# Universal Gravitation

```UNIVERSAL GRAVITATION
Law of Universal gravitation
“The force of gravitational attraction
between any two objects is directly
proportional to the product of the masses
of the objects, and inversely proportional
to the square of the distance between
their centres.”
As A Diagram
Universal Gravitation
The Law of Universal Gravitation is concerned with the
force of attraction between bodies.
FG = G m1m2
r2
Where:
G = 6.67 x 10-11 Nm2/Kg2
(universal gravitational constant)
m1 = mass of one object
m2= mass of a second object
r = distance between the centres of the
Objects (assumed to be spherical)
Note:
For force of attraction to be noticeable, at least
one of the objects must be very large.
Force of attraction diminishes rapidly as the two
objects move apart. But FG never equals zero,
every object exerts a force of attraction on every
other object.
The law only applies to two spherical objects (such
as earth & sun), to two objects whose sizes are
much smaller than their separation distance, or to
a small object and a very large sphere.

Example Earth:
If we replace m1 with 1kg, m2 with the mass of the
Earth, and r with the radius of the Earth, what do we
get for FG?
m1 = 1kg
m2 = 5.9742 x 1024 Kg
r = 6.3781 x 106 m
G = 6.67 x 10-11 Nm2/Kg2
Example - Earth:
If we repalce m1 with 1kg, m2 with the mass of the
Earth, and r with the radius of the Earth, what do we
get for FG?
m1 = 1kg
m2 = 5.9742 x 1024 Kg
r = 6.3781 x 106 m
G = 6.67 x 10-11 Nm2/Kg2
F G = G m 1m 2
r2
Example Earth:
If we repalce m1 with 1kg, m2 with the mass of the
Earth, and r with the radius of the Earth, what do we
get for FG?
m1 = 1kg
m2 = 5.9742 x 1024 Kg
r = 6.3781 x 106 m
G = 6.67 x 10-11 Nm2/Kg2
F G = G m 1m 2
R2
= (6.67 x 10-11)( 1)(5.9742 x 1024)
(6.3781 x 106)2
Example Earth:
If we repalce m1 with 1kg, m2 with the mass of the
Earth, and r with the radius of the Earth, what do we
get for FG?
m1 = 1kg
m2 = 5.9742 x 1024 Kg
r = 6.3781 x 106 m
G = 6.67 x 10-11 Nm2/Kg2
F G = G m 1m 2
R2
= (6.67 x 10-11)( 1)(5.9742 x 1024)
(6.3781 x 106)2
= 9.8 N
Notice that this is the same as
Fg = mg = (1 x 9.8) = 9.8 N
```

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