Question

I need help on session 21: Kepler's Second Law.
I don't understand how |r x v| vector could be a constant. Its direction, of course, is not changing. But, what about its length? An ellipse has different radius on its different parts, so the 'r' vector has different length on different parts of the ellipse trajectory. How is that possible?

Answer 1

***so the 'r' vector has different length***
yes, and the velocity vector v changes such that
| r cross v| is constant.
in other words, at those points furthest from the sun, the planet moves slower than at those points in its (ellipitical) orbit closest to the sun.

** How is that possible?**
follows from the inverse square law of gravitation.