Kepler-90 c

Are Kepler-90 b and c in a 5:4 resonance?

Kepler-90 c completes an orbit around its star every 8.7198 days, and the closer-in b orbits roughly every 7.008 days. While c completes four orbits, b completes about 4.977 orbits, making the two orbital periods close to a 5:4 ratio. However, the fact that the ratio of periods is close does not confirm that the two planets are in resonance. Resonance occurs when two planets influence each other gravitationally and maintain a repeated positional relationship.

• Approximately 8.7198 days Orbital period of c measured from repeated transits
• Approximately 4.977 orbits Number of orbits b completes while c completes four
• About 1.19 Earth radii Radius of c calculated from transit depth and star size
• About 236 times Earth's Calculated stellar energy received by c

Their orbital periods are close to a 5:4 ratio, but not an exact match

The time it takes for c to complete four revolutions is approximately 34.88 days. During that time, b completes not exactly five revolutions but about 4.977 revolutions. The missing 0.023 revolution corresponds to roughly 8 degrees in orbit. It is a small difference at a time, but if the same process is repeated, the location where the two planets meet keeps changing. Therefore, just the fact that the ratio of the two periods is 1.244, which is close to 1.25, does not mean that the same positional relationship is repeated consistently.

The two planets are positioned in the same direction relative to the stars approximately every 35.7 days, but that position shifts slightly. The misalignment that occurs in the 5-to-4 ratio is calculated to repeat with a period of about 378 days. Observing whether this change appears in the actual transit times can tell us how strongly the two planets influence each other. However, the calculated value of about 378 days alone cannot confirm resonance.

That the ratio of orbital periods is close to 5 to 4 is a clue suggesting the possibility of resonance. To confirm resonance, one must also determine whether the positional relationship of the two planets repeats within a certain range.

We need to check whether the planets return to the same relative positions

In a resonant state, not only are the numbers of orbits related, but the locations where the two planets meet also repeat within a certain range. Astronomers combine the planets' current positions with the directions in which their elliptical orbits come closest to the star into a resonance angle. If this angle moves back and forth within a limited range, that is evidence that the resonance persists. If it instead cycles through every direction, the planets are not considered to be in a full resonance even when their periods are close. This calculation requires the planets' masses, orbital eccentricities and starting positions.

The masses and orbital shapes of Kepler-90 b and c have not yet been accurately measured. In 2024, researchers calculated the motion of the two planets by changing possible values in various ways. In some calculations using nearly circular orbits, a 5-to-4 resonance appeared, but in other calculations, the resonance angle kept moving or stayed within the range only briefly. When assuming slightly more elliptical orbits, a complete 5-to-4 resonance was not maintained. Therefore, it can currently only be said that the periods of the two planets are close to 5-to-4 and may be influenced by resonance.

1. Transit repetition Measure the orbital periods of b and c, respectively.
2. Calculate the period ratio It is confirmed that b completes approximately 4.977 revolutions during c's four revolutions.
3. Orbital calculations Change the mass, orbit shape, and direction to check whether the resonance angle remains within a certain range.
4. Additional observations By measuring the transit time and the movement of the star, more accurately determine the masses and orbits of the two planets.

We know c’s radius, but not its mass or internal composition

c's radius is about 1.19 times that of Earth, slightly smaller than b's approximately 1.31 times. However, the amount of starlight blocked by the planet does not reveal the ratio of iron to rock or the amount of atmosphere. Even if the sizes are the same, the mass can differ if the internal materials are different. The listed mass of about 1.81 Earth masses is also not a directly measured value of c's gravity, but an estimate based on the mass distribution observed in several planets of similar size.

Therefore, the density calculated from this estimated mass alone cannot confirm that c is a rocky planet. The actual masses of b and c need to be measured in the same way to more accurately determine whether the two planets have migrated together to reach the current period ratio and how strongly they influence each other's orbits.

Intense starlight alone cannot reveal the actual surface conditions

c is about 0.089 AU, approximately 13.3 million km, away from its star. The energy c receives is calculated to be about 236 times what Earth receives from the Sun. Assuming a simple reflection of starlight and heat transfer, the temperature is about 987K, approximately 714 degrees Celsius. While it is clear that it is a planet exposed to very intense heat, this temperature is not measured at the actual surface.

If there is an atmosphere, it can transfer heat from the bright side to the dark side or trap certain light energy. Bright clouds or surfaces can reflect more incoming light. From the current transit data alone, we cannot know c’s atmosphere, surface, or internal materials. Knowing the ratio of the orbital period accurately is different from knowing the planet's environment.

The planet shown on the page is not an observation photo but an illustration to aid understanding. The orbital period of 8.7198 days and the radius about 1.19 times that of Earth are based on transit observations. The mass about 1.81 times that of Earth is an estimate compared to other planets, and the roughly 714 degrees Celsius is a value calculated using simplified conditions. The 5:4 resonance has not yet been confirmed.

Sources

• NASA Exoplanet Archive — Kepler-90 c Parameters and Mass Provenance
• Astronomy & Astrophysics — The Planetary System to KIC 11442793
• Monthly Notices of the Royal Astronomical Society — Analysing the Dynamics of the Kepler-90 Planetary System
• The Astronomical Journal — Dynamics of Tightly Packed Planetary Systems
• The Astrophysical Journal — Probabilistic Mass–Radius Relation
• NASA Science — Kepler Transit Method
• NASA Exoplanet Archive — Kepler Data Products Overview