In principle, this situation offers opportunities for new insights. However, it sometimes rather leads to the rejection of observational data without serious examination. So experimental data [1] that apparently confirm James C. Keith's prediction [2] about the energy loss of highly accelerated mass systems due to interaction with large external masses is not even considered for serious discussion, in particular, as it seems to confirm Mach's principle, see [2] on page 11. Other objections are based on purely theoretical grounds [3] and/or on inaccurate comparative data [4] without any comment on the experimental setup and procedures.
[1] Article Significant Deviation of Rotational Decay from Theory at a R...
[2] https://rmf.smf.mx/ojs/index.php/rmf/article/view/836/600
[3] Frehland E., 1973, Critique of the Gravitational Radiation Damping Effects Calculated by Keith, Lettere al Nuovo Cimento, 7 (12), 490-492
[4] Reinhardt M. and Rosenblum A., 1973, The Nonexistence of a Relativistic Effect Proposed by Keith, Lettere al Nuovo Cimento, 6 (5), 189-191