Robert Hatch

1. Every body persists in its state of rest or of uniform motion in a straight line, except or until that state is changed by some impressed force.
2. The force acting on a body is numerically equal to the rate of change of momentum of the body, and the rate of change of momentum is in the direction of the applied force.
   F = rate of change of (mv)
   or, F=ma when the mass, m, remains constant
   
3. To every action (some force exerted on body A by body B) there is an equal and opposite reaction (force exerted by body A on body B).

Newton eventually had the following information:

1. Kepler’s laws of planetary motion:
   1. Elliptical orbits, with the sun at one focus.
   2. Equal areas in equal times.
   3. For all planets,

   where p = planet’s period about the sun, R = average distance of planet from sun, k = a constant.

2. The law of free fall
   where D = distance, T = time of fall, A = acceleration due to gravity.
3. Newton’s three laws of motion:
   1. Law of Inertia.
   2. Law of relation between force, mass, and acceleration: F = ma.
   3. Law of action and reaction.
4. Law of force necessary to keep a body moving uniformly in a circle:

1. That the laws of motion hold everywhere in the universe;
2. (initially) that the orbits of the planets were circular rather than elliptical.

The result:
Newton’s Law of Universal Gravitation: Every body in the universe attracts every other body with a force directly proportional to the Foduct of their masses and inversely proportional to the square of the distance between them.

As a formula, this law is expressed as follows:
Force is equal to the Gravitational Constant times: Mass one time Mass two, divided by the radius (distance) squared.

Where F = the force of attraction, m and M = the two masses, R = the distance between the two masses, and G = the universal constant of gravitation.