Fedra Type Book

MO ON MAN’S ONLY ORBITING NEBULAE

THE STUDY OF FEDRA

BY TYPOTHEQUE

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

MO ON MAN’S ONLY ORBITING NEBULAE

THE STUDY OF FEDRA

BY TYPOTHEQUE

Copyright Š 2012 by Melissa Kelly All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

Typotheque Zwaardstraat 16 2584 TX The Hague Netherlands T: +31 70 322 6119 F: +31 84 831 6741 www.typotheque.com Printed in San Francisco, CA

THIS BOOK IS DEDICATED TO

ALL THE DREAMERS

TABLE OF CONTENTS

THE COLLISION

STUDY OF THE MOON

1

2

7

TO FORM

DEBRIS

9

10

CREATE

THE TIDES

15

8

11

12

16

EARTH MOVEMENT

17

18

5

6

.002 SECONDS

21

MOVEMENT

CALCULATION

23

24

29

31

ORBIT

20

27

28

22

SLOWLY MOVING

THE UNKNOWN

19

30

32

POSSIBILITIES

CONSTANT

35

36

33

34

THE STUDY OF THE MOON IS QUITE INTENSIVE

THE ONLY THING THAT IS CONSTANT IS CHANGE. IT IS ALL AROUND US IN SMALL AND BIG FORMS. FOR INSTANCE, THE MOON OF EARTH HAS CHANGED FOR BILLIONS OF YEARS AND NOW CHANGES OUR DAILY LIFE AS WELL. IT WILL ONE DAY FULLY CHANGE AND LEAVE EARTH’S ORBIT FOREVER AND ALWAYS.

stars each hour by an amount roughly equal to its angular

* The

solar system was forming and the Earth was an

eccentricity of 0.0549. The non- circular form of the lunar

inhabitable waste land of hot magma. It collided with a

orbit causes variations in the Moon’s angular speed and

small planet which made the Earth a new form and the off-

apparent size as it moves towards and away from an observer

shot circled around the Earth and slowly formed the moon.

on Earth. The mean angular daily movement relative to an

The moon was quite close to the Earth which made the tides

imaginar y observer at the barycentric is 13.176° to the east

much stronger and the days shorter. Since the tides from the

( Julian Day 2000.0 rate).

melted ice asteroids were so strong, it helped carve out the

is not fixed in space, but precesses over time. The nearest

terrain. Present day, the moon is at an optimal place where

and farthest points in the orbit are the perigee and apogee

life can thrive. However, the moon in time will fall out of

respectively. The line joining these two points (the line of

orbit and cause chaos. The Earth will tip from its axis, and

upsides) rotates slowly in the same direction as the Moon

the weather will cause unpredictable conditions.

itself (direct motion), making one complete revolution in

The

properties

of

the

orbit

described

in

this

diameter, or by about 0.5°.

* The Moon differs from most

satellites of other planets in that its orbit is close to the plane of the ecliptic, and not to the Earth’s equatorial plane.

The lunar orbit plane is inclined to the ecliptic by about 5.1°, whereas the Moon’s spin axis is inclined by only 1.5°.

* The

orbit of the Moon is distinctly elliptical with an average

* The

orientation of the orbit

3232.6054 days or about 8.85 solar orbits.

section are approximations. The Moon’s orbit around the Earth has many irregularities (perturbations), whose study has a long history.

* The

Moon

completes

its

orbit

around

the

Earth

in

approximately 27.3 days (a sidereal month). The Earth and Moon orbit about their bar ycentric (common center of mass), which lies about 4600 km from Earth’s center (about three quarters of the Earth’s radius). On average, the Moon is at a distance of about 385000 km from the center of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1,023 m/s, the Moon moves relative to the

STUDY OF THE MOON

1

2

Movement and Wind

1 creation ///

BY THAT CRITERION, THE EARTH AND MOON ARE A PLANET– MOON SYSTEM, BECAUSE THEIR MUTUAL DISTANCE IS ABOUT 60 EARTH RADII, BUT THEIR MASS RATIO OF 81:1 MEANS THAT THEIR BARYCENTRE LIES ABOUT 1,750 KILOMETERS (1100 MILES) BENEATH THE SURFACE OF THE EARTH.

* The

mean inclination of the lunar orbit to the ecliptic plane is 5.145°. The

rotation axis of the Moon is also not perpendicular to its orbital plane, so the lunar equator is not in the plane of its orbit, but is inclined to it by a constant value of 6.688° (this is the obliquity). One might be tempted to think that as a result of the precession of the Moon’s orbital plane, the angle between the lunar equator and the ecliptic would var y between the sum (11.833°) and difference (1.543°) of these two angles.

