- #1
Dirkg
- 13
- 1
I am having a problem with visualizing why Newton's Law of Universal Gravitation (NUGR) holds true when objects get close together. F=Gmm/r^2 makes sense for planets that are far away because each object can be treated as a point with gravity acting at the center of each object. For a person standing on the surface however, there is a significant portion of the mass of the Earth that is not directly below the person. Of course the mass is evenly distributed on each side, so the direction of the force is straight down, but only the vertical components of each part of the mass of the sphere is acting downwards, the horizontal components will all cancel out. If NUGR holds true for each portion of the planetary mass then the resultant force vector will calculate to a lower magnitude than the whole Earth because of the horizontal forces cancelling out. I know that I must be visualizing something wrong, but I don't see it. Before I started thinking about this, I just accepted that gravity acts from the center of the planet because the sum of the gravitational force from every point within the sphere adds up to the force we feel as if it is actually coming from the center. If that is the case then shouldn't NUGR take into account how much of the mass is not directly below?