2.13  Newton’s Law of Gravity:

Gravitational force   -an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.

Stated mathematically:

universal law of gravitation

Where G is the universal gravitational constant (meaning it has the same value throughout the universe), m1 and m2 are the masses of the objects in kilograms, and d is the distance between them in meters

G = 6.67 x 10-11 N m2 / kg2

Cavendish found the universal gravitation constant, allowing the earth to be "weighed." As we examine this equation we can note that the larger the masses, the larger the gravitational force.  The farther apart the masses are the smaller the force.  Because the force is proportional to 1/d2, If we double the distance between two masses, the gravitation force is not halve but 1/4 of the original value.  The other thingto note is the distances are based on the center of the mass (center of gravity) and so even though I am standing on the earth, I an quite a distance from the earth’s center.  (R=6400 km or 3980 mi.)