Every now and then I run into a paper that opens up an entirely new perspective on basic aspects of space exploration. When I say ‘new’ I mean new to me, as in the case of today’s paper, the relevant work has been ongoing ever since we began lofting payloads into space. But an aspect of our explorations that hadn’t occurred to me was the obvious question of how we coordinate time between Earth’s surface and craft as distant as Voyager, or moving as close to massive objects as Cassini. We are in the realm of ‘time transformations,’ and they’re critical to the operation of our probes.

Somehow considering all this in an interstellar sense was always much easier for me. After all, if we get to the point where we can push a payload up to relativistic speeds, the phenomenon of time dilation is well known and entertainingly depicted in science fiction all the way back to the 1930s. But I remember reading a paper from Roman Kezerashvili (New York City College of Technology) that analyzed the relativistic effects of a close solar pass upon a spacecraft, the so-called ‘sundiver’ maneuver. Kezerashvili and colleague Justin Vazquez-Poritz showed that without calculating the effects of General Relativity induced by the Sun’s mass at perihelion, the craft’s course could be seriously inaccurate, its destination even missed entirely. Let me quote this:

…we consider a number of general relativistic effects on the escape trajectories of solar sails. For missions as far as 2,550 AU, these effects can deflect a sail by as much as one million kilometers. We distinguish between the effects of spacetime curvature and special relativistic kinematic effects. We also find that frame dragging due to the slow rotation of the Sun can deflect a solar sail by more than one thousand kilometers.

Clearly, what seem like tiny effects get magnified as we examine their consequences on spacecraft moving under differing conditions of velocity and gravity. The measurement of time is a key aspect of this. And even the tiniest adjustments are critical if we are to build communication networks that operate accurately even in so close an environment as that between the Earth and the Moon. Thus the occasion for this musing, a paper from the Jet Propulsion Laboratory’s Slava Turyshev and colleagues that discusses how the effects of gravity and motion can be understood between the Earth and the network of assets we’re building around the Moon and on its surface. Exploration in this space will depend upon synchronizing our tools.

The Turyshev paper puts it this way:

As our lunar presence expands, the challenge of synchronizing an extensive network of assets on the moon and in cis-lunar space with Earth-based systems intensifies. To address this, one needs to establish a common system time for all lunar assets. This system would account for the relativistic effects that impact time measurement due to different gravitational and motion conditions, ensuring precise and efficient operations across cislunar space.

And in fact a recent memorandum from the White House Cislunar Technology Strategy Interagency Working Group was released on April 2 of this year noting the “policy to establish time standards at and around celestial bodies other than Earth to advance the National Cislunar S&T [Science and Technology] Strategy.” So here is a significant aspect of our growth into a cislunar culture that is growing organically out of our current explorations, and will be critical as we expand deeper into the system. One day we may go interstellar, but we won’t do it with a Solar System-wide infrastructure.

As an avid space buff, I should have been aware of this all along, especially since gravitational time dilation is easily demonstrated. A clock on the lunar surface, for example, runs a bit faster than a clock on Earth. Because time runs slower closer to a massive object, our GPS satellites have to deal with this effect all the time. Clearly, any spacecraft moving away from Earth experiences time in ways that vary according to its velocity and the gravitational fields it encounters during the course of its mission. These effects, no matter how minute, have to be plugged into operational software adjusting for the variable passage of time.

So moving from time and space coordinates in one inertial frame (the Earth’s surface), we need to reckon with their manifestation in another inertial frame, that aboard a spacecraft, to make clocks synchronize accurately and hence enable essential navigation, not to mention communications and scientific measurements. The necessary equations to handle this task are known in the trade as ‘relativistic time transformations,’ and it’s critical to have a reference system like the Solar System Barycentric coordinate frame (SSB) that is built around the center of mass of the Solar System itself. This allows accurate trajectory calculations for space navigation.

Image: The complexity of establishing reference systems for communications and data return is suggested by movements in the Solar System’s barycenter itself, shown here in a file depicting its own motion. Credit: Larry McNish / via Wikimedia Commons.

