# Strength of Gravity

1. Jul 20, 2009

### jbutcher

I have read through countless discussions, and have still to be convinced that gravity is weaker than the other fundemental forces, even though this is the accepted wisdom.

My argument is that it is mass which dictates gravitational attraction, whereas charge, for example, is responsible for electrical attraction or repulsion. These are two independent qualities, and so surely no such comparison can be made.

Two planets attract more strongly than two coulombs of opposite charge (of zero hypothetical mass) at the same separation. If the 'planet' was the SI unit of mass, would we say gravity is stronger?

The fact that the gravitational attraction of two electrons is much weaker than their electrical repulsion is because they have insignificnt mass and significant charge.

A singularity is theoretically just about the smallest entity known, yet it's gravitational pull is immense. In what sense, then, is gravity weak? Is it just that we live in a universe which has a greater charge density than it does mass density?

2. Jul 20, 2009

### pallidin

Some forces have very strong influence over a short distance; practically none over longer distances.
Gravity seems to be special, but is considered quite "weak" though pervasive.

Not sure why, and I'm not qualified beyond my simple comments to expound further.

Good luck... hope there will be comments to clarify this.

3. Jul 20, 2009

### nooma

thinking of it from a force perspective, the force able to be imparted by a single charge is much greater than the corresponding mass of the object that has the charge. So in a way it is due to the relative density of charge to mass on a particle.

he difficulty in comparing the two is that mass has no real smallest particle (well there has to be something but it can be darned small) whilst there is such thing as an electric charge, a base unit of sorts.

In comparing the two you need to think of the relative force available fro one charged particle. if the charge is ignored you can determine the force due to gravity, and likewise ignoring the mass figure out the force due to charge. It just so happens in this universe that the relationship between the mass of a charge and the size of a charge (if that makes sense) is such that the force due to the charge is much greater.
to think of it in terms of equal proportions, for the same force to be felt, a much larger corresponding mass needs to be present rather than the a relatively small charge. If however the mass of the smallest charged particles (i.e. electrons or protons) where extremely more dense than they actually are then the force due to gravity could well be stronger.

4. Jul 21, 2009

### mjacobsca

If you believe in string theory, m-theory, or other multi-dimensional theories, gravity is weaker in our experience because while the other forces act only in our 3-dimensional space, gravity acts in 10 dimensions or more at the same time, and is therefore dilluted in our 3-dimensional space. So I don't think gravity is weaker per se. It just appears that way to us.

5. Jul 21, 2009

### maverick_starstrider

Well if we think of the fundamental unit of charge as an electron (or a proton) and we imagine building up a mass of only one of these at a time (i.e. a mass of only electron or only protons) the strength of the electric force due to this mass relative to the gravitational force would be truely immense. If only the slightest fraction of a fraction of a fraction of a percent the negative charge on our planet was not balanced by a corresponding positive charge then the neutrally charged moon would swirl into us within the day.

6. Jul 21, 2009

### jbutcher

OK so I think I'm starting to get it. The gravitational field strength of a proton is significantly weaker than it's electric field strength. That makes sense. But to blandly say 'gravity is weaker than any other fundemental force' is not correct. We just need to clarify the terms of our comparison.

In a way, it's a bit like saying 'gold is cheaper than holidays'. Are we talking half an ounce of gold compared to a month in the seychelles or a ton of gold compared to a weekend in a tent?

I may be drawing this out, but as a physics teacher in a UK school, I feel it's really important that students examine 'facts' critically.

Anyway, a big thank you for your contributions.

7. Jul 21, 2009

### Naty1

yes it is...but it is not necessarily "obvious" as anyone first thinks about it.

If a small simple magnet, for example, can pick up a paper clip off a table then that magnetic force is stronger than the entire gravitational attraction of the earth on the paper clip. Now the magnet is a lot closer to the paper clip than the center of attraction of the earth, so that's not an ideal comparison, but still representative.

another way to think about the relative weakness of gravity is that a single electron and a single proton for example, will usually attract each other even in the presence of a huge source of gravity like the earth. In fact the gravitational force on each, which can be computed, is a tiny,tiny fraction of the electric force of attraction and can usually be ignored. An electron behaves almost the same earth as in free space as it "revolves" around a positive nucleus....although processes ARE imperceptibly slower in a strong gravititional potential.

In other words, as we look around us the strong force, weak force and electric/magnetic forces proceed on their own without much affect from gravity most of the time....so for example the electrons and protons of your skin are not peeled away from your body because the molecular/cellular structures are millions of times stronger than gravity.

On the other hand, gravity can be incredibly powerful, such as in the vicinity of a black hole singularity...there, the unusual concentration of mass creates such a powerful gravitational attraction that nothing can escape, not even light. And such concentrations of gravitational power DO rip the strong/weak/magnetic/electric forces to shreds resulting in a singularity. Even space and time cease to exist.

If gravity were REALLY strong, then the universe would be a single blob of matter all pulled together by gravitational forces instead of all the components we see in the heavens...