* However,

as was discovered by Jacques Cassini

in 1721, the rotation axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase (see Cassini’s Laws).

Thus, although the rotation axis of the Moon is not fixed with respect to the stars, the angle between the ecliptic and the lunar equator is 1.543°.

* During the June Solstice the Ecliptic reaches the highest declination

in the southern hemisphere, -23°29. When at the same time the ascending node has a 90° angle with the Sun in the southern hemisphere, the declination of the

Full Moon in the sky reaches a maximum at -23°29 - 5°9 or -28°36. This is called the major standstill or Lunistice in the southern hemisphere. Nine and a half years later, when the descending node has a 90° angle with the Winter Solstice the declination of the Full Moon in the sky reaches a maximum at 23°29 + 5°9 or 28°36.

The other major standstill or Lunistice, this time in the north hemisphere.

*A

growing number of astronomers consider the Earth–Moon system to be a double

planet. This is because of the relatively large size of the Moon, the Earth–Moon mass ratio that is about 81:1 is much smaller than that of most natural satellites in the Solar System, the fact that the Moon orbits only up to five degrees off the ecliptic instead of on Earth’s equatorial plane, and other reasons. An informal criterion for a double planet is that its barycentre must be exterior to both bodies.

* One might be tempted to think that as a result of the precession of the Moon’s

orbital plane, the angle between the lunar equator and the ecliptic would var y between the sum (11.833°) and difference (1.543°) of these two angles.

The giant impact hypothesis states that the Moon was formed out of the neat debris left over from a collision between Earth and a body the size of Mars, approximately 4.5 billion years ago.

THE COLLISION STARTED IT ALL

THE COLLISION

5

6

MOON CREATION

5

6

THE MOON CONTINUED TO FORM

The giant impact hypothesis is a favored scientific hypothesis for the formation of the Moon. Supporting evidence includes: the identical direction of the Earth’s spin and the Moon’s orbit.

Moon samples which indicate the surface of the Moon was once molten, the Moon’s relatively small iron core, lower density compared to the Earth, evidence of similar collisions in other star systems (which result in debris disks), and that giant collisions are consistent with the leading theories of the formation of the solar system.

TO THE BABYLONIAN ASTRONOMER KIDINNU (IN GREEK OR LATIN, KIDENAS OR CIDENAS) HAS BEEN ATTRIBUTED THE INVENTION (5TH OR 4TH CENTURY BC) OF A SYSTEM “B” FOR PREDICTING THE POSITION OF THE MOON, TAKING ACCOUNT THAT THE MOON CONTINUALLY CHANGES ITS SPEED ALONG ITS PATH RELATIVE TO THE BACKGROUND OF FIXED STARS. THE MOON HAS CHANGED IN THE LENGTH OF THE ORBIT.

* This

system involved calculating daily stepwise changes of lunar

speed, up or down, with a minimum and a maximum approximately each month. The basis of these systems appears to have been arithmetical rather than geometrical, but they did approximately account for the main lunar inequality now known as the equation of the center.

* The Babylonians appear to have been interested in calendars,

new moons and eclipses. Some time between the years 500 BC and

400 BC they identified and began to use the 19-year cyclic relation between lunar months and solar years now known as the Metonic cycle.

* They

built up a numerical theory of the main irregularities

in the Moon’s motion, reaching remarkably good estimates for the (different) periods of the three most prominent features of the Moon’s motion.

* The synodic month, i.e. the mean period for the phases of

the Moon. The so - called System B reckons the synodic month as 29 days and 3,11;0,50 time degrees (of 4 of our minutes): this converts to 29.530594 days 29d 12h 44m 3.33s, to compare with a modern value (as at 1900 Jan 0) of 29.530589, or 29d 12h 44m 2.9s. This same value was used by Hipparchos and Ptolemy, was used throughout the Middle Ages, and still forms the basis of the Hebrew calendar.

* The

mean

lunar velocity relative to the stars they estimated at 13° 10’ 35” per day, giving a corresponding month of 27.321598 days, to compare with modern values of 13° 10’ 35.0275” and 27.321582.

* The

anorthositic

month, i.e. the mean period for the Moon’s approximately monthly accelerations and decelerations in its rate of movement against the stars, had a Babylonian estimate of 27.5545833 days,to compare with a modern value 27.5.

