Talk:Center of mass

"The centre of mass of an object is the point through which any plane divides the mass of the object in half."

Are you sure this is true? If the center of mass is a weighted sum of all the points in an object, and the distance is part of the weighting, then the plane would not divide the mass in half, but the mass times distance. Later on in the page, the Jupiter-sun system is mentioned. This can be viewed as one object without loss of generality (think of the matter connecting them approaching zero mass in the limit). The center of mass is outside of the sun, so a plane perpendicular to the line between the objects would certainly not divide the mass of the object in half! I think I will wait for some comment and then remove the sentence from the article.

Other than that, it looks like a good article. It has a lot of good examples.

Cos111 04:38 24 Jul 2003 (UTC)

I agree, I changed it. - Patrick 08:54 24 Jul 2003 (UTC)

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For mass that is distributed according to a continuous, nonnegative density <math>\rho(\mathbf x)\ge0<math>...

We are not likely to encounter substances with negative density, but if we did, these integrals could still be evaluated and the result would be physically correct.

It seems to be a reminder that density is not negative, and also a clarification that we can integrate over the whole space, not just the masses, since we allow density to be zero. --Patrick 01:00, 23 Feb 2004 (UTC)

Also, ρ doesn't have to be continuous to be integrable. In fact, being composed of point masses (quarks and electrons) matter is never distributed continuously. More to the point, ρ is often discontinuous at the interface between two materials. A better formulation might be:

For a physical body with mass distribution <math>\rho(\mathbf x)<math>...

If the Earth-Moon distance is rounded to one significant digit (400000 km), it's silly to come up with 4 significant digits in the answer (4877 km). I call this 'calculator blindness'. I'm not fixing it because the Earth/Moon example is duplicated in the existing article on barycenter. Since that term seems to be in use primarily in celestial mechanics, wouldn't it be more logical to move all the astronomy stuff to the barycenter page?
Herbee 19:18, 2004 Feb 22 (UTC)

Example removed from page

I removed the following example from the page:

• To calculate the actual motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids, etc. of the solar system. The influence of each is approximately proportional to the product of mass and distance. That of Jupiter is largest, its large mass more than compensates its smaller distance to the Sun than several other planets. If all the planets would align on the same side of the Sun, the combined center of mass would lie about 500,000 km outside the Sun surface.

The first sentence of this example is incredibly vague, and doesn't apparently have to do specifically with center of mass. Because of this vagueness, the second sentence is inherently confusing: the influence on center of mass is proportional to distance, while the gravitational influence is inversely proportional. The same confusion holds in the third sentence with "smaller" versus "larger". Dbenbenn 10:21, 2 Jan 2005 (UTC)

I have clarified it, but to say things accurately makes the sentences somewhat complicated. Since you seem to understand the matter, you could have improved the formulation instead of just deleting everything. You are welcome to further improve the formulation.--Patrick 00:00, Jan 3, 2005 (UTC)