# Does gravity act equally on all points or just at the center of mass? [closed]

If every mass has an equal force of gravity — on, say, a circle — then wouldn’t gravity act towards every point equally and not towards the circle? Do we just say that gravity acts at the centre of mass to make calculations simpler? Also, is this true for every object… even those that are unequal and not symmetrical? Or is gravity not an intrinsic property of all matter and energy? Please let me know if this question makes sense

Of course if you have an object under gravity than gravity acts on each part of the object. E.g. if you are at the gym and lift weights: you have 2 masses on each and of a stick. Since both are equal then the center is in the middle. But when you lift this then you see the bar in the middle bends because the force on each of the weights at the end. So the forces create some inner tensions in the object. If the object is not rigid it will deform.

"Do we just say that gravity acts at the centre of mass to make calculations simpler?"

Yes. This makes calculations much simpler and this is why people do it. But it is not just an approximation but gives the right results:

"Also, is this true for every object… even those that are unequal and not symmetrical?"

Yes. You can define the center of gravity for every object. Not just symmetrical ones. For the symmetrical ones it is just easier to do. But you can calculate the center of mass for any object. You can convince yourself of this in 2 ways.

1.) you can imagine taking the object and balancing it on an edge: You will always find a position where the left and the right side pull equally strong. Then your center of mass is over this edge. Or you tie your object to a string and lift it up: the center of mass will be in the line of the string. With this method you can find the center of mass with an experiment. Balance it 3 times around different axes or lift it 2 times tied on different ends and you know where your center of mass must be. From the point of view of the string: the object looks like a point in the center with the total mass there.

2.) You imagine that your object is built from smaller objects. Initially maybe 2 points with mass $$m_1$$ and at distance $$l_1$$ and a mass $$m_2$$ at a distance $$l_2$$. The total mass of your object is then the sum of these 2: $$m = m_1 + m_2$$ . Now you calculate the momentum of these 2 (think of kids on seesaw ): $$m_1 \cdot l_1 + m_2 \cdot l_2$$ Now you replace the object with one where you imagine the mass in that one point: $$m \cdot l = m_1 \cdot l_1 + m_2 \cdot l_2$$ In order to get the same momentum you need: $$l = \frac{m_1 \cdot l_1 + m_2 \cdot l_2 } { m_1 + m_2 }$$

In case your points are the same mass then the resulting length would be in the middle, or the average of the 2.

If you move your pivot point to l then you are under the center of mass. And with the same procedure you can build up ever more complicated objects from simpler ones. So saying "every object has a center of mass" is kind of similar to saying: you can always calculate an average of numbers.

"Or is gravity not an intrinsic property "

The property here is "mass". Each mass causes gravitation on other objects. And mass is what is influenced by gravity from other objects. And then mass is what resists acceleration.

• So would that mean everything that has mass will have gravity as mass causes the gravitational force and since mass and energy are the same would that mean even energy will have gravitational properties Commented Feb 22 at 8:34
• In terms of relativistic mechanics it makes more sense to think of mass bending spacetime. The other post here points that out. E.g. if a ray of light is bent near a heavy star then it makes sense to think of it as it following a straight line within a "deformed" space-time...
– mond
Commented Feb 22 at 9:31

The question is a bit vague but if you dealing with newtonian gravity, then gravity can be thought of as a field. Field is basically an imaginary concept such that every point in space has a vector associated with it such that if we keep a mass on the point, it suffers a force or acceleration.

What maybe you are trying to say is that "gravity acts at the centre of mass to make calculations simpler" is concept of centre of mass, and yeah you are write. But it depends on cases to cases, especially when objects are very near to each other such that different parts of body experiences different forces (Look up tidal forces by moon on earth). You can imagine objects as points when distances are very large, such that dimensions of object are negligible.

This was newtonian gravity, and if you are talking about general relativity, its entirely different ball game, as gravity is not exactly though of as a force but as a curvature in spacetime. I hope this helped.

Yes, gravity indeed acts on every point separately. But there are some useful simplifications that you can often make.

Firstly, if your mass is perfectly spherically symmetric we can apply Newton's Shell theorem. This theorem says that a spherically symmetric mass produces a gravitational field as if all the mass were concentrated at a point located at its center. This means that the result of all the little gravitational forces produces by the earth sum up to produce a field that would be the same if all the earth's mass were located in a point. The earth is not perfectly symmetric though. For example, the interaction of the moon and the earth's oceans causes the moon to slowly move away from the earth.

Secondly, for objects on the surface of the earth you can usually assume the gravitational field is constant. The gravitational force varies as you move up or down. It even varies in direction if you travel far enough on the surface of the earth. But the distances on earth so small compared to the length scale of gravity that you almost never see it. As a result of this "constant" gravity, you can act as if gravity only acts on the center of mass of an object. Which is nice, because it greatly simplifies calculations.