Kepler-90: Compact 8-Planet System

• Kepler-90 is a compact planetary system with eight transiting planets, including small inner worlds and outer gas giants arranged within 1 AU.
• Its unique configuration, featuring an inverted gas giant order relative to the Solar System, challenges conventional theories of planet formation.
• Precise transit timing and radial velocity analyses enable refined ephemerides, making the system an excellent target for atmospheric studies with JWST and HST.

Kepler-90, also designated KIC 11442793 and KOI-351, is a Sun-like planetary system notable for hosting eight transiting planets, placing it, along with the Solar System, among the only two planetary systems currently known to host eight planets. Its architecture combines extreme compactness with high multiplicity: all eight known planets orbit within roughly $1$ AU, in the order $b,c,i,d,e,f,g,h$, with six smaller inner planets and an outer pair of transiting gas giants. The system is often described as a compact analogue to the Solar System, but the analogy is limited. In particular, the outer giants are “inverted” relative to Jupiter and Saturn in the sense that the lower-mass giant, Kepler-90 g, lies interior to the more massive Kepler-90 h, a configuration that likely bears on the system’s formation and dynamical history (Shaw et al., 18 Jul 2025, Shallue et al., 2017).

1. Discovery sequence and stellar characterization

Kepler-90 first entered the literature as an unusually rich transiting system with seven planets. In the 2013 discovery paper, planets $b$, $c$, $e$, and $f$ were reported for the first time, while $d$, $g$, and $h$ were revised and validated. At that stage the system was presented as the record-holder among transiting planetary systems and as a compact analogue to the Solar System, with small planets on inner orbits and gas giants farther out (Cabrera et al., 2013).

The host star was characterized from five medium-resolution spectra obtained with the Coudé-Echelle spectrograph on the 2 m telescope at the Thüringer Landessternwarte Tautenburg. Those spectra covered $472$–$b,c,i,d,e,f,g,h$0 nm at $b,c,i,d,e,f,g,h$1. The stellar analysis yielded $b,c,i,d,e,f,g,h$2 in the full grid, or $b,c,i,d,e,f,g,h$3 with $b,c,i,d,e,f,g,h$4 fixed, metallicity $b,c,i,d,e,f,g,h$5 in the full grid or $b,c,i,d,e,f,g,h$6 in the fixed-$b,c,i,d,e,f,g,h$7 case, $b,c,i,d,e,f,g,h$8, and $b,c,i,d,e,f,g,h$9. The star was interpreted as a solar-like dwarf, roughly late-F/early-G, with extinction $b$0, distance $b$1, and adopted radius $b$2 for planetary radii in the discovery analysis (Cabrera et al., 2013).

The eighth planet, Kepler-90 i, was identified in a later low-threshold search of known multi-planet systems using a deep convolutional neural network trained to classify threshold-crossing events as “planet” or “not planet.” For Kepler-90 i, the ranked signal had period $b$3 d, $b$4 in $b$5, duration $b$6 h, impact $b$7, $b$8, signal-to-noise ratio $b$9, and neural-network prediction $c$0. After transit modeling and statistical validation, the refined parameters were $c$1 d, $c$2, $c$3 h, and $c$4 K. The raw vespa false positive probability was about $c$5, and after applying the multiplicity boost appropriate to a high-multiplicity system, the false positive probability was reported as $c$6, leading to statistical validation of Kepler-90 i (Shallue et al., 2017).

2. Planetary architecture

The system’s basic radial scale was already striking in the seven-planet configuration: the planets extended from $c$7 AU to $c$8 AU. With Kepler-90 i inserted between $c$9 and $e$0, the modern eight-planet ordering is $e$1, and all eight still lie within roughly $e$2 AU. This compactness coexists with marked internal differentiation. The innermost planets $e$3, $e$4, and $e$5 are approximately Earth-sized to super-Earth-sized, planets $e$6, $e$7, and $e$8 are roughly $e$9–$f$0, and the outer planets $f$1 and $f$2 are gas giants with radii $f$3 and $f$4, respectively (Cabrera et al., 2013, Shallue et al., 2017, Shaw et al., 18 Jul 2025).

The insertion of Kepler-90 i is dynamically and architecturally significant because it fills the largest previously empty period gap, between Kepler-90 c at $f$5 days and Kepler-90 d at $f$6 days. The 2017 analysis also noted that the seven previously known planets obeyed a transit-duration trend approximately scaling as $f$7, whereas Kepler-90 i’s transit duration of about $f$8 hours was shorter than the $f$9 hours expected for circular and coplanar orbits. That result was interpreted as suggesting that Kepler-90 i is likely slightly inclined away from the line of sight (Shallue et al., 2017).

