How does stability lead to a wave? We can see wobble in stars to know they are getting tugged by planets. Are you expecting similar with gravity? I'm not a phy

How does stability lead to a wave? We can see wobble in stars to know they are getting tugged by planets. Are you expecting similar with gravity? I'm not a physicist nor astronomer. I wouldn't expect any gravity waves as I'd expect the star system to have a center of mass that stays in roughly the same space.