Center of Gravity

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The gravitational pull of an object always points toward the center of that, but what makes something an object? If you cut an object in half would each half of the object have a gravitational force toward its center of mass, or would the force point toward the center of mass of the original object?
 

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DaveC426913
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The gravitational pull of an object always points toward the center
This is only incidentally and approximately true.

To be perfectly accurate, the gravitational pull of an "object" is the sum total of the gravitational pull of each particle in it. The particles do not "know" that they are part of an "object".

To correctly determine the actual gravitational force on any given target, you would calculate the distance and mass to every single particle in your "object" and then sum them all.
 
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Stephen Tashi
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The gravitational pull of an object always points toward the center of that
There is a distinction between "center of mass" and "center of gravity". "Center of gravity" is defined in terms of torques on an object due to a uniform gravitation field, rather the gravitational pull the object exerts on other objects. "Center of mass" is not defined in terms of gravitational pull, although near the surface of the earth, balancing an object is a useful way to investigate both its center of mass and center of gravity.

but what makes something an object?
That is an arbitrary decision. The laws of mechanics are formulated in terms of "systems". They apply to any system you care to consider. When you consider a system, certain aspects will be "internal" to the system and certain aspects will be "external". When you change the system you consider, you change what things are external and what things are external. This changes the meanings of variables (an usually the values) of variables that you use in equations describing the system.

If you cut an object in half would each half of the object have a gravitational force toward its center of mass, or would the force point toward the center of mass of the original object?
If you leave the halves together in their original orientation, gravity would point to where it pointed before you cut them. But there need not be a single point that gravity points toward. Perhaps you are thinking of a uniform spherical object.
 
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jbriggs444
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The gravitational pull of an object always points toward the center of that, but what makes something an object? If you cut an object in half would each half of the object have a gravitational force toward its center of mass, or would the force point toward the center of mass of the original object?
The gravitational attraction of an object does not always point toward the object's center. An object's center of mass and its center of gravity (with respect to a particular gravitational field) will not, in general, coincide.

You can fool yourself into thinking that the force of gravity will always point in the direction of the center of an object if you restrict your attention to objects that are suitably symmetric. But even this much will fail to hold in general.

As DaveC426913 points out, it does not matter how you slice and dice an object. Its total gravitational attraction will be unchanged by the slicing and the dicing.

The "center of gravity" of an object is defined as the point where, if all of the object's mass were placed there, it would experience the same gravitational attraction (with respect to a particular gravitational field) as the entire object actually does experience. It is not an intrinsic attribute of the object. It is an attribute of the object in relation to a particular gravitational field.
 
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DaveC426913
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Frankly, I think you guys are overcomplicating the answer.

The moment the OP acknowledges that an object's gravity is the sum total of the gravity of its individual particles, he has the conceptual tools required to solve any configuration of object(s) he can imagine, without any further confusion about centre of mass or centre of gravity.
 
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