Lecture3

# Lecture3 - Orbital Energy An object moving with velocity v...

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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 vis-viva 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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Resonances 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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Lecture3 - Orbital Energy An object moving with velocity v...

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