[time-nuts] MJD and leap seconds

Tom Van Baak tvb at leapsecond.com
Tue Jan 10 06:14:07 EST 2006

> I've had many heated arguments with co-workers about what the right
> thing to do here.  Do you compute the day as if it had an extra
> second, thus breaking the ability to subtract two MJD numbers to get a
> meaningful elapsed time?  Or, do you ignore the leap second entirely,
> giving discontinuity around the leap second?
> In the end, we opted to report MJD and HH:MM:SS.
> Warner

I am familiar with the arguments. I think your solution
is a good one. The goal is to remove ambiguity and
your using both MJD and UTC (or TAI) does that. It's
always a pain to compute accurate time intervals when
leap seconds have to be considered.

Strictly speaking MJD (= JD - 2400000.5) is based on
an astronomical timescale such as UT1. In this case
a leap second has no effect since the UT timescales
have no leap seconds. Astronomers appear to avoid
using MJD altogether.

The time metrology community, on the other hand,
uses MJD a lot and in practice it's based on UTC.
And so one can ponder, as you mentioned, if the
fractional MJD value for 12/31/2005 should be based
on a 86400 s or 86401 s day.

The advice I was given was to just leave the ambiguity
alone; unless it really, really mattered, in which case
you the author should specify which timescale which
you are basing your MJD on, or not use MJD at all.
I've never run into a case myself where it mattered,
nor seen a paper where a graph axis or numerical
result depended in which timescale the MJD values
were based on.

It is interesting to note that if leap seconds were to be
eliminated the ambiguity between a true UT-based
MJD and a practical UTC-based MJD would be further
exposed. Still, if you consider how the timing community
generally uses MJD I suspect you'd have to look hard to
find a graph that would be off by as much as one pixel.
The other approach is the space and timing communities
could by accident or convention redefine MJD as a
UTC-based time value, leaving JD to the astronomers
as a true, pure UT-based time value. It's just one of many
subtle but non-showstopper details that would show up
in the next centuries if leap seconds were retired.


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