* The draconitic month, i.e. the mean period with

which the path of the Moon against the stars deviates first north and

then south in ecliptic latitude by comparison with the ecliptic path of the Sun, was indicated by a number of different parameters leading to various estimates, e.g. of 27.212204 days, to compare with a modern value of 27.21, but the Babylonians also had a numerical relationship that 5458 synodic months were equal to 5923 draconitic months, which when compared with their accurate value for the synodic month leads to practically exactly the modern figure for the draconitic month.

TO FORM

7

8

DEBRIS FROM THE COLLISION FORMED

THE MOON FORMED SLOWLY FROM THE DEBRIS OF THE COLLISION FROM THE TWO PLANETS. IT CONTINUES TO ORBIT AROUND THE EARTH.

north,

* At new moon it is zero and the Moon

roughly ever y 173.3 days. Lunar orbit

is said to be in conjunction. At full

inclination also determines eclipses;

moon the elongation is 180° and it is

shadows cross when nodes coincide

said to be in opposition. In both cases

with full and new moon, when the

the Moon is in syzygy, that is, the Sun,

sun, earth, and moon align in three

Moon and Earth are nearly aligned.

dimensions. This is important. The

When elongation is either 90° or 270°

orientation of the orbit is not fixed

the Moon is said to be in quadrature.

in

The nodes are points at which the

The nearest and farthest points in

Moon’s orbit crosses the ecliptic. The

the orbit are the perigee and apogee

Moon

ever y

respectively. The line joining these

27.2122 days, an interval called the

two points (the line of asides) rotates

draconic or draconitic month. The line

slowly in the same direction as the

of nodes, the intersection between the

Moon itself (direct motion), making

two respective planes, has a retrograde

one complete revolution in 3232.6054

motion: for an observer on Earth it

days or about 8.85 solar orbits ago

crosses

the

same

node

rotates westward along the ecliptic with a period of 18.60 years, or 19.3549° per year. When viewed from celestial

DEBRIS

9

10

the

nodes

move

clockwise

around the Earth, opposite the Earth’s own spin and its revolution around the Sun. Lunar and solar eclipses can occur when the nodes align with the Sun,

space,

but

precesses

over

time.

show that over hundreds of millions of years the Moon receded at an average rate of 22 millimeters per year and

the day lengthened at an av of

12

microseconds

per

y

about half of their current v

tidal acceleration for mor description.

* The

Moon is

receding from the Earth int orbit, and calculations su

this would continue for a

billion years. By that time,

and Moon would become cau

what is called a “spin–orbit r

or “tidal locking” in which

will circle the Earth in abo

(currently 27 days), and b landing.

* Earth

would rota

their axes in the same tim facing each other with the (This

has

already

happen

Moon -- the same side alw

Earth. This is slowly happen

Earth.) However, the slowdo

Earth’s rotation is not occu

enough for the rotation to le

a month before other effec

the situation: about 2.3 bil from now, the increase of

CREATE

11

12

THE MOON HELPED CREATE THE LANDSCAPE

THE MOON WOULD CONTINUE TO ORBIT THE EARTH BUT AT FIRST, IT WAS MUCH CLOSER TO THE EARTH AND AFFECTED THE TIDES MORE WHICH HELPED CREATE THE LANDSCAPE OF THE EARTH.

* In

1898, George Darwin made the

had

once

suggestion that the Earth and Moon been

one

body.

Darwin’s

hypothesis was that a molten Moon had been spun from the Earth because of centrifugal forces, and this became the dominant academic explanation.

[5] Using Newtonian mechanics, he calculated that the Moon had orbited much more closely in the past and was

drifting

away

from

the

Earth.

This drifting was later confirmed by American

and

Soviet

experiments,

using laser ranging targets placed on the

Moon.

calculations mechanics

* Nonetheless, could

required

not

to

Darwin’s

resolve

the

trace

the

Moon backward to the surface of the

Earth.

