Download Law of Universal Gravitation

 Newton wondered about the force that must act to
keep the Moon in its circular orbit around Earth.
 Newton realized that since falling objects accelerate
 Whenever a body has a force exerted on it, that force is
exerted by some other body. But what exerts the force
of gravity?
 Every object on Earth feels gravity directed toward the
center of Earth.
 Newton concluded that Earth itself exerts the
gravitational force on objects at its surface
 Newton’s “Apple Story” led him to think about how
gravity acts on the top of trees, and mountains, etc.
then maybe it could act all the way to the moon!
 There was much controversy at the time because
people were so used to the idea of contact forces only.
 If gravity acts between planets, their moons, and the
sun, then is it possible gravity acts between all objects?
 Is there a gravitation force between you and your
classmates?
YES!
Law of Universal Gravitation
- Every particle in the universe attracts every other
particle in the universe
- F = G m1m2 / r2
- This force acts along the line joining the two particles
G= 6.67 x 10-11 Nm2/kg2 (Universal Constant)
When this equation is applied to the gravitational force
between Earth and an object at its surface then the
equation becomes:
g = G mE / rE2
radius of Earth = 6.38 x 106 m
mass of Earth = 5.98 x 1024 kg
*Until the value of G was determined in 1798 the mass of
the Earth was unknown!
Examples:
A 50 kg person and a 75 kg person are sitting on a bench
about 50 cm apart. Estimate the magnitude of the
gravitational force each exerts on the other.
What is the acceleration due to gravity on the top of Mt.
Everest, which is 8,848 m above the Earth’s surface?