# How is gravity the weakest force?

1. Jun 18, 2010

### jason177

I have heard a lot about how gravity is the weakest force and after thinking about it for a while, I don't really see why it is. One argument I heard for gravity being the weakest is how the value for G in F=G*m*m/r^2 is so much lower than the value of k in F=k*q*q/r^2 but considering how the units on k and G are different, I don't see how that is a valid point. For example if you were to change the units on k into Nm^2/(picoCoulomb^2) the value of k would be a lot lower than the value of G. Another argument I heard was how the electrons in objects such as a chair are able to repel each other and fully overcome the downward force of gravity. But when you consider how close the electrons are to each other compared to how far the object is to the center of the earth and how the force is inversely proportional to the square of the distance, it doesn't really show which is stronger. And again, the units are different so unless there is a way to compare coulombs to kilograms, I don't understand how one can be declared stronger than the other. So if someone has a better way of explaining it, I would greatly appreciate it.

2. Jun 18, 2010

Think about two electrons. They will attract each other by the force of gravity, and they will repel each other by the electric force. Which force is stronger? Calculate it out and see which one wins.

3. Jun 18, 2010

### Naty1

Post #2 is one good way to think about it....you can also considers a paper clip sitting on a table. It sits there because of the (huge) earth gravitationally attracting it. Yet a small magnet can easily move or lift it....

In general the electromagnetic force is (many) bilions of times stronger than gravity. That's why a modest battery potential, for example, can move loosely bound electrons in a conductor along a wire...otherwise gravity would lock them in place.

4. Jun 18, 2010

### Feldoh

Just for comparison sake take two electrons 1m apart:

$$F_{grav} = (6.67*10^{-11} N m^2 / kg^2)(9.11*10^{-31}kg)^2 / (1m)^2 = 5.54*10^{-71} N$$

$$F_{elec} = -(8.99*10^9 N m^2 / C^2)(1.60*10^{-19} C)^2 / (1m)^2 = -2.30*10^{-28} N$$

4*10^42 times larger

5. Jun 18, 2010

### Nabeshin

Last edited by a moderator: Apr 25, 2017
6. Jun 19, 2010

### Phrak

I'm not convinced. Why is gravity 'weaker'? Both are, in the limit of small spatical curvature, inverse square. I can compare a neutron star with one one unit of electric charge, and say gravity is 'weaker'.

7. Jun 19, 2010

### stevenb

I think the basic idea is that charged particles always have mass. The only time gravity can beat electromagnetic force is when positive and negative charges cancel out.

8. Jun 19, 2010

### cragar

Or maybe between two neutrons or photons ,

9. Jun 19, 2010

Is it possible to have hypothetical particle, that has non-zero charge and mass, such that the gravity beats Coulomb force?

10. Jun 19, 2010

### cragar

A neutron has a magnetic field and mass , but i am not sure if the gravitational force of two neutrons is bigger than their magnetic attraction . Because i think the magnetic moment is pretty small .

11. Jun 19, 2010

### stevenb

That is a good point. To me, neutrons are not fundamental particles and can be viewed as having charges that cancel. Also, the photon has zero rest mass, but it does have energy and hence gravitational interaction.

Another example is the Z-boson which has zero charge, but its rest mass about 180000 times that of the electron.

I think the smallest known nonzero charge is 1/3 of the electron charge, so it is instructive to calculate how much mass is needed to counteract force from this charge.

12. Jun 19, 2010

### stevenb

Maybe someone can double check me because I tried doing this calculation on my cell phone while having coffee at the donuts shop.

I came up with a mass of 0.62 micrograms (or the mass of 0.37 billion billion protons, yes that's two billions I wrote) to equate to 1/3 of the electron charge.

I think this is what people mean when they say that gravity is a very weak force.

EDIT: Oops, I slipped a decimal point and needed to correct my original numbers.

Last edited: Jun 19, 2010
13. Jun 20, 2010

### jason177

I guess I should have been more clear, the problem I am having with this is mainly how there is no way to compare mass to charge. So in the first example with the 2 electrons, its the mass of the electrons that produces the gravitational force but the charge is what causes the electric force, so since the two forces are being produced by different things, I don't see how that can be used to show which is stronger.

14. Jun 20, 2010

### Phrak

Sooner or later someone should show up talking about coupling constants...

15. Jun 20, 2010

Staff Emeritus
It's an experimental fact that a tiny magnet's force can overcome the gravitational force of an entire planet.

One could explain this by saying gravity is weak. One could also explain this by saying an electron carries a great deal of charge. There's really no difference, as only the product of strength and charge (mass is the "charge" of gravity) is measurable. However, it's convenient to work with conventional units, and in these units, the strength of electromagnetism is 1020 times larger than gravity.

16. Jun 20, 2010

### K^2

The classification of the 4 fundamental forces by "strength" comes from atomic physics, where only forces on atomic particles are considered. It is plainly obvious that two protons are going to interact most strongly with a strong force, at sufficiently close range, and the weakest with gravitational force, at pretty much any range.

As far as comparing gravitational constant with electrostatic one, I agree. These aren't quantities that should be compared.

Electrostatic and strong forces can be further compared on the basis of elementary charge, but there is no such thing for gravity as far as I'm aware.

17. Jun 20, 2010

I agree,the forces are there as a result of different things.The statement that one of the forces is bigger than the other only makes sense when you put it into context as with some of the examples being discussed here.

18. Jun 20, 2010

### stevenb

You were perfectly clear. Also, the various responses make it clear that there is a way to compare mass to charge by looking at the charge and mass of fundamental particles. The fact two protons repelling due to charge can be equated to the gravitational force of particles with a billion billion protons and nuetrons does have physical meaning.

Actually, your question is the exact one we all ask when we first encounter this concept of comparing forces. Perhaps the motivation for teachers making the comparison is to turn the tables on our natural instinct that gravity is the strongest force.

19. Jun 20, 2010

### vandegg

The reason we rank the forces by strength has to do with much more complicated concepts than a magnet picking up paper clips. This though is unfortunately the answer that most teachers seem to give when asked. I would like you to expand your comparison of gravity to the weak and strong forces, which are both considered even stronger, and tell me how that comparison continues to hold.

20. Jun 20, 2010

### stevenb

I don't feel qualified to answer that question.

In my mind it is easier to compare EM and gravity force because they both fall off as a square of the radial distance. Yes, there is the issue of units, but if we are clear in defining how the comparison is made, we can get something useful out of a comparison.

It's clear that the nuclear strong force is strongest at close range, but both EM and gravity are stronger at long range. So, it seems to me this is another example of how the conditions of the comparison must be made clear.

I expect that Phrak is correct that quantum field theory can provide a normalized comparison, but I'm not sure how gravity is brought into that since gravity has not been unified with QFT yet. In any event, that type of comparitive description will not be understood by everyone.