A relativistic framework to establish coordinate time on the Moon and beyond

https://arxiv.org/abs/2402.11150

by croes • 2 years ago

130 72 2 years ago

arxiv.org

engineer_22• 2 years ago

In the abstract they hint that without a common clock communication could be inhibited

teruakohatu• 2 years ago

Do they? I don’t see that in the abstract, they do state that:

This understanding also underpins precise navigation in cislunar space and on celestial bodies' surfaces, thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing (PNT) systems spanning from Earth to the Moon and to the farthest regions of the inner solar system.

karmakaze• 2 years ago

[...] and their inter-comparisons using clocks onboard orbiters at relatively stable Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure.

davidw• 2 years ago

"I was in favour of space exploration until I realised what it'd mean for date time libraries"

https://x.com/joe_jag/status/510048646482894848?lang=en

jiehong2• 2 years ago

Nice!

It made me realise that we currently live in a time that can never be accurately referenced outside the planet.

So no software can ever truly define 2024-07-11T00:00 on Pluto.

It also makes me think that the Mass Relais in Mass Effects could actually also be atomic clocks forming this galactic time grid of reference, so in-game lore seems less implausible.

zokier3• 2 years ago

The whole point of the paper is to show that we can model the time for various bodies to very high degree of accuracy.

jiehong2• 2 years ago

Indeed! My point being that it’s gonna be true someday, just not yet.

pfdietz• 2 years ago

Or even on/in the planet. The Earth's core is about a year younger than the Earth's surface.

WorldMaker3• 2 years ago

There are interesting theories about how to use constellations of Pulsars as galactic "atomic clocks". Pulsars are generally extremely predictable in their emissions and with a big enough constellation, you can do old fashioned triangulation to get relative distance between yourself and enough pulsars to sync to some sort of standard time based on synchronicities in pulsar timing.

I've not yet seen a full proposed standard for such a thing, but it's also not far from how GPS itself works and how GPS forms its standardized time, which is synced to Earth based atomic clocks but includes more relativistic effects. Most cellphones actually use GPS time rather than "atomic time" today, because they need GPS services in general and also because cell towers use a variant of GPS time in their communications with cell devices for complicated three dimensional dances like tower to tower hand-offs.

It's kind of neat how even "Earth time" at its most accurate involves relative effects and triangulation in some of our most used and trusted devices. (Even NTP sync of non-cellphones uses IP pings as an approximate for triangulation to try to reduce error in syncing a laptop or desktop to nearby atomic clock sources. Though at least today in most internet usage, the Internet Protocol is less impacted by relativistic effects.)

zokier3• 2 years ago

how GPS itself works and how GPS forms its standardized time, which is synced to Earth based atomic clocks but includes more relativistic effects

While the GPS satellites internal clocks might operate on whatever timescale, it is important to note that the time signal that is broadcast through GPS is strictly fixed offset from TAI without any additional relativistic shifts. And TAI is defined to use the geoid as reference frame.

That is to say that if you have a clock synchronized to GPS signal then it should tick exactly at same rate as TAI and UTC.

bloopernova3• 2 years ago

Now I'm wondering just how timekeeping would work with distance and/or high relative velocity. Would you observe "ship time" until you returned to base, and would then sync ship to base time?

ianburrell• 2 years ago

The ship would keep local time because that is easy to measure and fits with what people are doing. The point of establishing Moon time is that it is hard to keep using non-local Earth time.

Keep in mind that there is difference between clock measuring seconds, and converting to days and times that requires choosing a calendar. The ship could use origin calendar, destination calendar to make people familiar, or some universal calendar. The problem with destination is that it won't sync properly until arrival. Or maybe they skew the calendar on the last leg.

