Researchers calculate how much faster time passes on the Moon

[Vanadium 50]

300 baud? How retro!

As you know, it may take some data for a new receiver to know "where it is in the stream". If every 8 bits is in a 10 bit stream, with bit 0 always 1 and bit 9 always 0 (or whatever), there may be multiple 0 -> 1 transitions that might be the start of a frame. But the next frame comes along, and the possibilities decrease. Even if you need 10 frames to figure out where you are, it's a fraction of a second.

Once you are synced, there's enough traffic to easily keep sync.

This global external syncing would save you a fraction of a second in the time between Power On and Ready, and possibly - possibly - let you use a frame with a little less overhead. At great expense.

 

[jbriggs444]

300 baud? How retro!

I started on an ASR-33 at 110 baud using an acoustic coupler. 1972 or so.

As you know, it may take some data for a new receiver to know "where it is in the stream". If every 8 bits is in a 10 bit stream, with bit 0 always 1 and bit 9 always 0 (or whatever), there may be multiple 0 -> 1 transitions that might be the start of a frame.

Not a problem if the line is idle when you hook up. An idle line is just sitting there at 0 volts.

In practice, I do not ever recall an issue. You could turn on a VT-100 connected to a cable was spewing data and it would just start displaying the text once the terminal was ready. You might have a gibberish character or two. [We did not use hardware flow control e.g. with RTS/CTS. I'd generally loop pin 4 back to pin 5 at the connector just in case the end point cared. Same with 6 and 20]

But the next frame comes along, and the possibilities decrease. Even if you need 10 frames to figure out where you are, it's a fraction of a second.

Yep.

 

[pervect]

This has gotten very long, so I'm going to make my main point in advance. That point is that one of the reasons we have so many standards is the relativity of simultaneity, a key feature of SR that is inherited by GR. For extremely high precision applications, when we adopt the concept of different ideas of spatial symmetry, we wind up with different notions of simultaneity.

Going a bit more into the weeds. I find that clock synchronization makes more sense from the viewpoint of a coordinate system, such as the GCRS and the ICRS.

I say this because that's what a coordinate system does - it includes not only clocks (which keep proper time) , but how to use them to specify locations and times. This ability implies the ability to synchronize clocks, by simply saying that clocks that share the same time coordinate are synchronized. It also addresses the rate issue - we can compare the rates of actual clocks to the rate of coordinate clocks, and perform appropriate adjustments as needed.

Thus, coordinates encapsulates not only how to keep track of time intervals, but also how to synchronize clocks and define coordinate numbers that represent time and place. The relativity of simultaneity comes into play here, that is why it is important to combine the discussion of spatial coordinates and time coordinates into a system of space-time coordinates. Definitions that do not include a complete coordinate system tend, unfortunately, to neglect the entire idea of simultaneity, which ultimateley winds up as a conceptual weakness.

The approach I am most familiar with is outlined in Misner's "Precis of General Relativity". https://arxiv.org/abs/gr-qc/9508043. I should not that it doesn't have an overwhelmingly high citation count, but it's key to my thought processes and I highly recommend it.

(1) dτ^2 = [1 + 2(V − Φ0)/c^2]dt^2 − [1 − 2V /c^2](dx^2 + dy^2 + dz^2)/c^2

....

Equation (1) defines not only the gravitational field that is assumed, but
also the coordinate system in which it is presented. There is no other source
of information about the coordinates apart from the expression for the met-
ric. It is also not possible to define the coordinate system unambiguously in
any way that does not require a unique expression for the metric. In most
cases where the coordinates are chosen for computational convenience, the
expression for the metric is the most efficient way to communicate clearly
the choice of coordinates that is being made. Mere words such as “Earth
Centered Inertial coordinates” are ambiguous unless by convention they are
understood to designate a particular expression for the metric, such as equa-
tion (1).

The IAU papers are very terse, but appear to follow the approach outlined by Misner, as they specify a metric associated with their various coordinate systems they define. The short version is that they specify using what is known as "harmonic coordinates".

The paper that originated this thread basically extends this to adding a Lunar-based coordinate system since we are talking about having people live there.

So, to recap, fundamentally, specifying a metric implies specifying a coordinate system. The metric can be thought of as a sort of mathematical "map" of space-time.

To recap my main point in more detail, I will point out again the role of the relativity of simultaneity. If one loosk at the transformation equations, clocks synchronized in the GCRS may not be synchronized in the ICRS, though the differences are tiny. To oversimplify, note that respecting the Earth's symmetry (axisymmetric for sure, and mostly spherically symmetric) does not respect a sun-based notion of symmetry.

This extra complexity with it's variety of coordinate systems is needed to realize the full accuracy of which General Relativity is capable of, though for many applications, one can get away with approximations which simplify things enormously. The extra complexity is really only needed for extremely precise work. For example, are as of yet few applications for Earth- based timekeeping where the lunar and solar tides have an important effect - as can be seen by Misner totally ignoring such effects in his equation (1), which is notably not necessary the same as any of the standards that I've mentioned.

There are applications in astronomy where we need to account for the varying distance of the Earth from the sun to account for effects on pulsar timing. As our timekeeping gets more and more precise, accounting for all the various effects will become more necessary to realize the full potential precision of the new methods.

 

[Nik_2213]

I sorta remember an analogous discussion about Martian time. That descended into near-farce as the embattled protagonists entirely over-looked the obvious...

Do you live on / near a coast with non-trivial tides ? Then you may have a 'Tide Clock', A 'standard' clock variously re-tuned to match the passage of Lunar' rather than 'Solar' time, it is a sufficient way to track 'Highs' and 'Lows'.

