The Attractive Forces of Non Spherical Bodies on Superphysics

The Attraction of Bodies

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 85 Theorem 43

If a body be attracted by another, and its attraction be vastly stronger when it is contiguous to the attracting body than when they are separated from one another by a very small interval; the forces of the particles of the attracting body decrease, in the recess of the body attracted, in more than a duplicate ratio of the distance of the particles.

The Attraction of Bodies

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 86 Theorem 44

If two bodies similar to each other, and consisting of matter equally attractive, attract separately two corpuscles proportional to those bodies, and in a like situation to them, the accelerative attractions of the corpuscles towards the entire bodies will be as the accelerative attractions of the corpuscles towards particles of the bodies proportional to the wholes, and alike situated in them.

Finding the orbits from the focus given

Mon, 01 Jan 0001 00:00:00 +0000

PROPOSITION 88 THEOREM 45

If the attractive forces of the equal particles of any body be as the distance of the places from the particles, the force of the whole body will tend to its centre of gravity ; and will be the same with the force of a globe, consisting of similar and equal matter, and having its centre in the centre of gravity.

Finding the orbits from the focus given

Mon, 01 Jan 0001 00:00:00 +0000

Proposition 89 Theorem 46

If there be several bodies consisting of equal particles whose forces are as the distances of the places from each, the force compounded of all the forces by which any corpuscle is attracted will tend to the common centre of gravity of the attracting bodies; and will be the same as if those attracting bodies, preserving their common centre of gravity, should unite there, and be formed into a globe. This is demonstrated after the same manner as the foregoing Proposition.

Finding the orbits from the focus given

Mon, 01 Jan 0001 00:00:00 +0000

If a solid be plane on one side, and infinitely extended on all other sides, and consist of equal particles equally attractive, whose forces decrease, in the recess from the solid, in the ratio of any power greater than the square of the distances.