Newton’s Law of Universal Gravitation
Newton’s insight:
The force accelerating an apple
downward is the same force that
keeps the Moon in its orbit.
Hence, Universal Gravitation.
Nothing yet. How
about you Newton?
Mechanical Universe 3:25‐24:50
8. The Apple and the Moon Sir Isaac's Most Excellent Idea
2
G is a very small number
this means that the force of gravity is negligible
unless there is a very large mass involved such
as the Earth.
Comparison of Four Fundamental Forces
Hold the nucleus together Force between electric charges
Regulates nuclear decay and neutrino interactions
Weakest of all forces
Newton’s Law of Universal Gravitation
The gravitational force is always attractive, and
points along the line connecting the two
masses:
The two forces shown are an action-reaction
pair.
F12 = ‐F21
A man takes his dog for a walk on a deserted beach.
Treating dogs and people as point objects,
find the force of gravity between the 105-kg man
and his 11.2-kg dog when they are separated by a
distance of (a) 1.00 m and (b) 10.0 m.
1m
10m
Clicker
Which is stronger, Earth’s pull on the Moon, or the Moon’s pull on Earth?
a) the Earth pulls harder on the Moon
b) the Moon pulls harder on the Earth
c) they pull on each other equally
d) there is no force between the Earth and the Moon
e) it depends upon where the Moon is in its orbit at that time
By Newton’s Third Law, the forces
are equal and opposite.
If an object is being acted upon by several different gravitational forces, the
net force on it is the vector sum of the individual forces.
This is called the principle of superposition.
n 
 




F1  F12  F13  F14  F15    F1n   F1i
Find the
Net Force
acting on
m1
i 2
y
θ
x