Gravitational waves are generated in a manner analogous to electromagnetic waves.
Classically, changing electric or magnetic fields can generate electromagnetic waves, a radio antenna being a good example, and also radiation is emitted by accelerating or decelerating particles. Maxwell's equations are "simple" enough as one is dealing with vector fields. This is reflected in the quantum mechanical carrier of the electromagnetic field, the photon, which has spin one.
In General Relativity the mathematics is more complex, still, gravitational waves are expected for "changing gravitational fields" , in quotes, because the gravitational field emerges from the space curvature posited by GR. Since one is dealing with tensor fields , the quantum mechanical carrier (in the effective quantizations of gravity used up to now) is the graviton of spin two.
gravitational waves transport energy as gravitational radiation. The existence of gravitational waves is a possible consequence of the Lorentz invariance of general relativity since it brings the concept of a limiting speed of propagation of the physical interactions with it. By contrast, gravitational waves cannot exist in the Newtonian theory of gravitation, which postulates that physical interactions propagate at infinite speed.
This illustrates the space distortions as the wave passes:
The effect of a plus-polarized gravitational wave on a ring of particles.
So, as with electromagnetic waves,
In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like an expanding or contracting sphere) or cylindrically symmetric (like a spinning disk or sphere). A simple example of this principle is a spinning dumbbell. If the dumbbell spins like a wheel on an axle, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. In an extreme case, such as when the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.
So under certain conditions an accelerating mass can radiate gravitational waves. The effect on planetary orbits , though present due to the emission of gravitational waves, is very small , because of the great weakness of gravity.
Gravitational radiation is another mechanism of orbital decay. It is negligible for orbits of planets and planetary satellites, but is noticeable for systems of compact objects, as seen in observations of neutron star orbits.