Quantifying the return arms in my Michelson-Morley.
Frank Russo - May 13, 2010.
It is very helpful if everybody can see how the two arms tally up... especially in the return phase where most persons have said they had trouble visualizing everything. So here's an attempt at providing some more intricate detail.
The return orbital arm of 9.078,076,718 m is of course only a particular proportion of a full return arm... the proportion being 0.984618107/1.000000000... hence in a version where the stationary arm has not been shortened, the return orbital would actually become 9.219,896,171 m which means that the bit travelled by the origin to meet it would be an equivalent of 1.610,903,011 m with the two actually adding to a relative length of 10.830,799,18 m... this would in turn give an arm of the same length, when one adds the equivalent hollow that would be formed by the mirror moving in the opposite direction to the reflected light beam.
The foregoing is very helpful in determining how much more than expected the perpendicular has already travelled down its return segment, when the orbital return segment is being started. Obviously there is 0.141819453 m extra which has to be travelled, which as far as the orbital components go, would make the longer one longer by that amount and the shorter one even shorter by that amount: this amount is deduced by subtracting the 9.078076718m from the 9.219896171m. Of course this is "total return" orbital length extra which is being considered, so you can't just transfer it and count it as extra return perpendicular-light-length, without first deducting the extra motion of the apparatus involved in travelling the 1.610903011m by light... namely 0.024778737m... (that is 1.610903011 minus the "normal" 1.586124274m)!
Naturally the 0.141819453m would then become 0.139638001m and the miraculous fantastic thing that happens, is that when you multiply this number by the SDR of 1.193072004 you get the pivotal 0.166598191m (with some slight error from the calculator carried on.)
The making of the longer arm even longer, and the shorter arm even shorter, is a key contributor to returning to an origin which has allowed a proper passage of orbital time so that everything is synchronized!
Hopefully I've gone a long way in elucidating some more very complicated inner workings of the Michelson-Morley and relativity!
P.S. - If you deduct the 0.139,638,001 m from the total perpendicular (pre-orbital mirror), of 1.892360466 (the latter being 1.921923284 along the hypotenuse), one gets the now very familiar 1.752722466 m ... truly amazing!