Confusion about Corotational and Lindblad resonance

[Aurorana]

Hi, I’m a bit confused about the definitions of corotational and Lindblad resonances. They’re given by;

Corotational resonance
This resonance occurs when the orbit moves at the same angular speed as the forcing.

Lindblad resonance
an orbital resonance in which an object's epicyclic frequency is a simple multiple of some forcing frequency.

I cannot seem to grasp these concepts when applying it to a ring particle and a satellite. What’s the difference between an orbital and corotational resonance? I’m also having difficulty understanding how inner and outer Lindblad resonances work too.

 

[stefan r]

Hi, I’m a bit confused about the definitions of corotational and Lindblad resonances. They’re given by;

Corotational resonance
This resonance occurs when the orbit moves at the same angular speed as the forcing.

Lindblad resonance
an orbital resonance in which an object's epicyclic frequency is a simple multiple of some forcing frequency.

I cannot seem to grasp these concepts when applying it to a ring particle and a satellite. What’s the difference between an orbital and corotational resonance? I’m also having difficulty understanding how inner and outer Lindblad resonances work too.

I think a space elevator might work as an example of corotational. The tension on the string is constant. Forces rotate with the station's orbit and the planet. Also the tide on the moon. The moon is tidal locked with the same face always pointing at earth. Pluto and Charon are co-rotating.

Deviant stars get kicked around. The resonant effect is in the empty space.

 

[Aurorana]

Thank you, that helps. As for Lindblad resonances, how can they be associated with a corotation resonance? I’m having difficulty understanding how a lindblad resonance works

 

[alantheastronomer]

A Corotational resonance is the first - the fundamental - Lindblad resonance. Higher order Lindblad resonances correspond to orbits with higher frequencies. Does that make any sense to you?