“The passage of time is fundamental to the theory of relativity: how you realize it, how you calculate it, and what influences it,” said Bijunath Patla, a physicist at the National Institute of Standards and Technology. That now has a concrete planetary case study Mars.
The physicists Neil Ashby and Patla, for the first time, estimated that on average, the clocks on Mars tick 477 microseconds faster per terrestrial day compared to the ones on Earth. This tiny difference for human purposes is actually dictated by Einstein’s general relativity. Accordingly, gravitational potential and velocity both influence the way time flows. Mars’s surface gravity, which is about one-fifth of Earth’s at sea level, speeds up the former while the latter slows it due to its slower orbital velocity around the Sun. The gravitational speed-up wins, and this net result is a faster tick rate.
To anchor their calculations, the team defined a Martian reference surface similar to Earth’s geoid, called the areoid. Using models of Mars gravity field data, such as MRO120D and GMM-3, they calculated the constant rate offset at the areoid relative to Earth’s geoid. The analysis included not just the gravity and orbital speed of Mars but also the gravitational pull of the Sun, Earth, and Moon. Although the Sun has over 99% of the solar system’s mass and thus is the overwhelming driver in the interactions, the tugging from the Earth–Moon system adds measurable perturbations.
Mars’s orbital eccentricity, 0.093 compared to Earth’s 0.017, further complicates matters. The result of its elliptical orbit around the Sun is large changes in heliocentric distance and velocity during the course of a Martian year, which causes daily fluctuations in the offset of up to 226 microseconds. These changes are not constant; over seven synodic periods-about 15.8 Earth years-additional modulations of ~40 microseconds occur due to the evolving Earth-Mars geometry.
Such variability creates a challenging environment for interplanetary time synchronization. On Earth, GPS satellites already require relativistic corrections: orbital velocity slows their clocks by about 7 microseconds per day, and reduced gravity speeds up the satellites by 45 microseconds to yield a net gain of 38 microseconds. Without these adjustments, positions from GPS would drift by kilometers daily. For Mars, the corrections need to be dynamic in nature, that is, continuously updated for orbital position and gravitational interplay, or navigation errors could reach 89 miles (143 km) per day.
Radio science experiments conducted during the Cassini mission illustrated the degree of precision achievable in deep-space timing-in particular, verification of general relativity to 20 parts-per-million-was reached by mitigation of solar plasma noise. Multi-frequency link approaches and ground-atmosphere noise mitigation will be similarly crucial for Mars-to-Earth time transfer, particularly if future networks seek accuracies of the order of one-tenth microsecond as needed for high-speed communications such as 5G.
The practical consequences are immense. An “interplanetary internet” would require that clocks on different planets run in concert, taking into account either light travel time-4 to 24 minutes between Earth and Mars-or relativistic offsets. Robotic systems and crewed missions will rely on accurate clock timing for navigation, coordination, and data integrity. Patla adds that the extension of Earth’s communication network to Mars will necessitate “a different way to communicate” so that several robots or habitats can share tasks without falling out of synchrony.
But beyond engineering, Mars represents a natural laboratory for testing relativity in a multibody gravitational environment. The four-body problem consisting of the Sun, Earth, Moon, and Mars brings in complexities not present in Earth-Moon comparisons, making this a fertile ground for probing the limits of general relativity and its interplay with quantum mechanics. Even with these refined models, residual inaccuracies of ±100 nanoseconds per day remain over long times due to unmodeled planetary perturbations and solar motion, which require periodic recalibration-about every 100 days-to maintain alignment.
These findings represent both a road map and a warning as humanity edges closer to sustained lunar operations with aspirations beyond toward Mars: timekeeping beyond Earth is not a question of merely carrying a clock but mastering spacetime itself.
