1 The Law of Universal Gravitation

2 A little background … Legend has it that Sir Isaac Newton was struck on the head by a falling apple while napping under a tree. This prompted Newton to imagine that all bodies in the universe are attracted to each other in the same way that the apple was attracted to the Earth. Newton analyzed astronomical data on the motion of the Moon around the Earth and stated that the law of force governing the motion of the planets has the same mathematical form as the force law that attracts the falling apple to the Earth.

3 Newton’s Law of Universal Gravitation every particle in the universe attracts every other particle with a force  The force is directly proportional to the product of their masses  The force is inversely proportional to the square of the distance between them. So, if the particles have masses m 1 and m 2 and are separated by a distance d, the magnitude of the gravitational force is:

4 A closer look … G is the universal gravitational constant, which has been measured experimentally as 6.67 x The distance, d, between m 1 and m 2 is measured from the center of m 1 to the center of m 2.

5 Remember Third Law ? By Newton’s third law, the magnitude of the force exerted by m 1 on m 2 is equal to the force exerted by m 2 on m 1, but opposite in direction. These gravitational forces form an action- reaction pair.

6 Properties of the Gravitational Force: The gravitational force acts as a long range force, which exists between two particles, regardless of the medium that separates them. The force varies as the inverse square of the distance between the particles.  This means force decreases rapidly with increasing distance between the particles. The force is directly proportional to the mass of each particle.  This means, a larger mass will yield a larger force

7 Weight and Gravitational Force Weight was previously defined as F W = m·g, where g is the magnitude of the acceleration due to gravity. So, The object’s mass, m, cancels out, giving us ( surface gravity ). Or, the gravitational acceleration experienced when above the surface of earth:

8 Formula Summary M E = 5.97 x kg r E = 6.37 x 10 6 m G = 6.67 x Nm 2 /kg ft = 1 mile 3.28 ft = 1 m

9 Try calculating these … 6.67 x x 2000 = 6.67 x x 52 = 6.67 x x 5.98 x =

10 Example 1) Two masses, kg and kg, are separated by 200 meters. What is the force of attraction between them?

11 Example 2) What is the force of attraction between a 2000 g mass and a 4000 g mass if their centers are 15 cm apart?