What is the difference between center of mass and center of gravity?

What is the difference between center of mass and center of gravity?

These terms seem to be used interchangeably.

Is there a difference between them for non-moving object on Earth, or moving objects for that matter?

• The Wiki link is very much satisfactory..! Jan 13 '13 at 13:10
• Of course these are not to be confused with "center of momentum," the rest frame of which is sometimes confusingly called the "center of mass frame."
– user10851
Jan 13 '13 at 14:31
• In a constant gravitational field (a flat, infinitely large earth would do), they would be the same... But in the case of the earth, the cog would actually be a bit lower than the com. Jul 4 '13 at 4:20

The difference is that the centre of mass is the weighted average of location with respect to mass, whereas the centre of gravity is the weighted average of location with respect to mass times local $g$. If $g$ cannot be assumed constant over the whole of the body (perhaps because the body is very tall), they might (and generally will) have different values.

I don't see an immediate connection with movement though.

• As an example of non-constant $g$ (and a "very tall body"), I remember a physics professor explaining that the center of gravity in the Empire State Building is about a meter lower than its center of mass (because of inverse-square law gravity). Feb 11 '17 at 10:31
• Nicely explained, but Can you add some pictures or mathematical form, in your formula. Dec 2 '20 at 5:35

Centre of mass & gravity coincides until they have unifrom gravitational field. The time uniform gravitational field is lost we rather consider centre of mass than centre of gravity. However, they both're interchangeable.

Quoting from tha wiki page:

Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish.

That means that for any rigid body, the two points are the same, because you can model rigid bodies in free fall as if gravity acted only on the center of mass, and forces on the center of mass make no torque.

• This is wrong. They are only the same if the gravitational field is not varying over the extent of the body. Jan 13 '13 at 16:39

Center of mass is actually the integral of mass density. Meanwhile, center of gravity is the integral of force of gravity!

• In both cases you have described the zeroth moment of something when you should mean the first moment. However, the distinction you in terms of what quantity you want to take the moment of is correct. Apr 25 '13 at 0:07