Orbital Energy
•
An object moving with velocity v has kinetic energy:
2
2
1
mv
K
=
An object in a gravitational field has potential energy:
r
GMm
U
−
=
•
The total energy of an orbit is
a
GMm
E
2
−
=
, and may be
positive, negative, or zero.
Since E=K+U this can be
rearranged to give the very useful visviva equation:
⎟
⎠
⎞
−
⎜
⎝
⎛
=
a
r
GM
r
v
2
1
1
2
)
(
2
¾
This allows you to calculate the semimajor axis
from just the current position and velocity of a
body.
•
The escape velocity is the velocity required for a
body to escape the gravitational pull of another.
That is, it’s total orbital energy is E=K+E=0.
This
gives us:
r
GM
v
esc
2
=
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View Full DocumentResonances and Perturbations
•
Orbits are dominated by the Sun, but perturbed by all
the other massive bodies in the SS
•
The effects of a perturbed orbit change with time:
¾
Periodic
changes vary smoothly between well
defined limits (e.g. precession of Earth’s rotation
axis)
¾
Secular
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 Winter '09
 HARRIS
 Solar System, Energy, Kinetic Energy, Mass, Potential Energy, Celestial mechanics

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