Equalizing when going into the wind!
Frank Russo - May 23, 2010.
Of course when changing our orientation and going into the orbital velocity, things still have to add up neatly: not only must the arms match-up, but the ratios of light-travel to apparatus-travel must also add-up!
As we have seen, the away-orbital into the wind is 9.219,896,171 m, and when we subtract this from the new perpendicular of 11.000000000 m we get 1.780,103,829 m. Now to envisage this remainder as going up the true perpendicular instead of the hypotenuse, we multiply it by Cr/Ca which is 0.984,618,107 and we get 1,752,722,46 m. To now envisage the full perpendicular we convert the 9.219,896,171 to the perpendicular equivalent of 9.078,076,718 and to this we add the 1.75272246... and we of course get the familiar true perpendicular arm of 10.830,799,18 m... so everything is fine!
Let's now take a perusal at the return perpendicular, which is of course the obvious 11.000000000 m. Now the away-orbital involved an equivalent of 1.610,903,011 m of apparatus motion, whereas the away-perpendicular 11 m involves 1.921,923,284 m, which is an extra 0.311,020,273 m. Hence the return orbital-arm of 12.780,103,83 must include this motion of apparatus in its going-ons! The total apparatus motion for this return arm is of course 12.78010383m multiplied by [Vorbital/Cabsolute] giving us 2.232,943,556 m. In view of the latter number, it is obvious that the apparatus motion all tallies up... as it would incorporate the 0.311,020,273 metres carried on from the away-perpendicular 11metres, on top of the 1.921,923,284 which would match the return-perpendicular 11 metres giving us a total of 2.232,943,557 metres! This of course is the same for all intensive purposes when you disregard the slight negligible calculator rounding-off, and the use of 'partial' numbers!
Furthermore this return-orbital represents an extra 1.780,103,83 metres more than the perpendicular-return 11 metres and this matches perfectly the extra 0.311,020,273 metres once again... so everything is perfectly okay!
I can now have a bit of a rest.