[time-nuts] WWV Doppler Shift

[Tom Van Baak]

Tom Holmes, N8ZM wrote:
> 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.

/tvb

[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
https://ieeexplore.ieee.org/document/4319282
https://www.ietf.org/mail-archive/web/dtn-interest/current/pdfnEfIcI08jz.pdf

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