Planet	Orbital period	Radius or role
b	$d$0 d	$d$1
c	$d$2 d	$d$3
i	$d$4 d	$d$5
d	$d$6 d	$d$7
e	$d$8 d	$d$9
f	$g$0 d	$g$1
g	$g$2 d	$g$3
h	$g$4 d	$g$5

The architecture is therefore not merely a count of planets but a hierarchical arrangement of small inner planets and outer giants compressed into a radial extent comparable to the orbit of Earth. A plausible implication is that Kepler-90 is an unusually stringent test case for theories that must jointly account for compact inner systems, giant-planet retention, and long-term stability in a high-multiplicity configuration.

3. The outer pair $g$6 and $g$7: transit timing, radial velocity, and updated masses

The outer pair dominates the system’s current physical characterization because Kepler-90 g and h produce the largest transit signals and the strongest transit-timing variations. In the Kepler primary-mission photometry, only six transits of $g$8 and three of $g$9 were observed, but their TTVs are exceptionally large. Earlier full N-body work modeled 9 TTV measurements and 9 TDV measurements for the two planets, obtaining $h$0 and $h$1, with Kepler-90 g’s apparent density reported as $h$2, placing it in the super-puff regime as defined in that work (Liang et al., 2020).

The 2025 reanalysis addressed the principal limitation of the Kepler-era data: the timing signal was strong but sampled at only a few epochs, leading to broad families of acceptable ephemerides when extrapolated forward. To reduce that degeneracy, the analysis combined Kepler transit timings, previously unpublished and post-Kepler timings from Swift and Spitzer, 34 HIRES/Keck radial velocities spanning April 2011 to June 2022, and a newly recovered ground-based transit of Kepler-90 g on UT 2024 May 28. The final fitted transit-time set comprised nine timings for $h$3 and four for $h$4. The 2024 transit midpoint was measured as

$h$5

with duration $h$6 hr and depth $h$7 ppt; it occurred about $h$8 days later than predicted by the initial Kepler+RV linear ephemeris, immediately showing that the Kepler-era average period for $h$9 had been underestimated (Shaw et al., 18 Jul 2025).

The adopted reduced dynamical model included only planets $472$0 and $472$1, assumed coplanar and edge-on orbits, and treated each planet with free parameters $472$2, $472$3, $472$4, and eccentricity-vector components

$472$5

Transit times were modeled with TTVFaster, radial velocities with RadVel, and the final “all transits” fit allowed the stellar mass to vary with a Gaussian prior $472$6. The linear ephemeris,

$472$7

served only as the baseline parameterization, since the observed transit times depart from it through mutual perturbations. After post-Kepler timings were included, the posterior was sampled with emcee using 128 walkers for 10,000 steps; after burn-in removal and thinning, 12,928 posterior samples were retained (Shaw et al., 18 Jul 2025).

The updated joint RV+transit fit returned

$472$8

The final orbital solutions were

$472$9

$b,c,i,d,e,f,g,h$00

and

$b,c,i,d,e,f,g,h$01

$b,c,i,d,e,f,g,h$02

A consistency check with the full N-body code TTVFast yielded parameters within $b,c,i,d,e,f,g,h$03 of the adopted solution. Physically, the new fit reinforced rather than overturned the earlier picture: Kepler-90 g remained a Saturn-sized but Neptune-mass, extremely low-density giant, while Kepler-90 h remained Jupiter-like in bulk properties (Shaw et al., 18 Jul 2025).

The informational asymmetry between RVs and transit timing is also explicit. In the RVs alone, Kepler-90 g was reported as “essentially undetected,” with a $b,c,i,d,e,f,g,h$04 upper limit

$b,c,i,d,e,f,g,h$05

whereas Kepler-90 h was clearly detected at

$b,c,i,d,e,f,g,h$06

Once post-Kepler transit timings were included, however, a TTV-only fit produced mass posteriors almost identical to the full RV+TTV fit. The decisive leverage therefore came from extending the transit-timing baseline, especially through the 2024 recovery of $b,c,i,d,e,f,g,h$07 (Shaw et al., 18 Jul 2025).

4. Resonances, secular structure, and long-term stability

Kepler-90 is dynamically rich across multiple radial scales. The original seven-planet analysis emphasized that planets $b,c,i,d,e,f,g,h$08 and $b,c,i,d,e,f,g,h$09 lie within $b,c,i,d,e,f,g,h$10 of the 4:5 mean-motion resonance, that $b,c,i,d,e,f,g,h$11, $b,c,i,d,e,f,g,h$12, and $b,c,i,d,e,f,g,h$13 are close to a 2:3:4 chain with the Laplace-like relation

$b,c,i,d,e,f,g,h$14

and that planet $b,c,i,d,e,f,g,h$15 showed a $b,c,i,d,e,f,g,h$16 h timing displacement, described there as the largest such perturbation known at the time. The same paper also described the system as dynamically delicate, with the outer giants dominating the richest interactions (Cabrera et al., 2013).

