# Gravitational mass & inertial mass

1. Dec 8, 2006

### luv_phy

Hey, first time here. I'm currently reading up on Physics, preparing for a selection test by myself. I need some help in understanding Newton's gravitational mass and inertial mass. Are they different? I read that there are some difference, and these masses ARE slightly different. Any reason why? I also met an interesting question.

"Our universe is expanding, which means that the large masses in it are moving away form each other. One theory states that this expansion is due to the gravitational mass of an object being very slightly different from its inertial mass. Which mass would have to be larger in order to produce an expanding universe? Justify ur answer"

2. Dec 8, 2006

### dontdisturbmycircles

I don't know why you would choose the forum feedback section to post this in... :tongue2: but, no they are not the same. One is weight, one is mass. Mass never changes, but your weight (I wouldn't call it gravitational mass) (expressed in newtons) changes according to the strength of the gravitational field you are in. Mass can be measured in inertial mass since even if truck is "weightless" in space, you would still have to do work on it to move it, hense inertial mass.

3. Dec 8, 2006

### vanesch

Staff Emeritus
Nono, this is not what is understood by "inertial" mass, and "gravitational" mass. Gravitational mass is not "weight", which is what you are talking about.

There are *in principle* 2 different kinds of mass (actually, 3, but hey, let's keep it simple).

There is the mass "m" in Newton's second law: m.a = F, or, in other words, the m in the formula for momentum: p = m.v. This is "inertial" mass. It is the constant of proportionality between the applied force (supposing we know that somehow, and we are not running in circles, but that's another debate...), and the acceleration of the object. You need this m in any form of dynamics. For instance, imagine that in the world, there is only Coulombic interaction, then the force between two particles would be given by:

F = q1.q2/(4 pi eps0 r^2), and if you fill in this force into Newton's equation, you have to do: m.a = F. The m in that equation is the inertial mass, and the q1 and q2 are the electric charges of the particles.

But Newton also discovered a specific interaction: gravitation. The force of gravitation, according to Newton, takes on a similar form as the one for electrostatic attraction:
F = -G.M1.M2/r^2

Here, G is Newton's gravitational constant (like the 1/4 pi eps0 for electrostatics), and there's a minus sign which makes it opposite in action to electrostatics. M1 and M2 are the "gravitational charges" of the two bodies.
This "gravitational charge" is what one calls the "gravitational mass". Now, one isn't used to say that, because of a principle:
"the gravitational charge equals the inertial mass"
In other words: M1 = m1.
The number entering in the formula for gravitational interaction, M1, is the same number, than m, the number that enters in Newton's second law, m.a = F

This didn't need to be so, in Newtonian gravity. But it is experimentally observed to be so. It is called the principle of equivalence. If this principle holds, then there's no need in giving different names to M1 and m, and we call it simply "mass".

The principle of equivalence is the corner stone of Einstein's general relativity, because Einstein realized that, if inertial and gravitational mass are the same, that the "force of gravity" can be an entirely geometrical effect (and not a genuine force), because no property of the object proper is needed to determine the trajectory (which can hence be a "bending of spacetime" itself, and not simply a trajectory of a specific object, related to its properties).

EDIT: as far as I know, no deviation from the principle of equivalence has ever experimentally been observed...

Last edited: Dec 8, 2006
4. Dec 8, 2006

### Chi Meson

Adding to what vanesch has said:

it is because of the equivavlence of gravitational and inertial mass that the acceleration due to gravity is equal to the gravitational field strength.

When you learn more physics, it becomes more and more bizarre that two completely different phenomena (gravitational attraction and resistance to change in motion) should be quantified by the same characteristic.

5. Dec 8, 2006

### turbo

There is a project underway at CERN to test the weak equivalence principle by comparing the properties of cold neutral antihydrogen to that of hydrogen.
http://athena.web.cern.ch/athena/

6. Dec 8, 2006

### luv_phy

ok. thanks alot. but now. 2 qns.

What's the third type of mass?
Can u answer my 'interesting question'?

I still hv some difficulty understanding gravitational mass. it says in my book, that newton came out with the theory of gravity, which says that any object with mass produces a force of attraction which acts on other masses.
I dun understand how, mass/having a mass/whatsoever can produce a force of attraction. And how does this force of attraction 'act on other masses'?

7. Dec 8, 2006

### luv_phy

Also, Vanesch said:
"Here, G is Newton's gravitational constant (like the 1/4 pi eps0 for electrostatics), and there's a minus sign which makes it opposite in action to electrostatics. M1 and M2 are the "gravitational charges" of the two bodies."

1. Why do we now have 2 bodies here? isnt this a simple matter of measuring the gravitational mass of one body/object?
2. Is 'gravitational charge' literally a form of charge? like positive charges..? i know i may sound stupid, but i really dun understand how it links to inertial mass.

Pardon me..

8. Dec 8, 2006

### Chi Meson

Don't worry about not understanding "how" and "why" gravity works.

Newton didn't understand why either. We still aren't that sure either. There are two explanations, both of which are very diificult to explain quickly in a forum. The two camps of "why" are: Einstein's theory of General Relativity, and Quantum Mechanics.

Both seem to work (as far as prediction outcomes), and Newton's Law of Universal Gravitation can exist within either of these theories, but strangely, the two theories don't seem to fit together nicely (yet).

9. Dec 9, 2006

### vanesch

Staff Emeritus
Well, "gravitational mass" can come in principle in two forms: passive and active. If you have a body A and a body B, then the force on body A by body B is given by F_A,B = - G M_A M_B/r^2

Here, M_B is the "active" partner (the one generating the force), and M_A is the passive partner (the one undergoing the force). M_B is the "amount of generation of gravitational interaction", and M_A is "the amount of sensitivity to gravitational interaction". The two masses enter in the formula a priori for different physical reasons.

