Gravitation

The Apple … From the surface of the earth, an apple thrown horizontally into the air will curve back to the ground. With enough velocity, the apple can curve around the earth never landing on the ground.

… and the Moon Like the launched apple, the Moon has enough velocity to curve around the earth, never landing on the ground.

The Apple and the Moon Newton deduced that the force responsible for the orbital motion of the moon around the earth is the same force acting on the apple. Newton compared the acceleration due to “gravity” acting on the moon and on the apple (on earth). gmoon= .00273 m/s2 gapple= 9.8 m/s2

The Force of Gravity Newton postulated that the acceleration due to “gravity” was diluted by the distance of separation from the earth. Newton compared the distances separating the earth from both objects.

Inverse Square Law The value of Fg and g for two positions in earth’s gravitational field can be compared by:

The Force of Gravity Newton knew that the force which caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. Since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. Weakest force in nature!

Law of Universal Gravitation The gravitational force (FG) between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance separating their centers. G is the universal gravitation constant.

Example 5

Gravitational Field The region surrounding an influencing body where any object of mass m experiences a gravitational force FG is called the gravitational field.

Gravitational Field The gravitational field strength ( g ) at any position in the gravitational field is defined as the amount of gravitational force experienced per unit mass.

Gravitational Field The gravitational field strength for an influencing body of mass M can expressed by the relationship where d is the position in the gravitational field measured from the center of the influencing body.

Example 6

Example 7