Aldworth

suggested that the Moon was formed by

Daly of Harvard University challenged

the tangential impact upon Earth of a

Darwin’s explanation, adjusting it to

body the size of Mars. It is hypothesized

postulate that the creation of the Moon

that most of the outer silicates of the

was caused by an impact rather than

colliding

centrifugal forces. Little attention was

whereas a metallic core would not.

paid to Professor Daly’s challenge until

Hence, most of the collisional material

a conference on satellites in 1974, during

sent

which the idea was reintroduced and

silicates, leaving the coalescing Moon

later published and discussed in Icarus

deficient in iron. The more volatile

in 1975 by Dr. William K. Hartmann

materials

and Donald R. Davis. Their models

the

suggested that, at the end of the planet

the Solar System, whereas, silicates

formation period, several satellite -sized

would tend to coalesce.

bodies had formed that could collide

the hypothesized protoplanet is derived

with the planets or be captured. They

from the mythical Greek titan Theia,

proposed that one of these objects may

who gave birth to the Moon goddess,

have collided with the Earth, ejecting

Selene. This designation was proposed

refractory, volatile-poor dust that could

initially by the English geochemist Alex

coalesce to form the Moon. This collision

N. Halliday in 2000 and has become

could potentially explain the unique

accepted in the scientific community.

geological and geochemical properties

According

of

the

was

In

1946,

Moon.

taken

by

*

Reginald

A

similar

Canadian

body

into

would

orbit

that

collision

be

would

were

consist

emitted

probably

to

vaporized,

modern

would

of

during escape

* The name of

theories

of

approach

planet formation, Theia was part of a

astronomer

population of Mars-sized bodies that

Alastair G. W. Cameron and American

existed in the Solar System 4.5 billion

astronomer

years ago from the beginning of time.

William

R.

Ward,

who

B e ca u se the l u n a r o r b i t i s a l so i n cl i n e d to the E a r th’ s e cl i p ti c p l a n e b y 5 .1°, the r o ta ti o n a xi s o f the M o o n se e ms to r o ta te to wa r ds a n d a wa y fr o m u s du r i n g o n e co mp l e te o r b i t.

T hi s i s r e fe r r e d to a s l a ti tu di n a l l i b e r a ti o n , whi ch a l l o ws o n e to se e a l mo st 7° o f l a ti tu de b e yo n d the p o l e o n the fa r si de o f i t.

2 our moon ///

THE MOON’S CONTROL THE TIDES

When viewed from the north celestial pole, from the star Polaris, the Moon orbits the Earth

THE GRAVITATIONAL ATTRACTION THAT THE MOON EXERTS ON EARTH IS THE MAJOR CAUSE OF TIDES IN THE SEA; THE SUN HAS A LESSER TIDAL INFLUENCE .

* If

the Earth possessed a global ocean of uniform depth,

counterclockwise,

the Moon would act to deform both the solid earth ( by a

it orbits the Sun

small amount) and ocean in the shape of an ellipsoid with

counterclockwise,

high points directly beneath the Moon and on the opposite

and the Moon

side of the Earth. However, as a result of the irregular

and Earth rotate

coastline and var ying ocean depths, this idealization is only

on their own axes

partially realized. While the tidal flow period is generally

counterclockwise.

synchronized to the Moon’s orbit around Earth, its phase can var y. In some places on Earth there is only one high tide per day, though this is somewhat rare.

* The

tidal

bulges on Earth are carried ahead of the Earth–Moon axis by a small amount as a result of the Earth’s rotation. This is a direct consequence of friction and the dissipation of energy as water moves over the ocean bottom and into or out of bays and estuaries. Each bulge exerts a small amount of gravitational attraction on the Moon, with the bulge closest to the Moon pulling in a direction slightly forward along the Moon’s orbit, because the Earth’s rotation has carried the bulge forward. The opposing bulge has the opposite effect, but the closer bulge dominates due to its comparative closer distance to the Moon. As a result, some of the Earth’s rotational momentum is gradually being transferred to the Moon’s orbital momentum, and this causes the Moon to slowly recede from Earth at the rate of approximately 38 millimeters per year. In keeping with the conservation of angular momentum, the Earth’s rotation is gradually slowing, and the Earth’s day thus lengthens by about 23 microseconds ever y year (excluding glacial rebound). Both figures are valid only for the current configuration of the continents. Tidal rhythmites from 620 million years ago show that over hundreds of millions of years the Moon receded at an average rate of 22 millimeters per year and the day lengthened at an average rate of 12 microseconds per year, both about half of their current values. See tidal acceleration for a more detailed description and references.

* The Moon

is gradually receding from the Earth into a higher orbit,

and calculations suggest that this would continue for about fifty billion years. By that time, the Earth and Moon would become caught up in what is called a “spin–orbit resonance” or “tidal locking” in which the Moon will circle the Earth in about 47 days (currently 27 days), and both Moon and Earth would rotate around their axes in the same time, always facing each other with the same side.

