How was Kepler-90 g’s mass recalculated?
The Kepler Space Telescope observed six transits of Kepler-90 g in front of its star. Because of the gravitational influence of its neighbor h, the actual transit times deviated by up to about 25 hours from the times calculated with a regular period. However, with only six transits, it was difficult to accurately determine the future transit times and the masses of the two planets. The research team analyzed the star's motions measured 34 times over 10 years along with additional transit data to predict the May 2024 transit. Ground-based telescopes actually observed this transit, and in the 2025 analysis, the mass of g was calculated to be 15.0±1.3 times that of Earth.
- 6 transits Number of g's transits recorded during the Kepler primary mission
- Up to about 25 hours Difference between the time calculated with a regular period and the actual transit time
- 34 measurements Motions of the star measured by Keck/HIRES from 2011 to 2022
- 15.0±1.3 Earth masses Mass of g determined by fitting all timing and velocity data together
Why is it difficult to determine mass from transit times alone?
If a planet is not disturbed by other celestial bodies, its transits repeat at almost regular intervals. g orbits the star roughly every 210.7 days, but the outer planet h pulls it from the front or pushes from behind, causing transits to occur earlier or later than scheduled. This change in transit times contains the gravitational influence of the two planets on each other and serves as a tool for measuring mass.
A large change in transit times does not mean the mass is uniquely determined. Six transits of g and three transits of h show only part of a long-term variation. Different combinations of mass, orbital shape, and orientation can produce similar transit times. A 2020 analysis found a very low mass for g, but predictions made farther beyond the observed interval quickly developed a wide range of possible transit times.
The large change in transit times is evidence that g and h strongly attract each other. However, to accurately determine mass, the star's motion and later new transits over a long period must also be observed.
How can the star’s motion reveal a planet’s mass?
The change in transit times shows the effect of g and h pulling on each other. By measuring the slight changes in the color of starlight, the speed at which the central star moves back and forth due to the two planets' gravity can also be determined. The research team measured this speed 34 times from 2011 to 2022 using the HIRES spectrograph at the Keck Observatory. Kepler-90 is distant, and with multiple planets pulling on the star together, it is difficult to distinguish the effects of each planet, but using transit timing data can narrow down the possible ranges of mass and orbit.
The research team also included additional transit timings obtained from Spitzer and Swift after Kepler's observations in their analysis. By calculating these data together, they predicted when g and h would next pass in front of the star. Therefore, the 2024 transit timing was not adjusted based on observations after the fact, but was a prediction calculated in advance using existing data and later confirmed by actual observation.
- 2009~2013 Kepler records six transits of g and three transits of h.
- 2011~2022 HIRES measures the radial velocity of the central star 34 times.
- Prediction The model, which matches both the transit time and the rate of motion across the line of sight, presents the transit time of g in May 2024.
- May 2024 Multiple ground-based telescopes observe the transit of g at the predicted time.
- 2025 By combining the new transit with additional data, g is found to have a mass of 15.0±1.3 times that of Earth, and h a mass of 203±16 times that of Earth.
Why was the new transit observed after a decade so important?
The mass was not measured based on the 2024 transit alone. This observation is important because there is more than a 10-year gap since Kepler’s last transit. Even a small error in the orbital period accumulates over about 20 orbits, resulting in a large difference in the predicted timing. By confirming when the actual transit occurred, orbit candidates that do not match can be excluded, significantly reducing the accumulated timing errors.
The final mass is calculated by combining the star’s brightness variations recorded by Kepler, the additional transit timings, the star’s motion measured over 10 years, and the ground-based observations in 2024. The research team statistically compared numerous mass and orbital combinations to find the range that best explains all of this data.
The 2024 passage did not directly measure the mass of g. This observation added a time gap of over a decade, and the mass was derived from calculations that included the timing changes of the passages of g and h as well as the movement of the central star.
How does Kepler-90 g differ from Saturn and Neptune?
The radius of g is about 8.1±0.8 times that of Earth, reaching about 86% of Saturn's radius. On the other hand, its mass is 15 times that of Earth, slightly lighter than Neptune. When combining these two values as an average of a sphere, the density is about 0.15 g/cm³. This is a very low value, about 15% of the density of water and only about a quarter of Saturn's density.
Planets with a mass very small relative to their radius are called 'super-puffs.' They are likely to have a wide and light atmosphere of hydrogen and helium, but the exact elemental ratios, clouds, and haze have not been measured. It is also possible that high-altitude dust or haze blocked starlight, making the planet's radius appear larger than the actual gaseous layer.
Why do we need to know the next transit time precisely?
Planets with long orbital periods rarely pass in front of their stars. If the predicted time is off by even a few hours, a space telescope could miss the transit. With observations in 2024, the error in predicting the next transit time has decreased, allowing for more precise planning of the date to observe g's atmosphere.
Starlight passing through the atmosphere during a transit could test whether g's low density comes from an extended hydrogen-helium atmosphere or whether high-altitude haze makes the planet look larger. What is currently known with confidence is g's size, mass, and average density. The colors and clouds shown on the page are not observational photographs, and the label “super-puff” does not mean its atmospheric composition has been directly confirmed.
Sources
- NASA Exoplanet Archive — Kepler-90 g Parameters
- The Astronomical Journal — Updated Masses for the Gas Giants in the Eight-Planet Kepler-90 System
- The Astrophysical Journal — Giant Transit-Timing Variations Reveal a Super-Puff
- Astronomy & Astrophysics — The Planetary System to KIC 11442793
- Astronomy & Astrophysics — Physical Properties of Giant Exoplanets within 400 Days
- NASA Science — Kepler Transit Method
- NASA Exoplanet Archive — Kepler Data Products Overview