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Gravitational force exerted by point mass M on point mass m.
F
=
GMm
d
2
M
m
d
F
=
ma
A net force on an object m leads to its acceleration:
F
=
mg
When the force is gravity, the acceleration is written as
g
:
g
=
GM
d
2
The acceleration of m
toward M is
G=6.67x10
11
m
3
kg
1
s
2
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View Full Document Consider a hollow shell
with radius R, but very
thin
Gravitational attraction of a
shell (assuming uniform
material) on mass m:
F
shell
=
GM
shell
m
d
2
d is distance to shell center
The same as if all the mass were concentrated at a point at the center
What is
g
on the Earth’s surface?
R
This equation holds for any distance from the center,
d
≥
R
…some calculus…
Since observer is outside
all smaller shells, same
formula applies
d
Consider the Earth made of
many hollow shells, each with
the same center
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View Full Document F
sphere
=
F
shell
!
=
Gm
d
2
M
shell
!
=
GmM
sphere
d
2
Force due to full sphere also acts as if
all mass were concentrated into a point.
Therefore, acceleration of gravity on the
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This note was uploaded on 11/22/2010 for the course GEOP 341 taught by Professor Sparks during the Spring '10 term at Texas A&M.
 Spring '10
 sparks

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