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Systemic - Characterizing Extrasolar Planetary Systems

## Epicycles

9 Feb 2015, 03:19 UTC
(200 words excerpt, click title or image to see full post)

Vladimir Arnold, he of the A in KAM Theory, wrote a classic graduate text entitled Mathematical Methods of Celestial Mechanics. This, as one might imagine, is a book that is not exactly a storehouse of easy homework assignments. There are, however, a scattering of problems that offer insights while, at the same time, not actually requiring the tough-guy methods that are the text’s primary focus.
During his walk in outer space [as part of the Voskhod 2 Mission on 18 March 1965], the cosmonaut Alexey Arkhipovich Leonov threw the lens cap of his movie camera toward the Earth. Describe the motion of the lens cap with respect to the spacecraft, taking the velocity of the throw as 10 m/s. Neglect the asphericity of the Earth.

(Ria Novosti/Science Photo Library)
Leonov’s space walk tipped off a hair-rising adventure which began with his being nearly unable to re-enter the spacecraft, and ended with a frigid way-off-course landing in the Siberian Tiaga, all of which is covered in a recent BBC documentary.
One can hand-crank the problem by noting that the radially directed, $${\bf v}_{i}=10\,{\rm m\,s^{-1}}$$, launch of the lens cap exerts no torque, so that $${\bf r}\times{\bf v}_{i}=0$$, whereas the total specific ...