How to Weigh an Invisible Planet That Hides Half of Itself ✛

Original: "The true masses of radial-velocity exoplanets constrained by stability"
· Xander Byrne, Amy Bonsor
arXiv:2608.26880v1 · 2026-08-27 · CC BY 4.0 · 1 min
A planet found by the star's wobble seems lighter than it is, but the fragility of the whole system gives it away.

A star shivers when a planet orbits nearby: the invisible companion tugs it toward us and away from us. From that wobble, astronomers know a planet is there and can even estimate its weight. But there's a catch. If the planet's orbit is tilted, like a plate seen edge-on, only part of its gravity acts on the star. What we see in the telescope is not the true mass but its shadow.

Orbital inclination is the angle between the plane in which the planet moves and our line of sight. If you look at the orbit from the side, the planet appears lighter than it really is.

A single planet can't be weighed this way. But when there are several planets jostling like commuters at rush hour, a simple idea comes into play: overly heavy neighbors will shove each other apart and tear the whole system apart. So if the system is still intact, the planets cannot be too massive. That limit reveals the true weight.

The authors of the new study applied this logic to five known systems. It turned out that around Barnard's star, all planets are lighter than 0.6 Earth masses, making them rocky worlds rather than gas giants. And around HD 184010, three large planets weigh as much as Saturn or Jupiter. Previously, heavier options were allowed, but now they are ruled out: such giants would have long since smashed the system to pieces.

If the orbital inclination were very small, some 'planets' would turn out to be brown dwarfs, objects above the deuterium-burning limit. For instance, for the star HD 215152, Gaia astrometry excludes inclinations below 0.2 degrees, which corresponds to masses greater than several Jupiters.

M_{\min} = M \sin i
The minimum mass equals the true mass multiplied by the sine of the inclination angle of the orbital plane to the line of sight
\Pr(i \mid \text{stable}) \propto \mathcal{L}(\text{stable} \mid i) \times \pi(i)
The posterior probability of inclination is proportional to the likelihood of system stability at that inclination times the prior probability from an isotropic distribution
\Delta = 2 \left(\frac{a_2 - a_1}{a_1 + a_2}\right) \left(\frac{3M_*}{M_{\min,1} + M_{\min,2}}\right)^{1/3} (\sin i)^{1/3}
Dimensionless distance between planets in units of mutual Hill radius; systems with Δ < 10 are usually unstable
Scientists
Christian DopplerD. B. McLaughlinDidier QuelozMichel MayorR. A. RossiterDavid Charbonneau
Concepts
mars earth mass exoplanet multi planet systems jupiter mass super earth exoplanets around red dwarfs radial velocity terrestrial exoplanet planetary system transit method mercury stellar planetary misalignment sub neptune jupiter planet exomoon asteroid belt direct imaging planetesimal formation