As you would guess, the SSB coordinate frame has been around for some time, becoming formalized as we began sending spacecraft to other planetary targets. It was a critical part of mission planning for the early Pioneer probes. Synchronization with resources on Earth occurs when data from a spacecraft are time-stamped using SSB time so that they can be converted into Earth-based time systems. Supervising all this is an international organization called the International Earth Rotation and Reference Systems Service (IERS), which maintains time and reference systems, with its central bureau hosted by the Paris Observatory.

‘Systems’ is in the plural not just because we have an Earth-based time and a Solar System Barycentric coordinate frame, but also because there are other time scales. We use Coordinated Universal Time as a global standard, and a familiar one. But there are others. There is, for example, an International Atomic Time (TAI – from the French ‘Temps Atomique International’), a standard that is based on averaging atomic clocks around the world. There is also a Terrestrial Time (TT), which adds to TAI a scale reflecting time on the surface of the Earth without the effect of Earth’s rotation.

But we can’t stop there. Universal Time (UT) adjusts for location, affected by the longitude and the polar motion of the Earth, both of which have relevance to celestial navigation and astronomical observations. Barycentric Dynamical Time (TDB, from ‘Temps Dynamique Barycentrique’) accounts for gravitational time dilation effects, while Barycentric Coordinate Time (TCB, from ‘Temps Coordonné Barycentrique’) is centered, as mentioned before, on the Solar System’s barycenter but excluding gravitational time dilation effects near Earth’s orbit. All of these transformations aim to account for relativistic and gravitational effects to keep observations consistent.

These time transformations (i.e., the equations necessary for accounting for these differing and crucial effects) have been a part of our space explorations for a long time, but they hover beneath the surface and don’t usually make it into the news. But consider the complications of a mission like New Horizons, moving into the outer Solar System and needing to account not only for the effects of that motion but the gravitational time dilation effects of an encounter not only with Pluto but the not insignificant mass of Charon, all of this coordinated in such a way that data returning to Earth can be precisely understood and referenced according to Earth’s clocks.

The Turyshev paper focuses on the transformations between Barycentric Dynamical Time and time on the surface of the Moon, and the needed expressions to synchronize Terrestrial Time with Lunar Time (TL). We’re going to be building a Solar System-wide infrastructure one of these days, an effort that is already underway with the gradual push into cislunar space that will demand these kinds of adjustments. These relativistic corrections will be needed to work in this environment with complete coordination between Earth’s surface, the surface of the Moon, and the Solar System’s barycenter.

The paper produces a new Luni-centric Coordinate Reference System (LCRS). We are talking about a lunar presence involving numerous landers and rovers in addition to orbiting craft. It is the common time reference that ensures accurate timing between all these vehicles and also allows autonomous systems to function while maintaining communication and data transmission. Moreover, the LCRS is needed for navigation:

An LCRS is vital for precise navigation on the Moon. Unlike Earth, the lunar surface presents unique challenges, including irregular terrain and the absence of a global magnetic field. A dedicated reference system allows for precise positioning and movement of landers and rovers, ensuring they can target and reach specific, safe landing sites. This is particularly important for resource utilization, such as locating and extracting water ice from the lunar poles, which requires high positional accuracy.

Precise location information through these time and position transformations will be, clearly, a necessary step wherever we go in the Solar System, and a vital part of shaping the activity that will build that system-wide infrastructure so necessary if we are to seriously consider future probes into the Oort Cloud and to other stars. Turyshev and team refer to all this as the establishment of a ‘geospatial context’ within which the placement of instruments can be optimized, but the work also becomes vital for everything from the creation of bases to necessary navigational tools. For the immediate future, we are firming up the steps that will give us a foothold on the Moon.

The paper is Turyshev et al., “Time transformation between the solar system barycenter and the surfaces of the Earth and Moon,” now available as a preprint. If you want to really dig into time transformations, the IERS Conventions document is available online. The Roman Kezerashvili paper cited above is R. Ya. Kezerashvili and J. F. Vazques-Poritz, “Escape Trajectories of Solar Sails and General Relativity,” Physics Letters B Volume 681, Issue 5 (16 November 2009), pp. 387-390 (abstract).