Unit 9
Gravitation
9.1
Universal Gravitation
9.2
Gravitational field
9.3
Gravitational potential energy
9.4
Satellite orbits
9.5
Launching a satellite
9.6
Mechanical energy of a satellite
9.7
Kepler’s laws
9.1
Gravitation
Newton’s law of universal gravitation states that the gravitational force
F
between any
two bodies of mass
m
1
and
m
2
separated by a distance
r
, is described by
2
2
1
r
m
m
F
∝
.
1
m
2
m
r
F
F
It is a center-to-center attraction between all
forms of matter. The force of gravity between
any two bodies varies directly in proportion to
the product of their masses and inversely with
their separation squared.
F
The proportional constant is referred to as the
universal gravitation constant
G
. Its value is
G
= 6.67
×
10
-11
Nm
2
kg
-2
. Now we can write
2
2
1
r
m
m
G
F
=
r
Example
Twin asteroids
X
and
Y
, having the same mass (
M
= 3.5
×
10
18
kg) are located 3.00 km
apart. Find the net gravitational force of the spaceship when it is located at positions
A
and
B
, as shown in figure. Given that the mass of the spaceship is
m
= 2.50
×
10
7
kg.
1

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