THE TIDES

15

16

EARTH MOVEMENT

17

18

THE MOON

CONTROLS

EARTH MOVEMENT

THE PRIMARY GEOLOGICAL PROCESSES THAT HAVE MODIFIED THE LUNAR SURFACE ARE IMPACT CRATERING AND VOLCANISM, AND BY USING STANDARD STRATIGRAPHIC PRINCIPLES.

*

The lunar geological time scale has been divided

into five periods (Pre -Nectarian, Nectarian, Imbrian, Eratosthenian, and Copernican) with one of these Nevertheless, at least one notable

being subdivided into two epochs. These divisions of geological time are based on the recognition

scientific work has

of convenient geomorphological markers, and as

advocated using

such, they should not be taken to imply that any

lunar geological timescale to the

fundamental changes in geological processes have

Hadean eon of

occurred at these boundaries. The Moon is unique in

Earth’s geological

the solar system in that it is the only body for which

timescale in here.

In particular, it is

we possess rock samples with a known geological

sometimes found

context. By correlating the ages of samples obtained

that the Hadean is

from the Apollo missions to known geological

subdivided into the Cryptic, Basin Groups 1-9.

units, it has been possible to assign absolute ages to some of these geological periods. The timeline below

represents

one

such

attempt,

but

it

is

important to note that some of the ages are either uncertain, or disputed. In many lunar highland regions, it is not possible to distinguish between Nectarian and Pre -Nectarian materials, and these deposits are sometimes labeled as just Pre -Imbrian.

* The

divisions of the lunar geological time scale

are based on the recognition of a few convenient geomorphological markers. While these divisions are extremely useful for ordering geological events in a relative manner, it is important to realize that the boundaries do not imply any fundamental change of geological processes. Furthermore, as the oldest geological periods of the Moon are based exclusively

on

the

times

of

individual

impact

events, these punctual events will most likely not correspond to any specific geological event on the other terrestrial planets.

This notation isn’t entirely consistent with the above lunar geological time scale in that the Cryptic and Basin Groups 1-9 (both of which are only informal terms that are not used in maps) comprise the Pre-Nectarian period.

0.0 THE MOON’S

ROTATION

CHANGES OVER TIME

Fi na l l y, bec a u se t he Mo o n is o nl y a bo u t 6 0 E a r t h ra dii a wa y fr o m th e Ea rth ’s c e nt er o f ma ss, a n observer a t t he e q u a to r w h o o b serves th e M o o n t h ro u gh o u t

THE EARTH’S ROTATION IS SLOWING BY .002 SECONDS PER DAY PER CENTURY. THE DAYS WILL GROW LONGER WITH THE TIME IN THE UNIVERSE.

on the Moon, the time that it

* Earth

the

will

become

tidally

locked on the Moon. Just as it is

locked

on

Earth.

However,

as Earth’s rotation is slowing,

t he ni gh t mo ves

angular

momentum

l a t e r ally by o n e

energy)

is

Ea r t h dia meter.

the Moon. This is causing the

being

(rotational

transfered

to

Moon to slowly spiral further out from Earth. As the radius of the Moon’s orbit increases, its period (the time it take to complete an orbit) increases. The result is that by the time Earth becomes locked

takes the Moon to complete an orbit will be something greater than 655.2 hours (27.3 “days”).

* However, story

this ends.

is

not

The

where

Sun

also

causes tides on Earth. So, Earth’s rotational velocity will continue to slow. As Earth’s rotation slows, the Moon induced tides will cause the Moon to stop moving away and cause it to start moving back toward Earth. If this is allowed to continue, then eventually the Moon will be drawn in so close that

tidal

stresses

caused

by

Earth’s gravity will tear the Moon apart. This will give Earth a ring.

002 .002 SECONDS

19

20

EARTH

IS FOREVER

AFFECTED

B e ca u se the l u n a r o r b i t i s a l so i n cl i n e d to the E a r th’ s e cl i p ti c p l a n e b y 5 .1, the r o ta ti o n a xi s o f the M o o n se e ms to r o ta te to wa r ds

This hypothesis states that the Moon was captured, completely formed, by the gravitational field of the Earth. This is unlikely, since a close encounter with the Earth would have produced either a collision or an alteration of the

a n d a wa y fr o m

trajectory of the body in question,

u s du r i n g o n e

so if it had indeed happened, the

co mp l e te o r b i t.

