it does look right. another way of looking at it is
if it does 1 rev in say 45 seconds, in 86164 secs it would do
86164/1 * 45 revs or 1914.756 revs
you get 45 if you do 86164/1914.756 = 45
you substitute your precise ratio and you get the result you've mentioned.
if the motor is a stepper, I'd calculate the pulse freq required considering the step angle and microsteps used and measure the input pulse freq of whichever controller you're using to see how far or close it is.
also need to consider all the backlash involved as you have several stages.
if you use 1.8 deg stepper, and use 1/8 microstepping, you'd need an input pulse as below using your reduction ratio
need to turn 360 deg of the output shaft in 86164.091 secs
Thats 0.004178075 deg in 1 sec
0.004178075 x 1929.886 = 8.06320844945 deg of the motor shaft in 1 sec
with 1/8 microstepping of a 1.8 deg stepper, 1 step turns 0.225 deg
or 360 deg in 1600 microsteps
you need 8.06320844945 deg in 1 sec of the motor shaft
thats 8.06320844945 x 1600 / 360 = 35.83648 steps
therefore step pulse freq should be 35.83648 Hz.
I had started a thread with a similar query, Gary and others have provided some very valuable information on various factors involved as the tracking rate is not a constant.
you'd need to track at the King rate which is a rough approximation.
all depends on what you want to do