Yes, some areas have a single 'daily' tide, some the usual double, some a bizarre 'Double High' due reversing coastal currents. No big deal, local variants easily accommodated.

Whatever, you track *two* time-systems. Your analogue 'tide-clock' shows, at a glance, the coming and going of the sea, to extent allowed by Spring/Neap and Equinoctial variations, storm surges etc, Your UTC clock gives you the digital cue for weather forecasts, storm alerts, official reports, pub-hours, docking fees etc etc.

Equivalent on Mars is sun-rise, sun-set. They are 'loose' enough for 'analogue', would suit a tweaked 'Tide Clock'. Beats getting 'caught out' at night because you 'Murphied' precise correction the wrong way.
For 'official' stuff, you have UTC...

 

[pinball1970]

Really? Whose intuition is better because of this? And why stop here? Why not Ganymede? Or Triton?

Because NASA do not have plans to send astronauts there, yet.
Just a guess.

 

[Vanadium 50]

Because NASA do not have plans to send astronauts there, yet.
Just a guess.

Same comment as before:

Good thing we had GPS and all these ppb-level corrections in 1969 or we never would have made it to the moon.

Why is this important?
Why do you need to know the time to a better accuracy than a good wristwatch?

 

[PeroK]

Why do you need to know the time to a better accuracy than a good wristwatch?

Why do you need a wristwatch when you have a cellphone?

 

[pbuk]

Why do you need to know the time to a better accuracy than a good wristwatch?

So that you can build a radionavigation system. It's a bit difficult to measure time of flight of a radio signal with a wristwatch.

 

[Vanadium 50]

OK, next question. Why do you need a radio navigation system? And how good does it need to be?

Taking all the navigation problems we have had with spaceflight, and I'll let you throw in Mars, to get the statistics up, has there ever been a case where a "LPS" or "MPS" would have improved anything?

What problem is this trying to solve?

 

[Vanadium 50]

Let's look at it from a cost perspective.

Geosync costs an order of magnitude more then LEO. The world spends about $1B/year on GPS and GPS-like systems, and they are in 12-hour MEO orbits. So a Lunar Positioning System will likely cost a few billion a year to operate.

That's about what the ISS costs. Would LPS provide the same benefits as ISS? When ISS is deorbited in a few years, will some blue ribbon committee say "don't replace it. Build a LPS instead."?

 

[pbuk]

Let's look at it from a cost perspective.

TL;DR: orbiting satellites around the moon to build an LPS the way GPS works is not cost effective.

But GPS is not the only way to use ToF measurements for accurate positioning, see e.g. https://technology.nasa.gov/patent/LAR-TOPS-361

 

[pbuk]

What problem is this trying to solve?

Mapping of and positioning on and near the lunar surface. https://www.unoosa.org/documents/pdf/icg/2023/ICG-17/icg17.02.07.pdf provides some good context.

 

[Vanadium 50]

I find that document is more about what can be done as opposed to what should be done.

Maybe I should turn it around. How good do you think this needs to be? One nanosecond? Ten? 100 picoseconds? And then the obnoxious question - would you rather have this, a new space station, a new space telescope, or a Mars sample return?

 

[pervect]

Same comment as before:


Why is this important?
Why do you need to know the time to a better accuracy than a good wristwatch?

Getting serious for a bit, I am thinking that humanity might do astronomy (automated or otherwise) on the moon. Astronomers probably really use the ICRS nowadays (I am actually not positive what current practice is, that's my impression from my readings). For that application they probably eventually want the appropriate solar barycentric time, but we don't actually have clocks at the barycenter of the solar system for obvious reasons, on Earth we compute the barycentric time from local clock readings, local clocks on the surface of the Earth. There are some theoretical clocks at the Earth's center that we use to create and organize our timekeeping system (most notably how we synchronize clocks), but the actual clocks we use are typically on or near the Earth's surface. The most popular idea for common use seems to be adjusting the clock rate for a clock on the geoid (loosely speaking, a clock at sea level), and just ignoring the small effects of things like the lunar and solar tides. Theorretical standards that don't perform a rate adjustment exist, people tend to just not like them.

The issue becomes more acute when we have more than one instrument and associated atomic clock on the moon. It pretty much begs us to set up a system to handle it.

So it may not be premature to think about the appropriate theoretical framework.

The gravitational field of the moon is noticably lumpy, I suspect this might complicate things a bit more than it does for what we do on Earth.

We currently have quite a mess of time standards already, and adding in the desire to do accurate time measurments on the moon is going to add a bit more to the mess. Key things that relativity adds are the difference in clock rates for different observers, and the relativity of simultaneity. The rate issue is not the only one, the simulataneity issues are at least as important. Sadly, people unfamilair with the concept just see a fnord (https://en.wikipedia.org/wiki/Fnord) when I mention that.

 

[Vanadium 50]

OK, so lets consider this is needed for an observatory on the moon. LSST, to meet its goals, needs to know the time to about 60 μs.* Because the moon turns 30x slower, I only need to do 1/30 as well: 2 ms.

Holding that for a year requires an Allan variance of about 10^-7. (τ = 1 s) This is easy with a quartz oscillator.

I don't see that ppb corrections are necessary if my use case says I need to know the time only to ms.


* Actually, the length of the earth's day varies by many tens of microseconds per day. No timekeeping is good enough to achieve this because the earth is not spinning srably enough - you need to use something else, like reference stars.

(Edited to fix formatting)

 

[berkeman]

Thread is closed temporarily for Moderation.

 

[PeterDonis]

The thread ran its course several months ago and will remain closed.