Chapter 2 of Kleppner & Kolenkow's An Introduction to Mechanics reads as follows –
Newton's Laws describe the behavior of point masses. In the case where the size of the body is small compared with the interaction distance, this offers no problem. For instance, the earth and sun are so small compared with the distance between them that for many purposes their motion can be adequately described by considering the motion of point masses located at the center of each.
Consider a system consisting of a block kept at rest on a table. Assume that friction is neglected. When drawing a force diagram for such a block, we assume it to be a point mass. (Also see: Section 2.4 of Kleppner & Kolenkow's book… Just to mention that such a step is followed in the book itself.) However, it doesn't seem to me that this assumption is valid, as the interaction distance between the block and the table is so small as compared to their sizes.
Then why is the point mass approximation valid in such a case?
Note: This chapter has not generalized Newton's laws to describe rigid bodies yet. So it would be great if you could answer my question without any reference to that (of course, if possible!).
Best Answer
I think you are comparing two pretty different cases. Motion of the Earth with respect to the Sun (and vise versa) is different from motion of a block on a table with respect to it. In the former, both of the Earth and Sun experience rotational motion and cannot be assumed as a particle without approximation error. But in the later, the block doesn't experience rotational motion and thus can be exactly substituted with a particle in the COM and with the same mass.
In the first case (Earth and Sun), we neglect rotational motion affects. But in the second case (block), we neglect nothing because there is no affects due to rotational motion.
I think the book are talking about approximation not modeling.