Subject: Re: [LPNY DISCUSS](OT) Mr. Science bad Date: Wed, 1 Oct 2003 11:05:55 -0400 To: From: Bob Armstrong ( Sorry , can't control self . ) In the tub this morning , while reading a few more pages of "When Genius Failed , The rise & fall of Long Term Capital Management " , the proper simplification of r % r ^ 3 % 2 which somehow eluded me when I wrote the note below , gelled in my head . Subtracting exponents , the expression simply reduces to : r ^ - 1 % 2 IE , planets slow by the square root of r . Which , while I still haven't groked the whole relationship , has a pleasant symmetry with the r ^ 2 reduction in gravitational force . Blay , can you take it from there ? I'd note , by the way , that of course Kepler died not understanding the cause of laws he found observationally . -- On Tue, 30 Sep 2003 09:37:09 -0400, Bob Armstrong wrote: >=A0On Mon, 29 Sep 2003 23:03:08 -0400, Blay Tarnoff wrote: >=A0>=A0Bob Armstrong wrote: >=A0>=A0> >=A0>=A0>=A0By Kepler's law . . ., if the radius of an orbit is >=A0>=A0>=A0increased by 1.1 times , the period increases by >=A0>=A0>=A01.1 ^ 3%2 =A0or about 1.1537 . >=A0> >=A0>=A0Why? > >=A0As I said > >=A0>=A0>=A0I have not had the product of time and interest to grok >=A0>=A0>=A0orbital energetics , but it's clearly not as simple as >=A0>=A0>=A0just saying the speed goes down as r ^ 2 . Obviously >=A0>=A0>=A0Kepler found it to be =A0r % r ^ 3%2 as I had in my table >=A0>=A0>=A0in message 19428 . --=A0 =A0Bob Armstrong -- http://CoSy.com -- 212-285-1864