scale small enough that quantization becomes important. While not surprising, this experiment does give us one number number that is quantized: spin; or rather, energy * time.

AFAIK, we've yet to be able to measure the gravitational mass of antimatter, so we've been unable to directly refute it having negative gravitational mass (the original conception of antimatter called for all numbers to be reversed), or slightly different gravitational mass (like some quantum gravity theories call for).
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### Re: What is the smallest object that has gravity?

I think that this is what the OP wanted to know.

Imagine you have a basket ball and a remote control, but instead of sound and channel, it says mass and volume. It also has a display that shows what the current mass and volume are.

You take a bathroom scale and put the basket ball on it. The scale gives you some measurement. The exact value does not matter, just the fact that it displays a number besides 0 is important. You press the lower mass button and watch as the measurement decreases. Eventually, your bathroom scale simple read 0. It is not sensitive enough to detect the force of gravity when it is that small. So you throw it away and run to a local high school. You a into the chemistry class's room take one of their small scales.

You press the lower volume button until the basket ball can fit on the scale. You put the basket ball on the scale and get some measurement. Again, the exact value does not matter. You press the lower mass button until the scale does not say anything. It is simple not sensitive enough to detect the force of gravity when it is that small. So you throw it away and run to a near by college and grab their...

You continue to do this until you have the most sensitive equipment on the planet. You put the 'basket ball' in it and measure its weight. You get some number. You press the lower mass button until this piece of equipment is no longer able to detect the 'basket ball'.

Look at the remote and record the information from its screen. Calculate how much the 'basket ball' should weight. What ever answer you get, that is the smallest force caused by gravity ('the smallest amount of gravity') that we can detect. What is the answer you calculated?
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