This is an original research work of Manmohan Dash, published here, 30 November 2011, 1.20 pm.
Why orbital motion of earth around sun, does not matter to GPS?
Because, it is not only earth, the satellite is also marching in a circle around the Sun and the Sun is simply too far.
Sun and earth distance is 1 AU ~ 149,597,871 kms — 15 karod kms, mere pyare bhaion aur behenon.
Earth-Satellite distance is about 26,000 kms = 0.000174 AU ~2 milli AU.
The angular speed of earth and satellite, due to Sun, will be almost same; w = r^(-1.5) = sqrt (1/ r.r.r), what difference it makes, if we change r, by 0.0002, when r is 1, the result is 1 changes to 0.9997.
So, if the angular speed of earth, is 1, the angular speed of satellite, assuming it is 26000 kms closer to sun-center, would be 0.9997. Thats a difference in the 4th digit. Now angular speed of earth itself is of 10^-5 order. So, this is 10^-9 order change. Why do we worry when earth spin itself is 1% of static effect, which is 1000 times at-least, smaller, than 1 nanosecond.
In other words, Sun’s effect, will be slightly more or less, between earth and satellite, by 10^-14, a digit in the 14th figure. If we adjust our digits, it will come to order 13 or go to order 15. So, we can safely say, the effect of Sun because of earth and satellite orbiting about Sun is, < 10^-12 nano-second = 10^-21 seconds. Anything at 10^-8 seconds is important.