However, if we want action=reaction, then we need to have that, for a body, active and passive gravitational mass are the same.

Do you understand electrostatic action any better ? Do you have difficulties with electrical charges which attract or repulse other charges ?

10. Dec 9, 2006

### dextercioby

The equivalence principle is a cornerstone in nonrelativistic mechanics as well. The classical theory of planetary motion (i.e. the Kepler problem of gravitostatics) postulates the equality between the gravitational mass and the inertial mass.

Daniel.

11. Dec 9, 2006

### devino

Is it wrong to think of inertia's resistance to motion a delay in time? As gravity attracts an object the inertia resists the motion creating a time delay in the acceleration. The greater the inertial mass the greater the time delay in any change of motion.

12. Dec 9, 2006

### vanesch

Staff Emeritus
I don't think it is a strict requirement. In fact, a central potential in -1/r is all that is needed for the Kepler problem. Of course, certain simplifications in coefficients might not happen that way, but I don't think that the overall approach is affected: the ellipse form of the orbits, as well as the "law of the areas" remains in place. However, the third law will now include a ratio of gravitational over inertial mass.

13. Dec 9, 2006

### Kurdt

Staff Emeritus
Just to add if the OP is interested in going a bit further. The equivalence principle as you may have gathered is very important in many areas of physics, but more recently its been thrust into the spotlight because it could shed light on which direction to take in the future. As was mentioned earlier there are two theories that further Newton's discovery of gravity, one being general relativity and the other side of the fence are several quantum theories. Also mentioned was the lack of ability to resolve these two different approaches toward gravity.

General relativity has as one of its postulates the equivalence principle (it even neatly explains how the two masses are the same in simple thought experiments). On the other hand quantum theories tend to show a discrepancy between gravitational and inertial mass at very low levels (~1 part in 1018). These levels are far beyond the range of previous tests of the equivalence principle. So new tests are being designed to try and reach those sensitivities and see if General relativity is the way forward to describe gravity or whether quantum theories are the future of gravitational physics. One such test is STEP (Satellite Test of the Equivalence Principle) and there is a fair amount of information on the web site that you can find by googling.

14. Dec 8, 2009

### Agatino

Last edited: Dec 8, 2009
15. Dec 8, 2009

### TurtleMeister

Newton's universal law of gravitation assumes that active gravitational mass is equivalent to inertial mass (and passive gravitational mass). If they were not, then there would be a violation of the conservation of momentum. That is not to say that a non-equivalence is impossible, just that Newton's laws of motion (as they are written) do not support it.

The equivalence of active gravitational mass has only been tested to a sensitivity of 5x10-5 (L. Kreuzer in 1966). Current torsion balance experiments far exceed this sensitivity. New experiments are much needed.

Unfortunately this experiment does not address the question of the equivalence of active gravitational mass.

16. Dec 8, 2009

### TurtleMeister

ah, I just noticed that this is an old thread.

Welcome to PF Agatino. It would be best to start a new thread for your question rather than posting in an old one. As you can see, it can cause confusion. Anyway, Cavendish made use of active and passive gravitational masses in his experiment. Passive gravitational mass is what causes your weight scales to deflect when you stand on them. It is the response of an object to the gravitational field of another object. Active gravitational mass is the gravity that an object (such as the earth) produces. Inertial mass is the resistance to change in motion.

Last edited: Dec 8, 2009
17. Dec 8, 2009

### Galap

1. Well, we can measure the inertial mass to determine the gravitational mass, because they have experimentally been shown to have the same value, but you cannot directly determine the gravitational mass without the presence of more than one body, because objects only show the property of gravitational mass in the presense of a gravitational field.

2. Yes and no. It works the same as electrical charge mathematically (except the different constant), but unlike electricity, where unlike charges attract and like charges repel, like gravitational charges attract and unlike ones repel. All matter you see around you has positive gravitational mass. You can imagine an object with Negative mass. Logically (and mathematically) it would be repelled by the earth's gravity. There is some debate over whether or not antimatter has negative gravitational mass.

Inertial mass, as has been said above, ends up being essentially a completely different phenomenon which ends up having the same value as gravitational mass. A demonstration of the difference, however, would come if antimatter ended up having negative gravitational mass. It would however have positive inertial mass (correct me if I'm wrong, but I think negative inertial mass for antimatter would violate CPT, right?), as opposed to a negative inertial mass, which would yield the quite absurd sounding result that a force applied on such an object would result in an acceleration opposite the direction of the applied force.

18. Dec 10, 2009

### Agatino

Thank you so much, TurtleMeister, for the warm welcome and reply to my question. When I tried to find information about initial mass and gravitational mass I found this thread and when I read Cavendish's experiment I found that to calculate the Earth's mass and density (then people used his results to calculate G) Cavendish used inertial masses. I know well that initial mass and gravitational mass are equal but my wonder is if at Cavendish's time people already had the concepts of inertial mass and gravitational mass or not. That's what I really mean to question and that's why I decided to post my question in this thread to save the forum's resources.

19. Dec 10, 2009

### TurtleMeister

My feeling is that physicists must have understood the concept at that time, but it appears that it was not specifically mentioned in any publications prior to the twentieth century.

From "Concepts Of Mass In Physics And Philosophy by Max Jammer":

20. Dec 11, 2009

### Agatino

Ok, thanks Turtle for the information!