Also, don't need high relative velocity to have a difference. Considering relativistic space travel may be impossible; the only may be proposed warp drives.

jerf• 2 years ago

That particular problem isn't necessarily materially different from the ships we already have that experience major time shifts every day. Time zones already create that problem and you can just look at the solutions we use today.

hlieberman• 2 years ago

Missed opportunity to name it "stardate".

jvanderbot2• 2 years ago

It strikes me as surprising to imply that we don't have time-keeping standards for solar system exploration that take into account relativistic differences.

the CSPICE toolkit from JPL/NAIF has a bunch of routines to calculate local time, local time of arrival of events from other places (light cone, I suppose?), down to the nanosecond.

nynx• 2 years ago

That code exists for calculating those things does not mean there are timekeeping standards that support them.

jvanderbot2• 2 years ago

True, should have mentioned (as sibling comment did) that the code _uses_ several timekeeping standards to do those calculations.

zokier3• 2 years ago

There definitely are various timescales and standards that take relativity into account

https://en.wikipedia.org/wiki/Barycentric_Coordinate_Time

https://en.wikipedia.org/wiki/Ephemeris_time

https://en.wikipedia.org/wiki/Coordinate_time

Etc

nickdothutton2• 2 years ago

I wonder if Sci-Fi novels contain any info on time representation, reference, and distribution.

bloopernova3• 2 years ago

Kim Stanley Robinson's Mars trilogy mentions the longer Martian day. The extra 39 minutes were represented by a 39 minute midnight clock freeze between 12:00:00 and 12:00:01. It was never mentioned how this worked across the entire planet.

Jack Campbell's Lost Fleet series (starting with Dauntless) has a lot of time involved, due to military fleets/flotillas maneuvers at light-hour distances:

Fleet A jumps into a system. Fleet B is 6 light hours distant across the system. B won't see light from A's arrival for 6 hours. A won't see B's reaction for 12 hours, less any distance covered. Ships can engage in combat at up to 0.2c relative velocity, at a maximum distance of about 1 light second.

Fleet A accelerates to 0.1c, Fleet B does the same and they approach. Time to contact is 30 hours, and the books discuss how difficult it is for humans to rest and focus on other things during that time. Our instinctive fight/flight/fawn/freeze reaction doesn't translate well to waiting 30 hours!

Fleet A and B approach, but because the ships take a few seconds to pivot/roll/yaw to maneuver, so there's a critical time period where A or B can change position and the opposing fleet won't have time to react before the fleets clash. This is used to great effect by the skilled fleet commander of the Good Guys.

The lost fleet books also discuss maneuvering fleet formations when everyone is at light-minute or multiple light second distances. There's lots of orders like "at time 15, Echo One pivot formation down 30 degrees and starboard 15 degrees". Learning to bring all your firepower to bear on the enemy at a single moment, while denying them the same opportunity, is a very difficult skill to learn in these books.

Aaand I've written way too much. And probably not done the fantastic combat in the lost fleet books any justice at all.

gamegoblin• 2 years ago

These concepts would make for a killer PVP real time strategy game, good write-up

shagie2• 2 years ago

Jack Campbell's Lost Fleet series (starting with Dauntless) has a lot of time involved, due to military fleets/flotillas maneuvers at light-hour distances:

I'll also mention Dread Empire's Fall by Walter Jon Williams - https://en.wikipedia.org/wiki/Dread_Empire%27s_Fall

You again deal with long communication distances and most fleet actions are done with missiles. This then has the challenge of "how do you control the missiles / select the targets at such distances (no AIs)" and there is a class of pilots that fly a 'pinnace' which is a small, one person ship that is capable of doing high acceleration to keep up with the missiles.

During peace times, the pinnace pilots tend to be more about prestige and racing.

There was also an instance of moving a jump point thingy that _really_ messed up a fleet action (since the fleet, traveling at high speed to the edge of the system missed the "go here to jump to the next system" and instead had to turn around and go back ... which represented a lot of time and acceleration (not all species in the universe don't have the same tolerance for acceleration).

hinkley• 2 years ago

In high school a significant fraction of the effort I put into doing math in my head was expended so that, when playing a game called Galactic Conquest, all of my attack fleets would show up in the same turn. Or two turns, if I was still manufacturing ships.

And then I got sneakier and would send a false fleet to attack the wrong planet in turn X, and the real fleet would show up one or two turns later on the opposite side of the victim’s empire, just after they had committed every spare ship in their navy to a jump in the wrong direction, tying up their logistics until after the fight was over and I was rebuilding planetary defenses, preparing for the counterattack.

SaberTail• 2 years ago

In Vernor Vinge's A Deepness in the Sky, ships in the far distant future are still counting time from the Unix epoch. The common belief in the novel, though, is that it's measuring time from when humans first became space-faring by walking on the moon. But I don't recall it mentioning that there's any attempt to account for relativity; ships all keep their own local time.

ceejayoz• 2 years ago

The exact quote is on Wikipedia: https://en.wikipedia.org/wiki/A_Deepness_in_the_Sky#Interste...