Moon probably would never return

T hi s i s r e fe r r e d

to meet again with the Earth.

to a s l a ti tu di n a l

For this hypothesis to function,

l i b e r a ti o n , whi ch a l l o ws o n e to se e a l mo st 7 o f l a ti tu de b e yo n d the p o l e o n the fa r si de . F i n a l l y, b e ca u se the M o o n

there would have to be a large atmosphere extended around the primitive Earth, which would be able to slow the movement of the Moon before it could escape. This very hypothesis is considered to

i s o n l y a b o u t 60

explain

E a r th r a di i a wa y

orbits

fr o m the E a r th’ s

This

ce n te r o f ma ss.

the of

irregular

Jupiter

hypothesis

and has

satellite Saturn. difficulty

explaining essentially identical oxygen isotope ratios of 2 worlds.

BY THE MOON’S

CONTROL

OVER MOVEMENT

MOVEMENT

21

22

THE MOON AND EARTH

ARE CONSISTENTLY

CHANGING

UNTIL THE RISE OF SPACE TRAVEL IN THE TWENTIETH CENTURY, THERE WAS LITTLE DISTINCTION BETWEEN ORBITAL AND CELESTIAL MECHANICS. THE FUNDAMENTAL TECHNIQUES, SUCH AS THOSE USED TO SOLVE THE KEPLERIAN PROBLEM, ARE THEREFORE THE SAME IN BOTH FIELDS. FURTHERMORE, THE HISTORY OF THE FIELDS IS ALMOST ENTIRELY SHARED.

* The geological history of the Moon has been defined into six major

epochs, called the lunar geologic timescale. Starting about 4.5 billion years ago, the newly formed Moon was in a molten state and was orbiting much closer to the Earth. The resulting tidal forces deformed the molten body into an ellipsoid, with the major axis pointed towards Earth.

* The

first important event in the geologic evolution of the

Moon was the crystallization of the near global magma ocean. It is not known with certainty what its depth was, but several studies imply a depth of about 500 km or greater. The first minerals to form in this ocean were the iron and magnesium silicates olivine and pyroxene.

Because these minerals were denser than the molten material around them, they sank. After crystallization was about 75% complete, less dense anorthositic plagioclase feldspar crystallized and floated, forming an anorthositic crust about 50 km in thickness. The majority of the magma ocean crystallized quickly (within about 100 million years or less), though the final remaining rich magmas, which are highly enriched in incompatible and heat producing elements, could have remained partially molten for several hundred million (or perhaps 1 billion) years. It appears that the final rich magmas of the magma ocean eventually became concentrated within the region of Oceanus Procellarum and the Imbrium basin, a unique geologic province that is now known as the Procellarum Terrane.

* Quickly

after the lunar

crust formed, or even as it was forming, different types of magmas that would give rise to the Mg-suite norites and troctolites began to form, although the exact depths at which this occurred are not known precisely. Recent theories suggest that Mg-suite plutonism was largely confined to the region of the Procellarum Terrane, and that these magmas are genetically related in some manner, though their origin is still highly debated in the scientific community. The oldest of the Mg-suite rocks have crystallization ages of about 3.85 Ga. However, the last large impact that could have excavated deep into the crust also occurred at 3.85 Ga before present.

CALCULATION

23

24

3 the future moon ///

Region IV, Outer Envelope

Region III, Moon and Environs

Region II, Circumferential Space

Region I, Earth and Atmosphere

Moon

Region IV, Outer Envelope

THE MOON

WILL SLOWLY

MOVE AWAY

EVERY ORBIT AND TRAJECTORY OUTSIDE ATMOSPHERES IS IN PRINCIPLE REVERSIBLE, I.E., IN THE SPACE-TIME FUNCTION THE TIME IS REVERSED. THE VELOCITIES ARE REVERSED AND THE ACCELERATIONS ARE THE SAME, INCLUDING THOSE DUE TO ROCKET BURSTS.

* Standard

assumptions in astrodynamics include non-

orbiting body is subject only to the gravitational force of

interference from outside bodies, negligible mass for one of

the central attractor. When an engine thrust or propulsive

the bodies, and negligible other forces (such as from the solar

force is present, Newton’s laws still apply, but Kepler ’s laws

wind, atmospheric drag, etc.). More accurate calculations

are invalidated. When the thrust stops, the resulting orbit

can be made without these simplifying assumptions, but

will be different but will once again be described by Kepler ’s

they are more complicated. The increased accuracy often

laws.

does not make enough of a difference in the calculation to

follows. The specific energy (energy per unit mass) of any

* Kepler ’s laws of planetar y motion may be

space vehicle is composed of two components, the specific

be worthwhile.

derived from Newton’s laws, when it is assumed that the

* The formula for escape velocity is easily derived as

potential energy and the specific kinetic energy.

