Well, there's interesting things with stuff like bistatic radar where microseconds matter.

But this is the kind of thing where the non-time-nuts might naively think "NTP does that" or "PPTP does that" or "I'll use a GPSDO" and not realize that relativistic effects actually get important at large distances and velocities.

On Tue, 07 Jan 2025 11:06:48 -0500, tme--- via time-nuts time-nuts@lists.febo.com wrote:

On 2025-01-07 02:53, Hal Murray via time-nuts wrote:

It depends on the desired timing accuracy and what you want to do.
Einstein synchronization (two way time transfer) works more or less the
same anywhere in the solar system, except that some of the clock
discrepancies will be caused by general relativity. That implies that if
you are doing 1 way time distribution (as, e.g., GPS does), you will at
some level need a relativistic time model.

For the Earth-Moon system, the lunar surface time (LCT) is blue-shifted
with respect to the Earth's surface. Based on the analysis of 4 separate
groups (including my own), the mean (LTC-TAI) rate is 6.48288 x 10-10
with a standard deviation about that mean of 1.90112 x 10-13 (i.e., that
appears to be ~ the current model error). This blue shift (i. e., LTC
running faster than TAI) corresponds to a clock rate difference of
56.012 μsec / day with a standard deviation of 0.016 μsec / day. (The
April 2 OSTP announcement with a claim of 58.7 µseconds per Earth-day
appears to neglect the 2.7116 µsec / day from the lunar surface redshift
due to lunar surface gravity)

Time-varying frequency / time shifts are dominated by the effects of the
lunar orbit eccentricity and solar perturbations in the lunar orbit. If
the lunar blue shift mean rate is removed, the RMS variation of LCT is
~398 nanoseconds, corresponding to a fractional frequency variation of
9.2752 × 10^−13, ∼ 5% of the mean lunar orbital redshift. General
relativistic 3-body effects come in at about 1 x 10^-13, and will in due
course be fun to look for.

So, if you only care about milliseconds, none of this matters. If you
care about microseconds, you should remove the rate, and have an
adjusted lunar time that roughly matches TAI. If you care about
nanoseconds, you need a relativistic model for lunar time. When we get
good optical clocks (with ffs ~ 10^-18 or better) on the Moon, we'll
have to model the frequency changes caused by the lunar solid body tides
(which cause radial motions of the surface with amplitudes of ~ 25 cm).

Regards
Marshall Eubanks

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hi,

This is highly interesting.

I'm quite a noob on this and most of my knowledge comes from a wikipedia
rabbit hole trip that started at Michelson Morley experiments and
expanded recursively to, basically, most of the linked pages.

I only have a limited understanding.

What I learned about Lorenz transforms and special relativity is that
objects moving fast appear length contracted and time expanded. Meaning
time on the moon should go slower, not faster.

But the moon is in orbit, which is not in an inertial frame.

So that's where we need general relativity, right? and the effect is
gravitational, because the moon is less massive than the earth so time
around it goes faster, is that it?

I'll have to rabbit hole even more, haha.

Sebastien

On 08/01/2025 01:55, Jim Lux via time-nuts wrote:

Yes..

But as a practical matter, the important thing is that there are various terms that are adequately modeled by things like sqrt(1-v^2/c^2), and as a function of local gravity, so one could probably create a model with generalized terms more than just mx+b, fit that model to observed data, and work with it. If one were building some sort of disciplined oscillator, for instance.

That's without having to actually figure out all the relativity in advance. Naturally, you'd want someone to figure it all out, because that would justify your modeling assumption and the uncertainty limits that come from it. But you don't have to have a detailed knowledge of special and general relativity.   We do this a lot with various things affected by orbital height -> you model it as some series approximation, take the ephemeris generated by others, figure out your approximation coefficients and run with it. You don't really care that Kepler's laws apply, etc.

I note that what the JPL DE (developmental ephemeris) does is just this - they have a big numerical integration that incorporates all observed data they have (back to Kepler and Brahe? Maybe?) and they generate output that is essentially coefficients for an interpolating polynomial in terms of time. The user of DE441 (or whatever the current version is) doesn't really need to worry about all the weighting and editing that goes on with the data, etc.  They can just consume the predicts (forward and backwards in time).

(That's one of the advantages of being an engineer vs a scientist, perhaps?)
 

On Wed, 8 Jan 2025 15:17:05 +0100, Sebastien F4GRX via time-nuts time-nuts@lists.febo.com wrote:

hi,

This is highly interesting.

I'm quite a noob on this and most of my knowledge comes from a wikipedia
rabbit hole trip that started at Michelson Morley experiments and
expanded recursively to, basically, most of the linked pages.

I only have a limited understanding.

What I learned about Lorenz transforms and special relativity is that
objects moving fast appear length contracted and time expanded. Meaning
time on the moon should go slower, not faster.

But the moon is in orbit, which is not in an inertial frame.

So that's where we need general relativity, right? and the effect is
gravitational, because the moon is less massive than the earth so time
around it goes faster, is that it?

I'll have to rabbit hole even more, haha.

Sebastien

On 08/01/2025 01:55, Jim Lux via time-nuts wrote:

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On 2025-01-08 09:17, Sebastien F4GRX via time-nuts wrote:

Basically. If we were observing (and had clocks at) the center of the
Earth, clocks on the Moon would be redshifted, because of

• The Moon sits in the Earth's gravitational potential well, which is a
  mean red shift of 0.9968 µsec / day
  ◦ Kinematic term = 5.83974 × 10−12 or 0.5046 µsec / day
• The Moon also has a 1/2 v^2/c^2 kinematic red shift, with a mean of
  0.5046 µsec / day
• and the lunar surface is sitting in the Moon's gravitational potential
  well, which is a red shift
  of 2.7116 µsec / day.

Add those up, and you get a red shift of 4.213  µsec / day.

But we - and our master clocks - don't sit at the center of the Earth.
We sit at the surface in the Earth's gravitational potential, which
causes a redshift of 60.2147 µsec / day*. Yes, the Moon runs slow, but
the Earth has more gravity and so we run slower than the lunar surface.

So, the lunar clock - Earth clock redshift is  4.213  µsec / day -
60.2147 µsec / day or −56.0017 µsec / day.

The minus here means a blue shift, so lunar surface clocks would be
blue shifted relative to Earth surface clocks, running faster by ~56
microseconds / day.

You'll get there when you start thinking about gravitational radiation,
which will come in at a fractional frequency stability somewhere around
10^-14 to 10^-18.

Regards
Marshall

• To be picky, the Earth numbers are for mean sea level.