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183_notes:examples:angular_momentum_of_halley_s_comet [2014/11/16 08:11] – created pwirving | 183_notes:examples:angular_momentum_of_halley_s_comet [2014/11/20 16:30] (current) – pwirving | ||
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=== Facts === | === Facts === | ||
+ | At $\vec{r}_{1}$ comet is 8.77$ x $10^{10}$m from the Sun. | ||
+ | The comets speed at $\vec{r}_{1}$ is $5.46$ x $10^4$ m/s. | ||
+ | At $\vec{r}_{2}$ the comets speed is $1.32$ x $10^{4}$ m/s. | ||
+ | The distance between the comet and the Sun at $\vec{r}_{2}$ is $1.19$ x $10^{12}$ m. | ||
+ | Angle $\theta$ in representation is $17.81^{\circ}$ | ||
- | === Lacking === | + | The mass of the comet is estimated to be $2.2$ x $10^{14}$ kg. |
+ | === Lacking === | ||
+ | |||
+ | Calculate the translational (orbital) angular momentum of the comet, relative to the Sun, at both locations. | ||
=== 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' | ||