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2018-11-27 13:53:42 UTC
Has any one bought the SRS FS740                                                   Bert Kehren

In a message dated 11/21/2018 11:11:18 AM Eastern Standard Time, ***@woh.rr.com writes:

Thanks Steve and Tom for helping me sort that out. Much appreciated.

Tom Holmes, N8ZM

-----Original Message-----
From: time-nuts <time-nuts-***@lists.febo.com> On Behalf Of Tom Van Baak
Sent: Wednesday, November 21, 2018 10:49 AM
To: Discussion of precise time and frequency measurement <time-***@lists.febo.com>
Subject: Re: [time-nuts] WWV Doppler Shift
So if the SI second is specified at sea level, and we know from Einstein and TVB's
work that going up a mountain changes a clock's period, how would the second be
affected at the center of the Earth ( ignore thermal problems, this is a conceptual
discussion) where the net gravity vector might conceivably zero? Or for that matter,
at a Lagrange point in space? We do have some data from those locations I would think.
By convention, the SI second is defined at sea level.
A clock at infinity runs about 6.95e-10 faster.
A clock at the center runs about 3.48e-10 faster.
There's a useful diagram in [1]. Image attached. Just follow the green "gravity speedup" line.

If by "gravity vector" you mean the acceleration of gravity (as in "g") then yes, that's 0 at the center, also 0 at infinity and roughly 9.8 m/s^2 at the surface. If the Earth were homogeneous then g would drop by 1/r^2 outside and 1/r inside the surface. In reality the earth is far more interesting and complex. For a good time see [2] and also google: earth PREM
A second  question (no pun intended) is that given the Earth's elliptical orbit around the
Sun, has there been observed an effect of the change in its gravity on atomic clocks?
Right, an elliptical orbit means both velocity and distance will vary from a mean, so, yes, relativistic effects will also vary from their mean. For GPS the eccentricity is a mere 0.02 so the peak effect is only about 45 ns (this correction is done in GPS receiver software). For a wild satellite orbit like Molniya with eccentricity 0.7, the peak effect is 1.6 us. This data from the "Table 1" in [3]; a very useful paper. But you asked about earth/sun not gps/earth. I'll hunt or calculate those numbers.


[1] https://en.wikipedia.org/wiki/Gravitational_time_dilation

[2] https://en.wikipedia.org/wiki/Preliminary_reference_Earth_model

[3] "Relativistic Time Transfer in the Solar System", Robert A. Nelson

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