> 12 replies to my question is not bad but the integral is actually about what > the gravity force is to a spherical mass distribution compared to a point > mass. The so called center of gravity can not be used as a center of gravity > since matter closer to a body attracts more than what the remote parts do.
Hi David, I'm sorry that your thread was hijacked. I suppose the answer to your initial question was "No." :-) > > How big can this effect be? Not very big for d >> r, d being the distance between bodies and r the radius of the more massive body. It could be interesting to solve the integral, to precisely see the magnitude of the effects at different distances, but at first sight, the effects must follow an inverse square law also. So, for a given distance d, they will have a 1/d^2 importance. It may also be the case that the closer masses compensate the loss of the farther masses, and then, for the spherical case, the approximation to a point mass is perfectly valid; provided that the distance is greater than the radius of the body, and that the density of the body is homogeneous. > > Can anyone solve the integral? I haven't even tried, yet. Can Maxima solve > it? > > David >
