# Does Gravity Depend on ratio of mass between objects?

1. Dec 10, 2005

### sigh hens

I'm no physicist but this really doesn't make sense to me.

Simple newtonian physics says that gravity is dependant on mass and that an object with more mass will have more gravity, right?

well here's an equation I'm sure most of you are familiar with...

F = G*m1*m2/r^2

heres my problem...

m1 = 20
m2 = 1
r = 10

then F will = .2G

another example...

m1 = 19
m2 = 2
r = 10

then F will = .38G

In each example the mass of m1 and m2 add up to 21 and yet the gravitational force (F) is different. What is the rationale behind this? I thought all objects with the same mass had the same gravitational force no matter how you diveded them (assuming the same r value).

2. Dec 10, 2005

### dicerandom

The issue is that gravity really produces an acceleration, not a force. You can easily see this by keeping m1 the same, but changing m2. Then if you use F=ma (m=m2 in this case) you'll see that it's always true that a=G*m1/r^2. I think the statement "all objects with the same mass had the same gravitational force" would refer only to two objects of identical mass which are an identical distance away from an object of a particular mass.

3. Dec 10, 2005

### sigh hens

so is there any real significance to the fact that F is different even though the mass of m1 and m2 in both examples add up to the same?

I understand that gravity = a = G*m1/r^2 I think I am more confused about what F is really representative of.

4. Dec 10, 2005

### Integral

Staff Emeritus
Gravitational force is proportional to the product of the masses. Why do you think that the sum of masses is relevant to anything?

5. Dec 10, 2005

### sigh hens

the more mass, the more gravity. I thought it would be logical to extend this so that.... the more mass, the more gravity, the more gravitational force. I think I'm just lost as to the true meaning of Fgrav.

I don't really understand how something can have more gravity but less gravitational force.

6. Dec 10, 2005

### Danger

Sigh, I'm wondering here if you're mistaking the gravitational concentration for force. Since gravity is measured from the centres of the masses involved, a dense body will have a higher local field than a less dense one. As an example, a 5 solar mass star that collapses into a black hole will still have the same original gravity field (adjusted for the mass lost during the transition), but you can get so much closer to the centre of the BH that the gravity you feel is incredibly concentrated. With the original star, you'd get fried a few thousand times farther away. (I'll leave the rest to Space Tiger or similar.)

Last edited: Dec 10, 2005
7. Dec 10, 2005

### KingNothing

Don't make it more complex than it is. Gravity and 'gravitational force' are the same thing.

Imagine a single pebble on the surface of the earth. It does not weigh very much, correct? In other words, it doesn't have a very large 'gravitational force' with the earth, even when held 1 inch above the surface.

Now imagine splitting the earth in two equal halves and trying to hold them 1 inch apart...the force would be tremendous. In both examples, the total mass involved is the same.

Last edited: Dec 10, 2005
8. Dec 10, 2005

### Danger

Excellent analogy, King. I wish that I'd thought of it. (Well, I'll steal it at the earliest opportunity.)

9. Dec 10, 2005

### Tide

Sigh,

Absolutely! But your example isn't talking about an object; it is about two objects. If you increase the mass of either object in your example then, clearly, the gravitational force it exerts increases, i.e. you have "more gravity."

The expression of Newton's Law of Gravity that you wrote shows the force on a second object due to the gravitational pull of the first object. That force depends on both the mass of the "gravitating" object and the mass of the object being acted upon by the gravitating object. Note that the magnitude of the forces each exerts on the other are the same in accordance with Newton's Third Law of Motion (action-reaction).

In your example, you increase the mass of one object (which "increases its gravity") but you decrease the mass of the other (which reduces the force acting on it). You succeeded in increasing the strength of the gravitational field but gave it a smaller mass to act on.