Lecture 23 Orbital Mechanics
1
Brief Review of Gravity
•
Gravitational force
–
In general
~
F
=

GMm
r
2
ˆ
r
where
r
=

~
r
2

~
r
1

is the distance between the centers of the two objects, and the minus sign indicates
that the force is attractive.
–
Near the surface of Earth, the gravitational force is approximately constant so we
can write this as
F
=

m
(
GM
R
2
)ˆ
r
=

mg
ˆ
r
Note, we often write this as acting in the y direction instead of using

ˆ
r
.
The
ˆ
r
here just means it points toward the center of Earth.
If we are approximating
Earth’s surface as Fat, we often use the coordinate y instead.
•
Gravitational Potential Energy
–
Since gravity is a conservative force, we can de±ne a potential energy between two
objects
U
=

GMm
r
where we have de±ned reference such that U=0 at r equals in±nity.
•
PUZZLERS
2
Orbital Mechanics
2.1
Special Case: Circular Orbit
•
²irst let’s consider a circular orbit from the energy standpoint
–
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 Spring '08
 Millan
 Force, Gravity, Potential Energy, Orbital Mechanics, circular orbit

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