No, it is not correct to say that all planets have a rotational gravitational field vector around the Sun that causes gravitational waves. Gravitational waves are primarily generated by asymmetric and accelerating masses. While planets do orbit the Sun and create gravitational fields, their motion around the Sun does not generate significant gravitational waves.
Gravitational waves are produced by extremely energetic events involving the acceleration or movement of massive objects. Examples include the merging of black holes, the collision of neutron stars, or the asymmetrical motion of highly massive objects. These events involve rapid changes in the gravitational field, causing ripples in spacetime that propagate as gravitational waves.
In the case of planets orbiting the Sun, their motion is relatively stable and predictable. The gravitational field they create is primarily responsible for keeping them in orbit around the Sun, rather than generating significant gravitational waves. The orbits of planets can cause subtle perturbations in the gravitational fields of other objects, leading to small deviations in their paths, but these effects are not gravitational waves in the same sense as those produced by violent astrophysical events.
To summarize, while planets do have gravitational fields and orbit the Sun, their motion does not generate gravitational waves in a significant manner. Gravitational waves are primarily produced by energetic and asymmetric events involving massive objects.