- #1
vbrasic
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Homework Statement
A comet orbits the sun. It's position in polar coordinates is given by, $$r(\phi)=\frac{1.8r_0}{1+0.8\cos{\phi}},$$ where ##r_0## is the position at closest approach. Its velocity at this point is given by ##v_0##. Use the concept of angular momentum to find the following:
- The comet's speed at ##\phi=180^{\circ}##.
- The components of velocity, ##v_r##, and ##v_{\phi}## at ##\phi=120^{\circ}##.
Homework Equations
$$L=r\times p$$
$$|L|=m|r||v|\sin{\theta}$$
The Attempt at a Solution
We have that angular momentum at closest approach is given by, $$L=r\times p=m|r||v|\sin{\theta}.$$ At closest approach, we then have that $$L=mr_0v_0\sin{\theta}.$$ If the orbit was a perfect circle, we would know for sure that the angle between ##r_0## and ##v_0## is ##90^{\circ}##. However, in this case, the orbit is an ellipse, so I'm unsure how to find ##\theta##.