Subsequent focused work on the outer pair sharpened that picture. The 2020 TTV/TDV analysis argued that Kepler-90 g and h exhibit large, non-sinusoidal TTVs up to 25 hours, unusually informative compared with the more common small, approximately sinusoidal TTVs in Kepler systems. Using TTVFast in a three-body model, that study obtained a best-fit $b,c,i,d,e,f,g,h$17 for 18 observables, decomposed as $b,c,i,d,e,f,g,h$18 and $b,c,i,d,e,f,g,h$19. The resonant diagnostics were written as

$b,c,i,d,e,f,g,h$20

and both resonance angles were found to circulate rather than librate. The pair is therefore close to, but not locked in, the 3:2 resonance. The same work reported low but nonzero eccentricities, near-coplanarity, apsidal alignment, and long-term stability in a REBOUND/WHFast integration over $b,c,i,d,e,f,g,h$21 billion years with a $b,c,i,d,e,f,g,h$22-day timestep. A Hill-stability check gave $b,c,i,d,e,f,g,h$23 against a threshold of $b,c,i,d,e,f,g,h$24, consistent with stability against close encounters (Liang et al., 2020).

A useful correction to a common shorthand follows from these results: “near resonance” in Kepler-90 does not imply present resonant lock. For the outer pair, the strongest published dynamical claim is precisely the opposite—proximity to resonance together with circulating resonance angles and long-lived stability (Liang et al., 2020).

The broader secular architecture has also been investigated under the hypothesis of an additional unseen outer giant. In a 7-planet model of Kepler-90 treated as a STIP, direct integrations and secular analysis showed that a nearly coplanar Jupiter analogue at most semimajor axes between $b,c,i,d,e,f,g,h$25 and $b,c,i,d,e,f,g,h$26 au mainly alters precession frequencies without destroying the inner system. A special regime appears near $b,c,i,d,e,f,g,h$27–$b,c,i,d,e,f,g,h$28 au, where a secular inclination resonance can drive planets $b,c,i,d,e,f,g,h$29 and $b,c,i,d,e,f,g,h$30 together onto a second plane tilted by about $b,c,i,d,e,f,g,h$31 relative to the rest of the system while preserving stability; in the forced-migration experiment, instability appeared only when the perturber reached about $b,c,i,d,e,f,g,h$32 au. The same study identified a 5:4 near-MMR for $b,c,i,d,e,f,g,h$33–$b,c,i,d,e,f,g,h$34 and a 3:2 near-MMR for $b,c,i,d,e,f,g,h$35–$b,c,i,d,e,f,g,h$36, and found that synthetic nodal frequencies agreed better with linear secular theory than apsidal frequencies, which showed stronger evidence of interactions beyond second-order secular approximations (Contreras et al., 2018).

5. Predictive ephemerides, observability, and atmospheric follow-up

Kepler-90’s observational value derives not only from multiplicity but from the fact that all eight known planets transit. The transits provide radii and orbital periods, while TTVs encode the gravitational coupling, making the system unusually information-rich for a compact multiplanet architecture. This is especially consequential for the outer giants because they remain transiting and have large transit depths (Shaw et al., 18 Jul 2025).

Before the post-Kepler recoveries, the predictive situation for future transits of $b,c,i,d,e,f,g,h$37 and $b,c,i,d,e,f,g,h$38 was poor. In the initial RV+Kepler-only model, the forecast uncertainty at the final predicted epoch reached $b,c,i,d,e,f,g,h$39 d for $b,c,i,d,e,f,g,h$40 and $b,c,i,d,e,f,g,h$41 d for $b,c,i,d,e,f,g,h$42, much larger than the transit durations of about $b,c,i,d,e,f,g,h$43 hr and $b,c,i,d,e,f,g,h$44 hr. After adding all transit data, the uncertainty on transit midpoints through 2029 dropped to about $b,c,i,d,e,f,g,h$45 minutes for both planets. This increase in ephemeris precision is the practical result of converting a previously degenerate long-period TTV problem into a predictive dynamical solution (Shaw et al., 18 Jul 2025).

The 2025 analysis explicitly identified this improvement as enabling time-critical atmospheric observations, arguing that the large transit depths and precise ephemerides make Kepler-90 g and h attractive targets for atmospheric characterization with JWST and HST. Because Kepler-90 g remains an extreme low-density giant and Kepler-90 h remains a more conventional Jovian planet, comparative transmission spectroscopy of the pair has particular architectural interest. A plausible implication is that Kepler-90 offers an uncommon opportunity to compare atmospheres across two outer giants embedded in a single compact eight-planet system (Shaw et al., 18 Jul 2025).

