When a distant planet passes in front of its star, it briefly blocks part of the light. Astronomers call this a transit and judge the planet's size by the depth of the dip. But light has a property: a massive body acts like a lens. Even a giant planet can slightly bend the star's rays, and the dip becomes a bit shallower than you might expect.
The authors took data on exoplanets with wide orbits (farther than Earth is from the Sun), collected by the Kepler and TESS telescopes. For six worlds, they could only set an upper mass limit — from 200 to 2000 Jupiter masses. The noise in the data prevented greater precision. So the scientists built synthetic light curves and found that to "weigh" a planet of 10 Jupiter masses at a distance of 20 astronomical units (beyond Uranus), you need a measurement precision of three parts per million.
The most surprising finding is the error in size. If you ignore this lensing effect, you can underestimate the planet's radius by 1–20%. For a giant of 5–10 Jupiter masses orbiting far from its star, the shadow becomes noticeably smaller than the true silhouette. That means some known exoplanets are actually larger than previously thought.
This approach opens the door to mass "weighing" of distant planets without cumbersome radial velocity measurements. All you need is a single transit, but with very high precision.
The gravitational lensing effect on an exoplanet transit is so tiny that it was first noticed only in the 2010s — even though the transit method itself has been working since 1999.
In Stanisław Lem's novel Solaris, the planet's ocean bent light paths, creating ghostly images — almost like a gravitational lens, but with a living participant.