###### 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 time measurements?*

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.

We knew this distance very closely, even in 1672, Cassini computed Sun-earth to be 14 Karod kms = 140 million kms, the truer, as we know today, is, 15 karod kms = 150 million kms.

Tyco Brahe measured: 8 million kms, Kepler measured 24 million kms, but Cassini’s was approximately correct 140 million kms, read the NASA account here.

Note that: **w** = (G.M_sun)^0.5 / r^1.5 = sqrt (G.M_sun / r.r.r). so v^2 = v.v = G.M_sun / r — where M_sun is large, but r is 1 AU. v.v is what gives the order of time, which is 1 / r, so r = 1 and r = 0.99983, have, a difference of 0.00017. That is, the first change in time, appears in the 4th decimal place — between earth and satellite.

We have to put the angular speed due to orbit around Sun, in the right order, before we can see, the order of time — so I am reviewing the above, but seems, if not 10^-21, it is at-least 10^-16 and only 10^-8 seconds matter.