Effective cross-section of catching a comet with the Sun

AI Thread Summary
To determine the effective cross-section (σ) for a comet being captured by the Sun, the formula σ=πb^2 is relevant, where b represents the maximum distance from the Sun at which it can still capture the comet. The challenge lies in calculating b, which relates to the semi-minor axis of the comet's elliptical trajectory, but requires knowledge of the semi-major axis or linear eccentricity. Initial velocity (v) of the comet is known, suggesting that energy or angular momentum conservation principles may be useful for further calculations. However, additional distances remain unknown, complicating the solution. Clarification on these parameters is essential for accurate computation.
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Hello.

1. Homework Statement
I have to find formula for effective cross-section (σ) of catching a comet with the Sun. I know mass of the Sun (M), radious of the Sun (R) and initial velocity (v) of the comet (at a big distance from the Sun).

Homework Equations


σ=πb^2, where b is on the picture (b>R)It is the biggest distance when the Sun still catch the comet.
obrázek.jpg


The Attempt at a Solution


I really don't know how to work with the b. It is semi-minor axis in in an elliptical trajectory of the comet. However, I don't know semi-major axis or linear eccentricity...
I just know the initial velocity v of the comet. I think I sould work with energy or angular momentum at the beginning and near the catching. However, I still have there some distances which I don't know.

Please, could you give me an advice?
Thank you.
 
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