Today being a snow day ( kind of irrelevant when you are retired), and since I had to wait for some too thick shellac to dry on my nightstand, I had time for more of the physics problems that Mr. Gilmore of Ridge sent me. I have to admit that, contrary to my normal philosophy of in rotational motion viz. angular velocity omega is everything - nearly, I used the velocity to find perigees for orbits, given the radius and velocity at the apogee. However, you can only use the total velocity x radius at the apogees and perigee to calculate the conserved quantity, angular momentum, because the velocity has non tangential ( i.e some radial ) components elsewhere in the orbits. Thus, if you need to know the velocity at other points you can find the total speed using conservation of energy given the radius, but to find the direction you would find the tangential or angular velocity using conservation of angular momentum and omega r^2 is the conserved quantity.
I am now waiting for Mr. Gilmore to let me know if my latest efforts yielded correct answers.
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