[LEAPSECS] What timekeeping system should the Terra Nova settlers use?

Zefram zefram at fysh.org
Mon Oct 3 06:50:46 EDT 2011

Daniel R. Tobias wrote:

>length of the day, but it was shorter than the current day, which

>would, I imagine, have an impact on timekeeping in this colony.

The magnitude of this difference is in the same ballpark as the present
difference between Terran and Martian days, so exactly the same range of
solutions are on the table as for colonisation of Mars. We can expect
that the colonists would biologically synch to the local diurnal cycle
without excessive hassle.

Systematically generalising from current Terran timekeeping, we can
foresee distinct time scales for physical time and for planetary rotation,
but with the difference between them being too large to fudge. The whole
culture would have to be conscious of the distinction, unless they go
native and define new time units that match the local planetary rotation.
I'm going to suppose a level of technological continuity that precludes
replacing the system of units.

There will be some tracking of proper time elapsed on the rotating geoid,
corresponding to the present TAI tracking TT. At base this is a count
of SI seconds. Whereas in present Terran timekeeping 86400 SI seconds
is very close to the length of a solar day, so it is possible to label
TAI times using something resembling the conventional calendar, the
Martian/Paleoterran situation would make such labelling nonsensical.
So the equivalents of TAI and TT would probably just be described in
the form of a linear count of seconds.

There will be some tracking of planetary rotation in the form of mean
solar time. Ignoring the longitude issue, for which the concept of
timezones applies unchanged, this will correspond to the present UT1
(Terra) or AMT (Mars). At base this is a count of mean solar days.
The integer part of the count would no doubt have a pure linear form
used for calculations, corresponding to MJD (Terra) and MSD (Mars).
This integer can also be described in terms of a calendar that relates
days to larger astronomical cycles, corresponding to the Gregorian
calendar (Terra) and Darian calendar (Mars). The fractional part of
the day count, i.e., time of day, can be sensibly described either as
a decimal fraction or divided into 86400 equal parts in the 24:60:60
fashion. Cultural continuity suggests that both forms would enjoy some
currency. The risk of confusing 1/86400 of a mean solar day with an
SI second (of close but substantially different length) might provide
cultural pressure to switch to only using decimal fractions here, but
I'm inclined to think that change would not fully occur.

Where it gets really interesting is when we want to have days that closely
match mean solar days and to count time within the days in SI seconds.
This corresponds to present UTC. I think the most viable approach is a
direct generalisation of UTC's 24:60:60 form. In UTC, every day has the
same number of minutes (1440), every minute has an integral number of SI
(well, strictly TAI) seconds, and UTC modulates the number of SI seconds
in the minute in order to approximate the progress of mean solar time.
Present UTC has to achieve a mean minute length of something like
60.0000005 s, so it can get away with having almost all minutes being
60 s long and treating only a tiny fraction of minutes as opportunities
for extension to 61 s. The obvious historical reasons behind that don't
apply in the Martian or Paleoterran situations, so unless you're very
lucky you'll need a lot more alternation of minute lengths.

The length of a Martian solar day is currently about 88775.24409 s
(per Wikipedia), yielding an average minute length for a UTC equivalent
of 61.6494751 s. On Paleoterra you'll want an average minute length
somewhere between 58.0 s and 59.4 s. So on Mars you'll want about
65% of minutes to be 62 seconds long and the rest 61 seconds long.
There'll have to be alternation of minutes within each day, which could be
mostly according to a regular pattern, but at least a small part of the
pattern will have to be variable on an observational basis. Likewise,
on Paleoterra you'll need to alternate between 58 and 59 seconds or
between 59 and 60 seconds per minute, depending on era.

The frequency of leap seconds in these generalised-UTC systems implies
that it won't be viable to ignore leap seconds, in most of the places that
currently ignore them. Wristwatches, for example, will have to get them
right at least most of the time, if they're trying to tick SI seconds
at all. A watch could perhaps get away with not handling occasional
observation-based irregular leaps, but it'll have to get the regular
pattern right to remain in synch for days at a time. An analogue watch
could get away with ticking mean solar seconds and not knowing anything
about the pattern of leap seconds, but then wouldn't be any good for
anything relating to the 1 Hz beat of TAI-equivalent.

The whole UTC-equivalent mechanism is conspicuously missing from present
Martian timekeeping. Current and recent rover missions have used mean
(or, in older cases, apparent) solar time of a lander location or a
nearby conventional longitude, thus using timezones based on Airy Mean
Time (equivalent of UT1). The researchers working on the Spirit and
Opportunity missions have used analogue watches yielding a 24:60:60
division of this mean solar day. Of course, they haven't yet had a need
to link precise interval time on the Martian surface to time of day, nor
is there any Martian equivalent of the 1 Hz TAI-derived broadcast time
signal. My prediction is that the UTC-equivalent will naturally arise
after we land atomic clocks on Mars and set up the Martian equivalent
of TAI.


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