Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

Paper discussion: Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Antonio Genova, Erwan Mazarico, Sander Goossens, Frank G. Lemoine, Gregory A. Neumann, David E. Smith & Maria T. Zuber. Nature Communications volume 9, Article number: 289.

Students of physics learn many interesting facts about the Sun across different lessons and courses. When learning orbital mechanics, students are taught that the Sun’s gravitational field exerts a long-range force proportional to its mass and causes planets to orbit in elliptical paths. In modern physics classes, students learn the Sun converts mass into energy by fusing hydrogen into helium; that energy is radiated from its surface and felt on Earth.

An astute student may ask: if the Sun is decreasing in mass to produce and radiate energy, is its gravitational influence on the planets getting weaker? For many years this was handwaved away as a negligibly small effect, but a probe orbiting Mercury has made the first direct measurements of the Sun’s loss of mass.

Estimating the effect

Before discussing the measurement, it helps to estimate the magnitude of the effect. The Sun’s luminosity is on the order of $10^{26}$ Watts. Applying Einstein’s relation and dividing this by $c^2$ gives a mass-loss rate on the order of a million tons per second — a rate that, through energy conservation, can be thought of as mass converted to energy by fusion. For context, this is roughly twice the mass of the largest ship ever built every second.

The fusion-radiation process is not the only way the Sun loses mass. There is also the proton outflow that forms the solar wind and more coherent losses such as coronal mass ejections. Compared to the Sun’s total mass, these losses amount to only a few parts per quadrillion per year. From Kepler’s laws, the orbital period scales with the inverse square root of the central mass, so even over billions of years we would not expect a noticeable orbital change. Measuring effects at the parts-per-trillion (or smaller) level is extremely difficult, so it would have been reasonable to assume the gravitational effect of the Sun’s shrinkage would remain unobserved — until now.

The MESSENGER probe, before launch.

MESSENGER

Mercury famously played a role in tests of gravity: its excess perihelion precession (about 43 arc-seconds per century) helped motivate Einstein’s general theory of relativity. From 2011 to 2015, Mercury hosted an Earth-built orbiter: Mercury Surface, Space Environment, Geochemistry, and Ranging — whose acronym spells MESSENGER. Its mission was to map Mercury’s surface and gravitational field to infer internal structure, and during its mission it returned striking imagery and precise tracking data.

The mission produced many papers on Mercury’s surface and interior (see, for example, this, this, and this). MESSENGER deliberately impacted Mercury on April 30, 2015, and since then the collaboration has continued analyzing the mission’s seven years of data. In its recent Nature Communications paper, the team used precise tracking of MESSENGER’s orbit to measure parameters tied to general relativity and potential violations.

The first image of Mercury taken from orbit.

One test is the Nordtvedt effect, which would appear if gravitational binding energy coupled differently to external gravity than rest mass does. That would violate the equivalence principle and cause objects of different composition to orbit differently. If a small Nordtvedt effect existed but had escaped earlier detection, it would shift the relative Earth–Mercury position by roughly three meters. MESSENGER’s data find this effect consistent with zero, constraining it to less than one part in ten thousand — about three times more precise than previous lunar laser-ranging limits.

The most striking result in the paper is the measured decrease in the Sun’s gravitational parameter, GM. Orbital equations depend on the product GM, so orbits alone cannot separate G and M without independent measurements. By precisely tracking the Earth–MESSENGER geometry, the collaboration measured a change in the Earth–Mercury distance of about two meters over the observation interval. This represents the first nonzero measurement of the changing gravitational parameter of the Sun. They report the Sun’s gravity weakening by $6.13 pm 1.47 times 10^{-14}$ per year (about 61 parts per quadrillion per year), implying a very slow expansion of the Solar System.

Causes for the decreasing gravity

Two possibilities can explain a changing GM: the Sun’s mass M is decreasing, or Newton’s constant G is changing. Solar models provide an independent estimate of the expected mass loss. More precise solar-physics calculations (beyond the simple luminosity/c^2 estimate) give a fusion-related mass-loss rate of roughly 68 parts per quadrillion per year, and the solar-wind losses are estimated at about 10 parts per quadrillion per year (the wind estimate is less precise because the MESSENGER observation did not span a full sunspot cycle). Combined, these predicted losses are consistent with the measured decrease in GM within the reported uncertainty.

A skeptic might wonder whether the laws of physics themselves are changing. To test that, researchers look for a time-varying Newton’s constant. Using the combination of solar-model expectations and the MESSENGER orbit data, the team constrained a changing G to below about 40 parts per quadrillion per year — consistent with zero. Earlier constraints (for example, from long-term observations of binary neutron stars) were much looser; the prior best limit was ~600 parts per quadrillion per year. The MESSENGER-based result therefore tightens the limits and finds no evidence that gravity is changing over time.

Conclusion

In summary, MESSENGER’s precise orbital tracking provides the first direct nonzero measurement of the Sun’s decreasing gravitational parameter. The measured rate matches expectations from solar mass loss (radiation plus solar wind) and places tighter constraints on any time-variation of Newton’s constant. The observed effect corresponds to orbital changes on the scale of a few meters over several years — tiny, but now empirically detectable.