# How accurately can you determine time from planetary/star positions?

I was reading this question which has to deal with the accuracy of on-board atomic clocks. In the question it mentions multiple times that only recently did we start including accurate enough clocks on spacecraft that they didn't need to "ask Earth" for the time. Instead they can use their "assumed clock accuracy" to know its position based on the position of the stars, and the current time.

My question is: Can we reverse this methodology for any celestial or solar objects? Is there a way that, from the star-fields (and possibly other available data E.G. velocity, acceleration, etc...) we could determine the time in an accurate enough manner to re-calibrate our spacecraft's clock?

My guess would be that this is a no, but I can't articulate why.

• Is your question How accurately... (in the title) or Can we reverse this methodology..." and "Is there a way..." (last paragraph) or all of the above?
– uhoh
Jun 11 '19 at 22:26
• Both- though it seems the answer is both yes/no and not very however. Jun 12 '19 at 6:12

There is a 3 way relationship between "Where am I?", "What can I see?", and "What time is it?".

From a navigation point the "What can I see" is known, the problem was knowing the time, which involved talking to earth. But when you have the time, you can deduce where you are. Having the clock on board means you don't need to do the talk-to-earth step to achieve the same result.

Once you've calculated where you are, you can indeed reverse this process to learn what time it is (from what you see too, but its not super sensitive to this), to a fairly high precision. The problem is we don't have a good way of knowing where you are in the first place without knowing the time (or none of this would have been an issue in the first place). So you need to know the time, to know location, to know the time.

In this process, you'd lose accuracy, not gain it, you couldn't use this to re-calibrate anything, with more accuracy than you already have.

However, in theory, you're right. If an oracle told you exactly where you are and you remember your trajectory, you could use this to re-calibrate a clock.

Probably the best approach would be equipping the craft with a pulsar clock - accuracy of 1.6:10^18. Optical clocks would not be that easy to implement - you could use a star tracker to determine positions of multiple known celestial bodies, compare with a model, and find the time basing on that, but the accuracy would be limited as no model of the solar system is 100% accurate and the error accumulates over time.

• The pulsar clock is interesting, but my focus for this question was intended towards an optical clock and, maybe, getting an estimate on the amount of drift per year a clock based on either a solar or celestial model would be. I mean, obviously even a clock drift of 10 ms can be fatal over long periods of time, but ballparking in terms of that may help quantify the drift which would be caused by using stars/solar bodies. In other words, I'm not grasping the scale. Jun 11 '19 at 14:54
• @MagicOctopusUrn: Thing is no matter how accurate your optical equipment for determining positions of celestial bodies, these bodies drift on their own due to countless minuscule forces we can't account for - variance in solar pressure, gravity of passing asteroids, weather on Jupiter, and so on. So after a time their position ceases to match the model and be indicative of exact time.
– SF.
Jun 11 '19 at 15:07
• So, seeing as "more" is known about our local system, using the solar system as a clock would have less drift than the stars? (Even though both are not viable wondering which option is worse quantitatively) Jun 11 '19 at 15:23
• @MagicOctopusUrn: The stars move very, very slowly so you can't determine time from their motion alone very well. You can determine the time if you know your craft's motion very well, but you won't - it's subject to the same perturbations as the solar system, and you have the chicken and the egg problem. You could get the time knowing the position of the craft relative to the star field with a very good accuracy, but to get that position you need to know the time.
– SF.
Jun 11 '19 at 15:35
• @MagicOctopusUrn: Oh, depends on what accuracy you need. If you pack some spare fuel, you can often adjust later.
– SF.
Jun 12 '19 at 6:09

How accurately can you determine time from planetary/star positions?

tl;dr: circa 1AU from the Sun, of the order of seconds.

Let's assume:

• The spacecraft is circa 1 AU from the Sun
• Drift/noise in the spacecraft's clock is only on long time scales (e.g. months)

A 30 cm telescope in space on the spacecraft can resolve about 0.5 arcseconds, and repeated measurements of planets and good astrometric software might be able to deliver 0.1 arcsecond accuracy of positions relative to background stars. That's 5E-07 radians.

At distances of order 1 AU that's about 100 km.

The velocity at 1 AU is of order 30 km/sec (faster for Mercury and Venus, slower for Mars) so perhaps using a campaign of frequent measurements of the four inner planets relative to background stars and comparing to ephemeris values, time can be recovered on the order of magnitude one second, but not milliseconds and certainly not microseconds.

There are moons available as well.

• The Earth's Moon's motion is tied up with that of the Earth, so you'd better measure both. You might be able to get some enhanced accuracy if you happen to be close to the Earth-Moon system at the time.
• The four Galilean moons of Jupiter could be measured fairly accurately as well. But they don't contribute much to accuracy, with hundreds of arcsecond amplitudes over days at 0.1 arcsecond accuracy, that only gives you tens of seconds, so combining with other measurements won't reduce overall accuracy much.