Distinction between local time and coordinated universal time
The concept of coordinate time is provided by the theory of relativity and should not be confused with the more familiar concept of proper time. Proper time 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; that is, it is defined and can be used anywhere and by any observer. Two distant observers can thus compare the primacy of their respective local time measurements by converting (via a mathematical procedure) their proper time measurements into the same coordinated time scale.
Three coordinated time scales for the Moon
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 defined by the theory of general relativity: it is the lunocentric coordinated time. The duration of one second in E1 coincides with one second on a clock located at the Moon’s center of mass; E1 is thus the lunar analogue of geocentric coordinated time. The second scale (E2) is obtained by artificially applying a multiplicative factor to the duration of one second in E1, such that one second in E2 coincides with the second ticked by a clock at rest on the lunar geoid; E2 is thus the lunar analogue of terrestrial time. Finally, the third scale (E3) is also artificially constructed by applying a multiplicative factor to the duration of one second in E1, ensuring, this time, that the duration of one second in E3 is as close as possible to one second on the Coordinated Universal Time scale.
Advantages and Limitations of the E2 Scale for Lunar Calendars
The E2 scale can be advantageous if multiple clocks placed on the Moon’s surface need 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, thereby masking the mathematical process of converting proper time to coordinated time. However, since the Moon’s surface is highly level, an atomic clock will generally not be located on the lunar geoid; it will therefore not tick at the same second 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 on the order of 10^(−11), 10^(−13), and 10^(−10) (relative) for scales E1, E2, and E3, respectively.
Physical consequences of time scaling
At first glance, E2 therefore appears to be the most advantageous. However, E2 and E3 are scaling of E1, which, within the framework of the theory of general relativity, implies that the masses must also be scaled. This scaling of physical parameters is problematic in that the same mass can then be assigned multiple numerical values! For example, adopting E2 or E3 would require using a mass of the Earth that would not have the same numerical value as that naturally defined by the barycentric coordinate time scale.
Why choose the E1 moon-centered scale?
Since the mathematical procedure that transforms proper times into E1 coordinate times, E2, and E3 cannot be avoided for clocks located on the Moon’s surface, 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 adaptable to other bodies in the solar system, notably Mars.