Thanks Steve and Tom for helping me sort that out. Much appreciated. Tom Holmes, N8ZM
-----Original Message----- From: time-nuts <time-nuts-boun...@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-nuts@lists.febo.com> Subject: Re: [time-nuts] WWV Doppler Shift 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 _______________________________________________ time-nuts mailing list -- time-nuts@lists.febo.com To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
