# Can a planet be in spin-orbit resonance with its parent and in resonance with other planets at the same time?

Mercury is tidally locked in a 3:2 spin-orbit resonance with the sun. Other resonances like 1:1, 2:1, 5:2 can occur as well. Many objects, like the moons of Jupiter, are locked in mean-motion resonance, meaning that each object orbits an integer amount of orbits for each integer amount of orbits its neighbors complete. This means that the system is very stable and will return its initial state eventually.

I was wondering if a member of a resonance chain could be locked into a higher order, non 1:1 spin-orbit resonance with it parent, while still being in mean-moton resonance with the other planets?

Specifically, I was wondering if this roughly drafted system is realistic?

• Valhalla A: early F-type star
• Valhalla b: super-earth, lava world with sodium atmosphere
• Valhalla c: super-earth, lava world with frozen nightside
• Valhalla d: ice-giant, helium dominated atmosphere due to proximity to the sun
• Valhalla e: super-earth, carbon-planet that formed due to a variation in the composition of the protoplanetary disc
• Valhalla f: gas-giant in the habitable zone, almost 9 $$Mj$$

Valhalla b to e are really tightly grouped close to the star in mean-motion resonance. All of them are locked in a 1:1 spin-orbit resonance, except for Valhalla e, which is in a Mercury like 3:2 spin-orbit resonance. I was wondering if Valhalla f, could explain this state of the inner system. It has herded the planets together so close to the star and interacts with Valhalla e so that it is more eccentric than the other planets. Is that a believable and stable setup?

The structure of the system is supposed to be similar to the innermost system of Kepler 90.

• "resonance with other planets" means orbit-orbit resonance? Jun 11 '20 at 21:00
• @Alexander Yes. I tried to use spin-orbit and mean-motion to distinguish the two. I hope I got the naming conventions right. Jun 11 '20 at 21:01
• If I understand the question correctly, then yes, it's more than plausible. In a tightly packed system, all orbits and spins would be in resonance with others. Jun 11 '20 at 21:04
• @Alexander Yes, but I'm not certain that Valhalla e can spin around its axis 3 times for every two orbits while being in resonance with the other 3 planets like the moons of Jupiter are. Do spin-orbit and mean motion resonance effect each other? Jun 11 '20 at 21:10
• All depends on which gravitational influence is stronger. For spin resonance, it's the influence from parent. Jun 11 '20 at 21:14