SLOWLY MOVING

27

28

IT IS UNKNOWN

WHAT WILL HAPPEN

IN THE FUTURE According to Gennady Raykunov, General Director of the Central Research Institute of Mechanical Engineering, the Moon may eventually leave the Earth’s orbit and become an independent planet. In this case, the Earth will turn into a lifeless desert.

*

Raykunov says that the Moon may repeat the fate

of Mercur y, which supposedly was once a satellite of Venus, but then “flew ” away. After that, the conditions on Venus became unfit for life, despite the fact that it is an Earth-like planet.

*

“ The

Moon, too, is moving away from Earth every year, and if no reverse process happens, it may leave its orbit,” he made this statement for the air show in Le Bourget. ‘Could earth follow the path of Venus and form conditions not suitable for existing life forms - aggressive atmosphere, great pressure, greenhouse effect, etc. space

exploration

is

*

According to the scientist,

currently

being

conducted

that will help to determine whether the conditions will change life on our planet, whether it loses its natural satellite, and how to prevent the worst case scenario.

*

Gennady Raykunov has long been

concerned with the fate of the Moon. Earlier, he called the satellite the “seventh continent” and stressed the need to create a continuously operating base on it, whose members would conduct research and use the resources of the celestial body.

*

Now

the Moon moves around Earth in an orbit close to the elliptical, counter- clockwise (as viewed from the North Pole) with an average speed of 1.02 kilometers per second. In fact, the movement of our natural satellite is a fairly complex process influenced by various disturbances caused by the attraction of the sun, planets and the Earth’s oblate shape. How likely is the scenario proposed by Raykunov?

*

Sergei

Popov, a researcher with the State Astronomical Institute of the Moscow State University of Sternberg (SAI), confirmed that the Moon is really moving away from Earth, but very slowly - the removal rate is approximately 38 millimeters per year. “In several billion years period the Moon will rise by

resources to escape.”

* Vladimir

Surdin, another

employee of SAI, added that even this process of removing the Moon from Earth will not last forever: eventually the satellite will begin approaching the planet again.

* According

to Surdin, under

the influence of solar tides, rotational speed of the planet is gradually reduced, and the rate of removal of the satellite will gradually decrease.

After approximately five billion years the lunar orbit radius would reach a maximum value - 463 thousand kilometers, and the duration of Earth days would increase to 870 hours.

* “ The statement

“ The Moon could leave Earth’s orbit and become a planet “is wrong,” Surdin said. “ Solar tides will continue to inhibit the Earth. But now the Moon will outstrip the Earth’s rotation, and tidal friction will slow down its motion. As a result, the Moon will approach the Earth, albeit very slowly, because the force of solar tides is low.”

* But

even if we

imagine that the Moon is no longer a satellite of the Earth, it still will not turn our planet into a lifeless resemblance of Venus, scientists say. Alexander Bazilevsky, head of the Laboratory of Comparative Planetology of the Institute of Geochemistry and Analytical Chemistry RAS named after Vernadsky, commented: “ The conditions on the surface of the Moon have little effect on Earth. There will be no ebbs and tides, and the nights will be moonless. We will survive.”

* Colleagues of Raykunov do not fully

agree with his assertion to the effect that Mercury was once a companion of Venus. “ The calculations show that it is possible, however, it does not prove that it was the case,” said Bazilevsky. He added that the development of Earth and Venus cannot be the same as the Venusian atmosphere is enriched with heavy isotope of hydrogen - deuterium.

* “ This could

be due to the fact that Venus once had a relatively

large amount of water. During the decomposition of water in the upper atmosphere into hydrogen and oxygen, light hydrogen isotope escaped into the space faster than the heavy ones, causing the

Without the applying thrust (such as firing a rocket engine), the height and shape of the satellite’s orbit won’t change, and it will still maintain the same orientation with respect to the fixed stars.

THE UNKNOWN

29

30

not be as hot there at the time as it is now.”

* In

diagram

can

be

repeated

for

many

different

short, we still have nothing to fear, and earthlings

positions of the Moon in its orbit. For each position,

will be able to walk under the Moon for at least

the result is a perturbation vector like LS1 or LS2

five billion years.

Newton’s diagram ‘to find the

in the second diagram. Shown here is an often-

force of the Sun to perturb the Moon’ accompanying

presented form of the diagram that summaries

Book 3, Proposition 25 of the Principia.

