Nº 7 2013 > The future of time –
To abolish or not to abolish the leap second?

Space odyssey
Time-scales and global navigation satellite systems

Han Chunhao, Beijing Satellite Navigation Center

A clock face and Earth represent time travel and the warping of time at speeds near to the speed of light and in strong gravitational fields Standard time zone clock in the lobby of the News Building in New York Han ChunhaoAn engineer in the timekeeping lab poses in front of a clock showing Beijing Time at 07:59:60 next to another clock showing Coordinated Universal Time
A clock face and Earth represent time travel and the warping of time at speeds near to the speed of light and in strong gravitational fields
Standard time zone clock in the lobby of the News Building in New York
Han Chunhao
An engineer in the timekeeping lab poses in front of a clock showing Beijing Time at 07:59:60 next to another clock showing Coordinated Universal Time (UTC) at 23:59:60 at the National Time Service Centre of the Chinese Academy of Sciences in XiAn city, China, on 1 July 2012. An extra second (leap second) was added to the world’s atomic clocks on Saturday (30 June 2012) as they underwent an adjustment to keep them in step with the slowing rotation of the Earth. On that night, atomic clocks read 23 hours, 59 minutes and 60 seconds before moving on to midnight UTC.

In the large-scale space-time continuum around the Earth, a global navigation satellite system is in reality a system for the precise measurement of time.

A global navigation satellite system usually consists of three segments: a space segment (the satellite constellation); a ground control segment (a master station, uplink stations and monitor stations); and a user segment (user receivers). The basic observables are pseudo-ranges, which are defined as the product of the speed of light multiplied by the observed signal travel time (the time difference of the clocks) between the signal source and the observer. All navigation information, such as satellite orbits, clock offsets and ionospheric time delays, are obtained by using these time observables.

Satellite clocks

Given the large scale of space-time involved in satellite trajectories (about 1 × 105 km in space, and several days or even months or years in time) and the precision requirements (accuracy to the 1 metre or even 1 centimetre or 1 millimetre level), the data processing for global navigation satellite systems must be dealt with in the framework of relativity and quantum theory.

There are two kinds of conceptually different time-scales in global navigation satellite systems. These are proper times and coordinate times. Essentially, the observed space interval and time interval between any two events is dependent on the observer. The time readings given directly by ideal clocks located onboard satellites, in stations or by observers are proper times. These are related to the observer — in other words to the space-time environments of the clocks. This means that different observers have different clock times because of their relative velocity and position in the gravitation field.

In order to have a common time reference for all observers, we must choose a special observer and construct a reference system. A reference system contains a three-dimensional space reference frame and a time reference. The former determines the spatial position (with three space coordinates) of an event, the latter gives the happening time, which is called coordinate time.

A non-rotating geocentric reference system is used to describe the orbits of Earth satellites, and these are the type of satellites included in global navigation satellite systems. The reference time is usually the geocentric coordinate time or the terrestrial time. Both the geocentric coordinate time and the terrestrial time can be deemed to be the proper time of the observer located at the geocentre, but subject to a different gravitation potential. The geocentric coordinate time supposes that there is no Earth gravitational potential or that the observer is not affected by it. In contrast, the terrestrial time supposes that the observer is subject to a gravitational potential equivalent to that on the geoid (the surface of the ocean as shaped by the influence of the Earth's gravity and rotation alone) or at mean sea level.

Telling the time

The system times of global navigation satellite systems, such as GPS Time, GLONASS Time, Galileo Time and BeiDou Time, are different realizations of terrestrial time. It should be noted that a system time is used only within the system itself, being designed simply for the convenience of system operation. It is impossible to make all the system times the same. However, in order for the system to realize the function of time service, the time offset relative to Coordinated Universal Time (UTC) must be given (with some predetermined uncertainty) in the navigation data broadcast by the global navigation satellite system. Here UTC is the unique choice because it is the standard for civil time all around the world.

Sunrise and sunset

Obviously, having to insert the leap second at irregular periods in UTC is troublesome. For the operation of global navigation satellite systems in particular, the leap second is inconvenient both in regard to timekeeping and time service. Specialists in other technical fields — such as communications and transport — would probably have the same viewpoint.

But we must bear in mind that UTC is used not only in science and technology, but also in every aspect of society. Simply eliminating the leap second means conceptually that UTC has no relation to solar time. Yet sunrise and sunset have always been the natural foundation of civil time.

It should however also be noted that the term “day” as used today is not the real solar day but the mean solar day, as defined at the end of 19th century. We know that the equation of time (the difference between apparent solar time and mean solar time) can reach 16 minutes. In contrast, the current time difference between International Atomic Time (TAI) and Universal Time (UT1, an astronomical time-scale defined by the Earth’s rotation used in celestial navigation) is 35 seconds. In the past 40 years, 25 leap seconds have been inserted in UTC. This counters the argument that we could not accept UTC without leap seconds as a civil time, given that even today UTC is not exactly the same as solar time.

The time difference between TAI and UT1 is mainly caused by the deviation of the SI second relative to the mean solar day. All 25 leap seconds are positive; this means that the offset of the SI second is about 1.98 × 10–8 referred to the average solar second. If the definition of SI second could be modified, however, that difference could become even smaller.

In any event, UTC — however defined — should still have some relation conceptually to UT1 as a civil time. The velocity of the Earth’s rotation is changing. Maybe in the future the length of a day will change to 86 401 seconds or even longer. What should we do if this happens? This is a good reason for maintaining conceptually some coordinate relationship between UTC and UT1.

New ways of defining Coordinated Universal Time

Other than providing the standard for civil time, UTC also plays the role of representing the approximate value of UT1 (the difference between UTC-UT1 is kept within 0.9 second). If the leap second is eliminated, this difference will no longer be limited.

Some people are not in favour of the leap second, arguing that it requires software to be modified. For ground systems, software modification is neither complex nor particularly expensive. But for some space systems, this may not be the case.

The redefinition of Coordinated Universal Time is a matter of great significance. Stopping the leap second would be convenient for most users. But the name of UTC and the related time zones should not be changed, in order to keep some conceptual link with UT1 or solar time. It would be preferable to establish some clear and definite relation between UTC and UT1, for example requiring the phase difference between them to be less than some fixed value (such as 10 minutes), or the relative frequency offset to be less than 1 × 10–7 (about 10 milliseconds in a period of 24 hours).

One option would be to add a leap minute at the end of a century. Indeed, various approaches are possible that would eliminate leap seconds for a sufficiently long period in the foreseeable future.

If UTC were to be redefined in such a way as to stop inserting leap seconds, then global navigation satellite systems should compensate by broadcasting Earth orientation parameters. Indeed, this may be a better way for users to obtain information on the Earth’s orientation. In that case, global navigation satellite systems could provide not only a position, navigation and timing service, but also an Earth orientation service.


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