# [time-nuts] NPR Story I heard this morning

Peter Monta pmonta at gmail.com
Tue Nov 4 14:04:58 EST 2014

```Hi Tom,

> Based on mass and radius, a clock here on Earth ticks about 6.969e-10
> slower than it would at infinity. The correction drops roughly as 1/R below
> sea level and 1/R² above sea level. For practical and historical reasons we
> define the SI second at sea level.
>

Yes, the change in clock rate at sea level is about 1e-18 per centimeter,
and the geoid is known only to about 1 centimeter uncertainty at best.

> The non-local gravity perturbations you speak of are 2nd or 3rd order and
> so you probably don't need to worry about them. Then again, if you want to
> get picky, it's easy to compute how much the earth recoils when you stand
> up vs. sit down. So it's best to avoid the notion of "arbitrary" precision;
> that's for mathematicians. For normal people, including scientists, we know
> that precision and accuracy have practical limits.
>

Let me rephrase what I'm after.  The geoidal uncertainty sets a hard limit
on clock comparison performance on the Earth's surface (for widely-spaced
clocks).  At some point, as Chris Albertson noted, the clocks will measure
the potential and not the other way around.  (It should be possible to
express this geoidal uncertainty as an Allan variance and include it in
graphs with the legend "Earth surface performance limit".)

What I'm curious about is this:  what are the limits on clocks in more
benign environments?  How predictable is the potential in LEO, GEO,
Earth-Sun L2, solar orbit at 1.5 AU, solar orbit at 100 AU, etc.?  I
imagine the latter few are probably very, very good, because the tidal
terms get extremely small, but how good?

Suppose a clock dropped into our laps with 1e-21 performance, just to pick
a number.  Where would we put it to fully realize its quality (and permit
comparisons with its friends)?  And is the current IAU framework adequate
to define things at this level (or any other arbitrarily-picked level)?
```