Last edited: Jul 21, 2009
8. Jul 21, 2009

### jbutcher

Agreed. So under conditions like this, gravity is stronger than anything else known. If super dense matter like this were the norm rather than the exception then we wouldn't exist, but if we did we would be saying how strong gravity is.

I fully accept the points you make, but the relative weakness of gravity is surely down to the paucity of matter local to us, rather than an intrinsic quality of gravity.

I still maintain that the comparison is fallacious, on the basis that we are comparing the force due to fairly arbitrary units of mass and charge. Sure, in our local universe, the strong nuclear and electromagnetic forces win, and it's good that they do. But elsewhere, gravity wins. As I said earlier, if the unit of mass was the 'Jupiter' rather than the kg, then unit for unit, gravity would fair pretty well. Likewise, isn't it just as valid to talk about what a vast amount of charge an electron has, rather than how strong electromagnetic forces in general are?

The point is a subtle one, but I think it's important.

9. Jul 21, 2009

### Naty1

It's not fallacious, but it's not always perfect either. It is intrinsic for the most part. But arbitrarily units have their effect as well....

If you take an electron and a proton, their naturally opccurring electric charge completely overpowers gravitational foprces between them. by maybe billions. Likewise, two electrons will move apart due to repulsion...

Load the earth up with all the electric charge it will hold and say, the moon, with all the opposite charge it will hold....they will be HIGHLY attracted and crash into each other (real fast) whereas gravity is slowly losing its hold on the two entities....they are moving apart about an ince or two annually and will eventually separate.

Anyway, gravity is cool because it shapes space and time!!!

10. Jul 21, 2009

### DaveC426913

Surely one wants to compare the force of a common unit.

How much gravitational force does a single proton have compared to how much electroweak force or any other fundamental force it has?

11. Jul 21, 2009

### maverick_starstrider

Well no, "super dense" matter is only going to showcase the strength of gravity if it was made of neutral material or painstakingly built by balancing each smallest unit of charge. As i've said, if even the slightest fraction of a percent of that bodies charge has no been balanced (no matter how dense) then electric forces are going to dominate its actions, even when interacting with neutral objects (electric fields induce dipoles). And no it's not a units thing. The strength of the forces is usually compared by calculating the dimensionless (i.e. unitless) coupling constant of either a proton or an electron in which case the electromagnetic coupling constant is 1/137 where the gravitational coupling constand is $10^{-39}$ or $10^{-40}$ respectively. So yes, it's an extremely weak force. That's not a slight. In fact even a neutron for example is really made of quarks (as are all hadrons, neutral or otherwise) and each of those quarks have a fractional charge which would dominate its interaction if not balanced (as it is in a neutron which is made of udd quarks).

12. Jul 21, 2009

### jbutcher

OK, I like the idea of a small percentage change making a significant difference from a once balanced system, so thanks for that, maverick. I can see how the angle I was looking from was seductive but flawed though I was evangelical about it earlier!! I'm now reading up on hamiltonians but remember finding them tough as a 19 yr old. My next trick is finding a way to explain this to an intelligent enquiring A'level student, but that's all part of the fun.

Thank you all for being so patient with a 'newbie'. I hope to post again soon.

Last edited: Jul 21, 2009
13. Jul 21, 2009

### Pupil

I'm still a bit confused, so I did a bit of math to find what would happen if we scaled up the kg and this is what happened:

Let us use a different standard of mass we will call the boopie. We define the boopie as $$1 boopie = akg$$, so we scaled up the $$kg$$ by the factor $$a$$ and will use it in our units. By Coulomb's Law: $$F = k_e *\frac{q_1q_2}{r^2}$$. To switch to our new units, we convert: $$k_e=\frac{9*10^9kgm^3}{(s^2c^2)}*\frac{1 boopie}{akg} = \frac{9*10^9}{a}*\frac{(boopie)m^3}{s^2c^2}$$, thus the new force constant measurement for a charge is scaled down by the factor $$a$$. If we do the same conversion for the gravitational force, we get $$F = 6.67*10^{-11}a*\frac{m^3}{(boopie)s^2}*\frac{M_1m_2}{r^2}$$.

The only difference is that, by converting our mass units from kg to the scaled up boopies, we get an inverse relationship between the factor $$a$$ and the electrostatic force between charges, and a direct relationship between the gravitational force and $$a$$.

So it seems to me that changing the mass standard will result in different measurements of the force constants and thus if you choose $$a$$ to be sufficiently large for your standard unit, you can get a larger number for the gravitational force constant than for the electrostatic force constant.

But wait...If I choose 1 $$kg$$ and 1 C for my charge and mass and plug them in I get $$\frac{6.67*10^{-11}kgm}{s^2}$$ a for the strength of gravity, and $$\frac{9*10^9kgm}{s^2}$$for the strength of the electrostatic force, and if we *then* convert to our new force units measured in boopies meters per second squared we get $$\frac{6.67*10^{-11}kg*m}{s^2}*\frac{1 boopie}{akg}$$ and the same thing for the electrostatic force, so they're both just scaled down by a factor $$a$$! What did I do wrong with all that math at the top?

14. Jul 21, 2009

### maverick_starstrider

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