How Do You Calculate the Final Speed of a Comet in Orbit?

AI Thread Summary
To calculate the final speed of a comet in orbit, one must apply the principle of conservation of angular momentum. The angular momentum at the closest approach (r1) can be expressed in terms of the initial speed (v1) and the distance from the Sun. At a later distance (r2), the angular momentum must equal that at r1, allowing for the determination of the final speed (v2) using the angle θ between the position and velocity vectors. The initial attempt using mv1cos(90-theta) was incorrect, indicating a need for a different approach. Ultimately, setting the angular momentum equations equal will yield the correct final speed of the comet.
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Homework Statement



(a) A certain comet of mass m at its closest approach to the Sun is observed to be at a distance r1 from the center of the Sun, moving with speed v1. At a later time the comet is observed to be at a distance r2 from the center of the Sun, and the angle between rvec2 and the velocity vector is measured to be θ. What is v2?


Homework Equations





The Attempt at a Solution



I thought it would be mv1cos(90-theta). But it's counting that wrong, and I only have one more attempt at this problem, and I'm not sure how to approach it.
 
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Angular momentum is conserved, so find expressions for the angular momentum at the two points and set them equal.
 
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