Take the Traders' method of timekeeping. The frame corrections were incredibly complex - and down at the very bottom of it was a little program that ran a counter. Second by second, the Qeng Ho counted from the instant that a human had first set foot on Old Earth's moon. But if you looked at it still more closely ... the starting instant was actually about fifteen million seconds later, the 0-second of one of Humankind's first computer operating systems.

krisoft• 2 years ago

Exactly! Also that they measure time not in minutes, hours and days, but in the kiloseconds, megaseconds, and gigaseconds.

WorldMaker3• 2 years ago

There's a lot of fascinating discussion around Star Trek's Stardate and its seemingly universal metric calendar and times referenced as decimal units of day: How does it adjust for relativity? Why did they choose the epoch they seemingly chose? (Not that many days before Enterprise's 5-Year-Mission, and seemingly still years into Starfleet's existence.) How do you account for the various obvious real world facts that many episodes just picked numbers that sounded cool or random and didn't pay attention if they were in the right order in the season or overall timeline? (Is that relativistic problems creeping in?) They are called Stardates implying the base unit is a Day, but it is an Earth-like 24 hour day or was it something else, perhaps in a compromise with other Federation planets?

From the TNG era onward the various Writer's Bibles took an approach of 10,000 days per season to make the math easy if a script was given a Stardate in the right season and plenty of room for all the scripts in a season to have their own Stardates. If the Stardate day is a 24 hour Earth day equivalent then seasons were expected to take roughly 3 earth years. Or was that a sign that the Stardate day was about a third shorter than an Earth day and "five-year mission" did still just refer to Earth standard years?

There are all kinds of fan theories. Some weird things in canon. Some weirder things in the books and other bits of Beta and Gamma "canon".

(I did a bit too deep of a dive into Stardates recently as an offshoot of getting the idea to try to display a Stardate-like calendar and date stamps in the configurable calendar system of the Fantasy Grounds TTRPG hosting application.)

Rhapso2• 2 years ago

It is very clear that relativity and time dilation due to relative velocity is not part of Star Trek cannon. They live in a "Toy" universe where everything is easy and quartz crystals can be used for FTL travel.

nickdothutton2• 2 years ago

And I can see already from the child comments you folks did not disappoint :-)

akira25012• 2 years ago

Famously Orson Scott Card just invented a device that explicitly ignores it.

akozak• 2 years ago

It's a neat idea that you could publish a paper like this that establishes a framework for thousands of years.

alganet14• 2 years ago

yielding 58.721 μs/day

Can someone kind explain this unit for me? microseconds per day.

Does that mean that the relativistic difference is cummulative? In other words, does it add up over time?

unholiness• 2 years ago

That's right. While a day passes on earth, a day minus 58.721 μs passes on the moon (which is moving faster than the Earth).

This multiplies, so after a million days a clock on the moon will read 58 seconds behind a clock on the earth.

alganet14• 2 years ago

Thanks!

pdonis13• 2 years ago

It's the other way around: while a day passes on Earth, a day plus 58.721 microseconds passes on the Moon. The Moon clock gradually gets ahead of the Earth clock.

In an Earth-centered inertial frame, the Moon is moving faster than the Earth, but it is also at a very high altitude, and the altitude effect, which speeds up the Moon clock relative to Earth, is much larger than the speed effect, which slows it down.

(Note that the above only takes into account the effects of the Earth's gravity. The paper also takes into account the effects of the Moon's gravity, which don't change the above answer qualitatively but do add small corrections numerically, so the 58.721 microseconds per day is not the actual value the paper ends up with.)

mr_mitm• 2 years ago

Moves faster than than the Earth relative to what? Isn't it the gravitational time dilation that is the relevant effect here?

nh23423fefe• 2 years ago

its actually not a unit either. its a dimensionless ratio

akira25012• 2 years ago

6.79641e-10

argumentofperi• 2 years ago

Numerical evaluation of Eq. (4) yields a value 1.2695 × 10^−12(cos(f ) + e) or 0.1097(cos(f ) + e) μs/day.

Typo?

A relativistic framework to establish coordinate time on the Moon and beyond

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