Kayton suggests that the deflection of the vertical is "commonly less than 10 seconds of arc and rarely greater than 30 seconds of arc", as I quoted. Taking his 30 sec figure, that would yield a correction of cos(30 sec) to TAS, therefore to GS. Cos(30 sec) = cos(0.0001454 rad) = 0.0001454, which is about 1/6 of 0.000873. Cos(10 sec), which is what Kayton suggests "commonly" is the case, is 0.00004848, about 1/18 of 0.000873.
Wow, you've lost me now. Last time I checked, the cosine of a very small angle was almost 1, but they might have changed that in the mean time
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The fractions of 1/6 and 1/18 do work out though, but I have no idea how you come up with 0.000873
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Maybe you need to finish your morning coffee before posting...
Assuming the figures of 30 arcsec and 10 arcsec are right, the ratio of the speeds in the two different reference frames (vertical orthogonal to ellipsoid & vertical = aligned with gravity) is then 1/cos(30 arcsec) =1.000000011
That difference is really too small for me to worry about.
ATCast