Kepler-90 i is also significant from the standpoint of observability methodology. Its discovery demonstrated that low-S/N residual transit searches in known multiplanet systems can be made tractable by ranking threshold-crossing events with deep learning and then subjecting the best candidates to conventional vetting. In the Kepler-90 search, the neural-network score of $b,c,i,d,e,f,g,h$46, combined with centroid analysis, photometric false-positive tests, and vespa validation, elevated a weak $b,c,i,d,e,f,g,h$47-day signal into a statistically validated eighth planet (Shallue et al., 2017).

6. Alternative structural models and major caveats

Beyond mainstream transit, TTV, and RV modeling, Kepler-90 has also been used as a test system for the so-called global polytropic model. In that framework, a planetary system is treated as if it were in hydrostatic equilibrium, the Lane–Emden equation is solved in the complex plane, and successive roots of $b,c,i,d,e,f,g,h$48 define polytropic shells that are interpreted as preferred orbital regions. For a seven-planet Kepler-90, the 2014 application reported an optimum polytropic index

$b,c,i,d,e,f,g,h$49

with shell assignments $b,c,i,d,e,f,g,h$50, $b,c,i,d,e,f,g,h$51, $b,c,i,d,e,f,g,h$52, $b,c,i,d,e,f,g,h$53, $b,c,i,d,e,f,g,h$54, $b,c,i,d,e,f,g,h$55, and $b,c,i,d,e,f,g,h$56, and a summed absolute percent error of about $b,c,i,d,e,f,g,h$57, or about $b,c,i,d,e,f,g,h$58 on average. In that model, shells 4 and 8 were doubly occupied, using combinations of maximum-density and average-density orbit radii (Geroyannis, 2014).

A later eight-planet version used the two-dimensional implementation of the same model, scanning the polytropic index over $b,c,i,d,e,f,g,h$59 and the stellar radius over $b,c,i,d,e,f,g,h$60. For Kepler-90 it reported

$b,c,i,d,e,f,g,h$61

with total mismatch

$b,c,i,d,e,f,g,h$62

That solution placed the eight planets in shells 4 through 11, one planet per shell, using $b,c,i,d,e,f,g,h$63 for $b,c,i,d,e,f,g,h$64, $b,c,i,d,e,f,g,h$65 for $b,c,i,d,e,f,g,h$66, $b,c,i,d,e,f,g,h$67 for $b,c,i,d,e,f,g,h$68, $b,c,i,d,e,f,g,h$69 for $b,c,i,d,e,f,g,h$70, $b,c,i,d,e,f,g,h$71 for $b,c,i,d,e,f,g,h$72, $b,c,i,d,e,f,g,h$73 for $b,c,i,d,e,f,g,h$74, $b,c,i,d,e,f,g,h$75 for $b,c,i,d,e,f,g,h$76, and $b,c,i,d,e,f,g,h$77 for $b,c,i,d,e,f,g,h$78 (Geroyannis, 2020).

These shell-based studies are mathematically explicit but methodologically distinct from the dynamical literature. The 2020 numerical-method paper itself describes the framework as a strong physical idealization and notes that it is not standard dynamical planet-formation theory. The model is therefore best understood as a phenomenological structure-fitting approach rather than as a substitute for N-body constraints, transit photometry, or RV inference (Geroyannis, 2020).

The mainstream dynamical solutions also retain explicit caveats. The 2025 mass update adopted a reduced two-planet model for $b,c,i,d,e,f,g,h$79 and $b,c,i,d,e,f,g,h$80, assumed coplanarity and edge-on orbits, and used TTVFaster’s first-order-in-eccentricity approximation rather than a full photodynamical treatment of all eight planets and all light curves. The Swift and Spitzer timings were less precise than the Kepler and 2024 timings, one Spitzer point for $b,c,i,d,e,f,g,h$81 was identified as a notable outlier, and allowing the stellar mass to vary broadened the planet-mass posteriors. The most effective stated route to further improvement was additional precise transit timings of $b,c,i,d,e,f,g,h$82 and $b,c,i,d,e,f,g,h$83, with further RVs expected to help chiefly for $b,c,i,d,e,f,g,h$84, since $b,c,i,d,e,f,g,h$85 is so weak in RV (Shaw et al., 18 Jul 2025).

Taken together, the current research picture is internally consistent on the system’s main points. Kepler-90 remains the archetypal eight-planet transiting system: compact, dynamically active, observationally rich, and especially informative in its outer pair, where a Saturn-sized but only $b,c,i,d,e,f,g,h$86 planet coexists with a $b,c,i,d,e,f,g,h$87 Jupiter-like companion whose mutual perturbations make the system both challenging and unusually constraining for exoplanet dynamics (Shaw et al., 18 Jul 2025).