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As small as it may be, does every 'thing' have a gravitational pull? That is, something with mass or energy. No matter how obsolete or negligible it may be, is it there? If so, how is it calculated? What does 'it' affect?

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up vote 9 down vote accepted

Yes, everything generates a gravitational field, whether it is massive or massless like a photon.

The source of the gravitational field is an object called the stress-energy tensor. This is normally written as a 4 x 4 symmetric matrix, and the top left entry is the energy density. Note that mass does not appear at all. We convert mass to energy by multiplying it by $c^2$ (as in Einstein's famous equation $E = mc^2$) and then put in the energy. So even a photon generates a gravitational field because although it has no mass it does have energy.

It's surprising what else is in the stress-energy tensor and can therefore generate a gravitational field. For example pressure and shear stress appear. It's even been suggested that a gravitational field could be generated by gravty itself i.e. the energy of the gravitational field generates the curvature that creates the field. The resulting object is called a geon, though I should emphasise that no-one has proved these could exist and most of us think they probably can't.

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+1: I think I slept, thereby forgetting the "mass-energy" while writing the answer ;-) – Waffle's Crazy Peanut Apr 4 '13 at 14:54
wait - stress-energy can generate a magnetic field? next you tell us anti-gravity is real (SCNR ;)) – Christoph Apr 4 '13 at 15:02
@Christoph: :-) thanks. – John Rennie Apr 4 '13 at 15:10

As small as it may be, does every 'thing' have a gravitational pull?

Newtonian: Not everything. But, only massive objects. Definitely not a photon...

GR: Every single energetic object curves spacetime the same way as massive ones, as a consequence of mass-energy $mc^2$. So, a photon does curve spacetime, as it contains energy. (as John mentioned...)

No matter how obsolete or negligible it may be, is it there? If so, how is it calculated?

For instance, let's take a proton. As it has charge, it is affected by electric & magnetic fields. So, Mass spectrometers can be used to deflect them. By applying a magnetic field perpendicular to the plane of the particle, it's made to traverse a circular path and in this way, it's mass can be determined.

What does 'it' affect?

This is the most important part. A massive body (though it's negligible) does affect another massive body. The force is much negligible. Even then, there's always the force. If there isn't any force like that, these interstellar clouds wouldn't have had any gravitational pull and no stars, planets, etc...

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Actually photons do have a gravitational field (though you must use GR to calculate it). You can even make a black hole with enough electromagnetic energy together in one place. – Michael Brown Apr 4 '13 at 13:50
Here is a (paywalled) article which apparently deals with gravity mediated photon-photon scattering. It is also in Zee's QFT textbook. – Michael Brown Apr 4 '13 at 13:52
@MichaelBrown: Ahh... Okay. Man, You guys point out everything. Damn.. Good thing that I've used an under-quote at the last. Or else, I'd have got a bunch of downvotes ;-) – Waffle's Crazy Peanut Apr 4 '13 at 13:54
To be fair to you it is an effect that nobody will ever observe. :D – Michael Brown Apr 4 '13 at 13:56
I'm the kind of person that likes to nitpick about the existence of in-principle-unobservable signals (have you heard of standard model baryon number violation? How about laboratory scale effects of certain dark energy models..?), but I completely understand that there exist people who have better things to do with their time. :) – Michael Brown Apr 4 '13 at 14:08

$$F_{gravitational}=G\times \dfrac{m_1 m_2}{r^2}$$ For as much small mass as you get eg. $m_e=9.1\times 10^{-31}kg$.

$m_1,m_2$ are masses of objects between whom force is calculated and $r$ is distance between them.It is always attractive in nature along the line joining two particles.$G$ is a gravitational constant of the order $10^{-11}$.

Though for large distances and small masses this force is negligible.That is why you can't feel a attraction towards your pc :) and for large masses it is too important eg. earth - sun system is bound by the gravitational force only.

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I provided the answer to second part how is it calculated? – ABC Apr 5 '13 at 3:50

Why would mass be negligible or obsolete? You can assume a mass to be negligible to facilitate your calculations, but in reality every mass has its own gravitational field and affects every other mass in its environment. If you want to go more into the the reason why matter has gravity, you'd probably need to research quantum mechanics.

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this intrigues me since Einstein was wrong in his theory of relativity , first its a theory which by definition means "unproven hypothesis" and believe me its wrong. the math doesn't work. lets look at it I'm not going off half baked here iv'e really considered this and Einstein's theory is no longer a theory because of scientific rules to a theory demand it must be unproven . I will prove its wrong . lets look at Einstein's theory .now for lack of a better computer (could be the operator) I cannot put the 2 in the squared in upper right to the mc. so I will cheat and mix words and numbers as follows to describe his theory E=MC squared. . . or energy equals mass times the speed of light times its self . the very information on this page being discussed proves it wrong.were all going in circles to get what we already have the correct way to do this is as follows (energy equils the power of mass) that's it period. all mass has a different energy value and can not be put in a box or classed as having the same energy value. something like gold has a different value then carbon or sulpher . true energy comes from two sources both being the same

1)magnetic pull or as its called here gravity

2) chemical reaction ( example put any base substance with any acidsubstance and you get a salt and water as a byproduct as gasses like carbon are released )

 both are caused by the structural makeup of the atom but gravitational pull is responsible for all reactions in its infancy. if matter did not pull against all other matter it would not connect and have chemical reactions , nor would friction occur which is responsible for heat , light, and energy on this planet.
 when large amounts of mass pile up the friction of gravity causes heat , then melt, then more friction and expansion till matter breaks down as electrons , protons, and nutrons and then gets spray painted across the universe as light , and can be collected for energy as we do here on earth..
 Einstein basically said the following . and bear with me because of the nature of science and math both combined I must belegalistic in every definition in my recreation of einstein's theory .
what Einstein said was this

energy a byproduct of mass rubbing against mass is equal to the whole sum of mass.... multiplied... by the speed of light.... with light being another byproduct if mass rubbing against mass the product of this being again multiplied by its self or squared can you imagine that number , fist of all anything being multiplied by the speed of light. since all mass pulls against all other mass this formula can never be accurate since it would take two or more atoms to create friction to produce light , but only one atom is needed to create pull and that is work , which by definition is what energy is required to be able to do. light it just a byproduct of something releasing energy , heat , radio waves microwaves . and then theres the electricity that stars inevitably make (earth makes it it must be in the sun also . caused by positively or negatively charged atoms .

 No einstien did not consider that light was only part of the energy being released by mass , and when its all said and done take a damp papertowl and wipe the underside of your table and get the dust that has pulled itself uphill to connect to the wood .
 the question is did the star pull the asteroid into it or did the asteroid commit suicide by pulling itself into the star.
 a single atom has energy without producing light or heat or anything but pull .
 this is where all the energy in the universe comes from .
where did the atom get its energy from . .god I suppose.
  but no matter how you do the math Einstein did not consider all the factors when he created his theory of relativity and 

                             the math doesn't work .

the power of mass equals energy with each form of mass having its own mass and/or power

the intellectual property of DUANE WOODBURY and I hold no claim or responsibility to anyone or thing attempting to use this information in any way shape or form , do not play with energy it can be dangerous or even kill you

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