The concept of coordinated time is provided by the theory of relativity and should not be confused with the more familiar concept of proper time. The latter has a local dimension and represents the time physically indicated by an ideal clock. In contrast, coordinated time is purely conventional, but has a global scope, meaning that it is defined and can be used anywhere and by any observer. Two distant observers can thus compare the primacy of their respective local dating by converting (via a mathematical procedure) their measurement of proper time into the same coordinated time scale.
In the lunar environment, three coordinated time scales may be of practical interest. The first, E1, is the most fundamental time scale; it is naturally given by the theory of general relativity: it is the lunocentric coordinated time. The duration of one second of E1 coincides with one second of a clock located at the centre of mass of the Moon; E1 is thus the analogue for the Moon of geocentric coordinated time. The second scale (E2) is obtained by artificially applying a multiplicative factor to the duration of one second of E1, so that the second of E2 coincides with the second beaten by a clock at rest on the lunar geoid; E2 is therefore the analogue for the Moon of Earth time. Finally, the third scale (E3) is also artificially constructed by applying a multiplier to the duration of a second in E1, ensuring, this time, that the duration of a second in E3 is as close as possible to a second in the coordinated universal time scale.
The E2 scale may be advantageous if several clocks placed on the surface of the Moon wish to exchange their measurements. This is because the proper time of each lunar clock will remain close to the E2 coordinated time used for comparison, which masks the mathematical procedure of transforming proper time into coordinated time. However, as the surface of the Moon is very flat, an atomic clock will not generally be located on the lunar geoid; it will therefore not tick at the same rate as E2 and the mathematical transformation procedure cannot generally be avoided. This procedure must be applied if the coordinated time scale is E1 or E3. In all three cases, it can still be circumvented by artificially changing the frequency of the lunar clocks. The frequency corrections to be applied are of the order of 10-11, 10-13 and 10-10 (relative) for the E1, E2 and E3 scales respectively.
At first glance, E2 therefore appears to be the most advantageous. However, E2 and E3 are scales of E1, which, in the context of general relativity theory, implies that masses must also be scaled. This scaling of physical parameters is problematic in that the same mass can then be assigned several numerical values! For example, adopting E2 or E3 would require using a mass for the Earth that would not have the same numerical value as that defined naturally by the barycentric coordinated time scale.
In conclusion, since the mathematical procedure that transforms proper times into coordinate times E1, E2, and E3 cannot be avoided for clocks located on the surface of the Moon, and because E1 does not involve scaling physical parameters unlike E2 and E3, we recommend adopting the lunocentric coordinated time (i.e., E1) as the coordinated time scale associated with the lunar reference system. In the near future, this approach will be easily transposable to other bodies in the solar system, notably Mars.
Contact
Adrien Bourgoin, Astronome adjoint, LTE, Observatoire de Paris
adrien.bourgoin@obspm.fr
