[tz] Sol 5000 for Opportunity

Marshall Eubanks marshall.eubanks at gmail.com
Sun Feb 18 04:48:34 UTC 2018

On Sat, Feb 17, 2018 at 9:46 PM, Paul Eggert <eggert at cs.ucla.edu> wrote:

> Tim Parenti wrote:
>> Today, 16 February 2018, at 01:26:20.092 UTC, it is 01:01:06 Coordinated
>> Mars Time on Mars Sol Date 51235
> What's the source for these timestamps? It's an Earth reference frame,
> surely?

The short answer is that so far, it effectively is.

Mars spacecraft keep (so far) an effective Earth time.Their clocks (so far)
typically aren't that good, and so they are just treated as if they were on
TAI or even UTC and adjusted from time to time to keep close to Earth time.

Mars Coordinated Time (or MTC) is the Mars Mean Solar Time (the Mars
equivalent of UT1) for the Mars reference longitude (crater Airy-0).
However, I believe that all of the lander/rover missions to date use
actually the mean solar time for their latitude and longitude (roughly, UT0
+ a longitude correction) in setting their sols and the local solar time.
No spacecraft clock is AFAIK set to run at MTC.

The Martian local solar time undergoes fairly large variations over a
Martian year, much as the local solar time does on Earth, but more so, due
to the larger orbital eccentricity. The wikipedia article describes these
and provides a formula for getting MST from terrestrial time (TT = TAI +
32.184 seconds).

I helped to determine the mean Mars length of day (LOD) and what little is
known about its variations from Viking and Pathfinder data. There is a
fairly large seasonal variation of Mars LOD (due to the seasonal transfer
of CO2 to and from the poles) but little is known about any long period
changes in Martian LOD, and thus it is not known whether leap seconds would
be needed to keep Mars atomic time (once that is set up) and Mars mean
solar time aligned.

The Wikipedia article does not discuss the relativistic differences between
time on the Earth and time on Mars, but these are significant; Mars is both
traveling slower on its orbit and further out in the Sun's gravitational
potential. Atomic time on Mars would run faster than AT on Earth by about
5.1 x 10^-9, or ~0.16 seconds per year, on average, and there are seasonal
and other variations. This is taken into account in great detail in the
Martian ephemeris work, but so far as far as I know the people setting the
spacecraft clocks ignore it.

The long awaited arrival of the first Deep Space Atomic Clock into Mars
orbit will change all of this. That will not be adjusted in rate and thus
would run fast by 3.4 parts per billion (on average) compared to its
cousins back here on or near Earth, or roughly 7 orders of magnitude above
its hoped-for sensitivity level.

How (or even whether) future Mars colonists will align their time with the
Earth's remains to be seen.


> Because of relativistic effects, if an observer on Earth sees that Mars's
> 51235 01:01:06.000 CMT timestamp corresponds to Earth's 2018-02-16
> 01:26:20.092 UTC timestamp, then I guess that an observer on Mars should
> see that the same CMT timestamp corresponds to a slightly-different UTC
> timestamp, even assuming both observers have error-free measurements, and
> that the difference will be observable with millisecond-precision
> timestamps. This is due to both the relative velocity of the Earth and Mars
> and to gravitational-field effects. For millisecond/year precision Pan and
> Xie write that you need to figure in not only the gravitational effects of
> the Earth, Mars, and the Sun, but also those of Jupiter, Saturn, the Moon,
> and Venus (!). See their analytic model of timekeeping for a Yinghuo-1-like
> mission in:
> Pan J-Y, Xie Y. Relativistic algorithm for time transfer in Mars missions
> under IAU resolutions: an analytic approach. RAA. 2015. 15(2):281-92.
> https://dx.doi.org/10.1088/1674-4527/15/2/011
> http://www.raa-journal.org/raa/index.php/raa/article/download/1875/1791
> The whole idea of time transfer between Mars and Earth brings into stark
> relief what an easy job it is to track civil timekeeping on Earth, compared
> to how it would be elsewhere. And Mars is an easy case. Someone should
> alert Elon Musk.
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