Parts

sizes and directions of the perturbation vectors for

of this diagram represent distances, other parts

many different positions of the Moon in its orbit.

gravitational accelerations (attractive forces per

Each small arrow is a perturbation vector like LS,

unit mass). In a dual significance, SQ represents

applicable to the Moon in the particular position

the Earth-Sun distance, and then it also represents

around the orbit from which the arrow begins.

the size and direction of the Earth-Sun gravitational

The perturbations on the Moon when it is nearly in

acceleration. Other distances in the diagram are

line along the Earth-Sun axis, i.e. near new or full

then in proportion to distance SQ. Other attractions

moon, point outwards, away from the Earth. When

are in proportion to attraction SQ. The moon is

the Moon-Earth line is 90° from the Earth-Sun axis

celestial.

they point inwards with a size.

*

*

*

Solar perturbation vectors analogous to

From a circular orbit, thrust in a direction which slows the satellite down will create an elliptical orbit with a lower periapse (lowest orbital point) at 180 degrees away from the firing point. If thrust is applied to speed the satellite, it will create an elliptical orbit with a higher apoapse 180 degrees away from the firing point.

ORBIT

31

32

THE T WO

POSSIBILITIES

BECOME MORE

The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the same circular orbit and wish to dock, unless they are very close, the

T o the degree tha t the sta nda rd a ssum pti ons of a strodyna mi cs do not hold, a ctua l tra j ectori es wi ll va ry f rom those

trailing craft cannot simply fire

ca lcula ted. F or

its engines to go faster. This will

exa mple, si mple

change the shape of its orbit,

a tmospheri c

causing it to gain altitude and

dra g i s a nother

miss its target. One approach is

compli ca ti ng

to actually fire a reverse thrust to slow down, and then fire again to re -circularize the orbit at a lower altitude. Because lower orbits are faster than higher orbits, the trailing craft will begin to catch up. A third firing at the right time will put the trailing craft in an elliptical orbit which will intersect the path of the leading craft, approaching from below.

f a ctor f or obj ects i n Ea rth orbi t.

THE TWO

POSSIBILITIES

BECOME MORE

T o the de g r e e

The consequences of the rules of

tha t the sta n da r d

orbital mechanics are sometimes

a ssu mp ti o n s o f a str o dyn a mi cs do n o t ho l d, a ctu a l tr a j e cto r i e s wi l l va r y fr o m tho se ca l cu l a te d. F o r

counter-intuitive. For example, if two spacecraft are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire

e xa mp l e , si mp l e

its engines to go faster. This will

a tmo sp he r i c

change the shape of its orbit,

dr a g i s a n o the r

causing it to gain altitude and

co mp l i ca ti n g

miss its target. One approach is

fa cto r fo r o b j e cts

to actually fire a reverse thrust to

i n E a r th o r b i t.

slow down, and then fire again to re - circularize the orbit at a lower altitude.

Because

lower

orbits

are faster than higher orbits, the trailing craft will begin to catch up. A third firing at the right time will put the trailing craft in an elliptical orbit which will intersect the path of the leading craft, approaching from below.

POSSIBILITIES

33

34

THE ONLY

CONSTANT

IS CHANGE

CONSTANT

35

36

The tidal

bulges

are carried ahead of the Earth–Moon axis

by a small amount as a result a direct energy

of the Earth’s rotation.

consequence of friction

as water moves over the ocean bottom

estuaries.

This is

and the dissipation and into or out of

of bays and

Each bulge exerts a small amount of gravitational attraction on the Moon,

bulge closest to the because

on Earth

the Earth’s rotation has

effect, but the closer

Moon pulling in a direction slightly

Moon. As a result, gradually being transferred the Moon to slowly

forward along the Moon’s orbit,

carried the bulge forward. The opposing bulge

bulge dominates due to its

with the

has the opposite

comparative closer distance

some of the Earth’s

to the Moon’s

recede from Earth at the rate

rotational momentum is

orbital momentum, and this of approximately 38 millimeters

per year. In keeping with

the conservation of

angular momentum,

the Earth’s rotation is

gradually slowing,

and the Earth’s day thus

lengthens by about

23 microseconds ever y year (excluding glacial

rebound).

Both figures are valid only for

the current

to the

causes

CHAOS

COLOPHON Paper

Plotnet

Melissa Kelly

Instructed by Ariel Grey

Academy of Art University

Summer 2012

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *