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

[Qnslaught]

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.

 

[kuruman]

Angular momentum is conserved, so find expressions for the angular momentum at the two points and set them equal.

 

[kerimek]

I would approach this problem by first understanding the concept of angular speed. Angular speed is defined as the rate at which an object rotates around a fixed point. In this case, the fixed point is the center of the Sun and the object is the comet.

To solve for the angular speed of the comet, we can use the equation ω = v/r, where ω is the angular speed, v is the linear speed, and r is the distance from the center of rotation.

In the given problem, we know the mass of the comet, its initial distance from the Sun (r1), and its initial speed (v1). We also know the change in distance (r2) and the angle between r2 and the velocity vector (θ).

To find the final speed (v2), we can use the equation v2 = ωr2, where ω is the angular speed we calculated using the first equation. We can find the value of ω by using the given information and solving for v2.

Therefore, the final speed of the comet (v2) can be calculated using the equations ω = v/r and v2 = ωr2.