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183_notes:examples:angular_momentum_of_halley_s_comet [2014/11/20 01:01] – pwirving | 183_notes:examples:angular_momentum_of_halley_s_comet [2014/11/20 16:30] (current) – pwirving | ||
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=== Approximations & Assumptions === | === Approximations & Assumptions === | ||
+ | No other interactions the rest of the solar system. | ||
+ | Assume main interaction is with the sun. | ||
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{{course_planning: | {{course_planning: | ||
+ | $\left|\vec{L}_{trans}\right| = \left|\vec{r}_A\right|\left|\vec{p}\right|\sin \theta$ | ||
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Direction: At both locations, the direction of the translational angular momentum of the comet is in the -z direction (into the computer); determined by using the right-hand rule. | Direction: At both locations, the direction of the translational angular momentum of the comet is in the -z direction (into the computer); determined by using the right-hand rule. | ||
- | At location 1: | + | Given this information we know at location 1 the translational angular momentum of the comet relative to the sun will be: |
+ | |||
+ | $\left|\vec{L}_{trans, | ||
+ | |||
+ | We don't know the momentum but we do know the mass and velocity of the comet at $\vec{r}_{1}$ so our equation becomes: | ||
+ | |||
+ | $\left|\vec{L}_{trans, | ||
+ | |||
+ | Substituting in for the known variables we get: | ||
$\mid\vec{L}_{trans, | $\mid\vec{L}_{trans, | ||
+ | |||
+ | Solving for $\mid\vec{L}_{trans, | ||
$= 1.1$ x $10^{30}$ $kg \cdot m^2/s$ | $= 1.1$ x $10^{30}$ $kg \cdot m^2/s$ | ||
+ | |||
+ | In vector form $\vec{L}_{trans, | ||
$\vec{L}_{trans, | $\vec{L}_{trans, | ||
- | At location 2: | + | The same step by step process is used to solve for $\vec{L}_{trans, |
$\mid\vec{L}_{trans, | $\mid\vec{L}_{trans, | ||
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$\vec{L}_{trans, | $\vec{L}_{trans, | ||
+ | |||
+ | Even in the highly elliptical orbit, the comet' | ||