There will be Doppler effect between the gravitational wave caused by the sun's revolution and the sun, and will affect the gravitational field around the sun. The density distribution of this gravitational wave is very similar to the spatiotemporal depression of GR. We can deduce the gravitational equation under the influence of this gravitational wave and apply the gravitational equation to the calculation of planetary orbit. You can find that the obtained planetary orbit is very accurate, even exceeding the calculation of GR.
Preprint Gravitational Fields and Gravitational Waves
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