- #1

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- TL;DR Summary
- Many texts state that Kepler's second law can be derived from conservation of angular momentum, however all demonstrations I have found make an assumption that is not clear for me

Many texts state that in an elliptic orbit you can find angular momentum magnitude as

$$ L = r m v = m r^2 \frac {d \theta} {dt} $$

I wonder if

$$ v = r \frac {d \theta} {dt} $$

is valid at every point. I understand this approximation in a circumference or radius r but what about an arc of ellipse?

Thank you.

$$ L = r m v = m r^2 \frac {d \theta} {dt} $$

I wonder if

$$ v = r \frac {d \theta} {dt} $$

is valid at every point. I understand this approximation in a circumference or radius r but what about an arc of ellipse?

Thank you.