1. Ch 12 Notes
The Apple & the Moon
Isaac Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.

2. Universal Gravitation
Ch 12 Notes
Universal Gravitation
Newton’s idea was that gravity was a universal force acting between any two objects.

3. At the Earth’s Surface W = mg
Ch 12 Notes
At the Earth’s Surface
Newton knew that the gravitational force on the apple equals the apple’s weight, mg, where g = 9.8 m/s2.
W = mg

4. Weight of the Moon ? Fc = mg
Ch 12 Notes
Weight of the Moon
Newton reasoned that the centripetal force on the moon was also supplied by the Earth’s gravitational force. ?
Fc = mg

5. Ch 12 Notes
Weight of the Moon
Newton’s calculations showed that the centripetal force needed for the Moon’s motion was about 1/3600th of Mg, however, where M is the mass of the Moon.

6. Ch 12 Notes
Weight of the Moon
Newton knew, though, that the Moon was about 60 times farther from the center of the Earth than the apple.
And 602 = 3600

7. Universal Gravitation
Ch 12 Notes
Universal Gravitation
From this, Newton reasoned that the strength of the gravitational force is not constant, in fact, the magnitude of the force is inversely proportional to the square of the distance between the objects.

8. Universal Gravitation
Ch 12 Notes
Universal Gravitation
Newton concluded that the gravitational force is:
Directly proportional to the masses of both objects.
Inversely proportional to the distance between the objects.

9. Law of Universal Gravitation
Ch 12 Notes
Law of Universal Gravitation
In symbols, Newton’s Law of Universal Gravitation is:
Fgrav = G
Where G is the universal gravitational constant of proportionality.
G = 6.67 x N m2/kg2
M1m2
r 2

10. Law of Universal Gravitation
Mass 1
Mass 2
Force (N)
F =G m1m2 r2
Distance between
masses (m)
Universal Gravitational Constant
G =(6.67 x N.m2/kg2)

11. Ch 12 Notes
Inverse Square Law
Newton’s Law of Universal Gravitation is often called an inverse square law, since the force is inversely proportional to the square of the distance.

17. Knowledge of Gravity
As Galileo wrote almost 400 years ago in response to a statement that “gravity” is why stones fall downward, – What I am asking you is not the name of the thing, but its essence, of which essence you know not a bit more than you know about the essence of whatever moves the stars around. …we do not really understand what principle or what force it is that moves stones downward. The question of why objects attract each other is still not answered.